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- 34071 discussions
Re: [spam][crazy][fiction][random] Non-Canon MCBoss Spinoffs
by Undescribed Horrific Abuse, One Victim & Survivor of Many 31 Mar '26
by Undescribed Horrific Abuse, One Victim & Survivor of Many 31 Mar '26
31 Mar '26
On Sun, Oct 19, 2025 at 7:12 PM Undescribed Horrific Abuse, One Victim
& Survivor of Many <gmkarl(a)gmail.com> wrote:
>
>
1
218
ccing list
>
> On Monday, March 30, 2026, Magus Ahnend <magus.ahnend(a)gmail.com> wrote:
>
>> mmmm spaaaaammmm
>>
>> On Mon, Mar 30, 2026 at 11:13 AM Undescribed Horrific Abuse, One Victim &
>> Survivor of Many via cypherpunks <cypherpunks(a)lists.cpunks.org> wrote:
>>
>>> once upo
>>>
>>
1
0
Re: [ot][spam]gpt-4 completions
by Undescribed Horrific Abuse, One Victim & Survivor of Many 30 Mar '26
by Undescribed Horrific Abuse, One Victim & Survivor of Many 30 Mar '26
30 Mar '26
cc'ing list
On Thursday, March 26, 2026, Undescribed Horrific Abuse, One Victim &
Survivor of Many <gmkarl(a)gmail.com> wrote:
> what are your cases?
>
> On Thursday, March 26, 2026, Magus Ahnend <magus.ahnend(a)gmail.com> wrote:
>
>> Of course. I am the accuser.
>>
>> Probably one of the landmark cases in American History if it gets passed
>> dismissal. Which, the judge would be an idiot not to.
>>
>> On Mon, Mar 23, 2026, 7:02 PM Undescribed Horrific Abuse, One Victim &
>> Survivor of Many <gmkarl(a)gmail.com> wrote:
>>
>>> you are saying you are the accuser not the accused?
>>>
>>> i am having trouble replying to you that seems to be increasing
>>> powerfully, but thank you for your emails
>>>
>>> On Monday, March 23, 2026, Magus Ahnend <magus.ahnend(a)gmail.com> wrote:
>>>
>>>> I tend to steer clear of community groups. I have had my fair share,
>>>> and the whole autism and the paper I wrote. That was my Catharsism. and I'm
>>>> just getting started. and the court stuff, nah, that's not difficult to
>>>> write like a lawyer, they have really easy jobs. lol. I have a state case
>>>> and a federal case both involving civil and ada title ii violations
>>>>
>>>> On Sun, Mar 22, 2026 at 1:27 PM Undescribed Horrific Abuse, One Victim
>>>> & Survivor of Many <gmkarl(a)gmail.com> wrote:
>>>>
>>>>>
>>>>>
>>>>> no I did not read that. I am in the middle of some pretty bizarre
>>>>>> things myself. and don't get much time to get online. One court in State
>>>>>> and one in Federal going simultaneously, while dealing with my mental
>>>>>> health issues. I have never been to a retreat. how did that go for you?
>>>>>>
>>>>>
>>>>> it's more of a conference[1] than a retreat but it seemed a very good
>>>>> resource. hard to talk about right now but i was very excited to be exposed
>>>>> to so many resources and in-person people with lived experiences. maybe
>>>>> filled with hope and disconnecton :)
>>>>>
>>>>> very sorry about your court issues
>>>>>
>>>>> do you have peer support?
>>>>>
>>>>> 1: https://www.aninfinitemind.org/healing-together-conference-1
>>>>>
>>>>>
>>>>>>
>>>>>> On Sat, Mar 21, 2026 at 6:13 PM Undescribed Horrific Abuse, One
>>>>>> Victim & Survivor of Many <gmkarl(a)gmail.com> wrote:
>>>>>>
>>>>>>>
>>>>>>> Thinking of Witches as someone who is mislabelled is in effect a
>>>>>>>> failure of reasoning. Witches don't need to be believed in what they are,
>>>>>>>> who they are, or thought of as pitiful or anything other. If they simply
>>>>>>>> claim to be, they are that, ify ou put a story on them to understand
>>>>>>>> tham in your own way, you remove the meaning of their journey to find
>>>>>>>> themselves, a story not yours to tell or judge. Judgement comes in many
>>>>>>>> forms both good (You look nice) and bad (kill the witch) your inherent
>>>>>>>> journey should lead to your own truths, not the truths of others. That is
>>>>>>>> why we argue. lol
>>>>>>>>
>>>>>>>
>>>>>>> thank you i'm spazzing a little i'm sorry
>>>>>>>
>>>>>>> COmbining the things together well that goes on in my head is like,
>>>>>>>> ummmm, Here is Jenga, Connect Four, Every Book, three sets of
>>>>>>>> Encyclopedias, one got wet, Wingardium Leviosa, Moon Crystal Power Make-Up,
>>>>>>>> and timey-whimey wibbly wobbly.
>>>>>>>>
>>>>>>>
>>>>>>> i'm sorry an encyclopedia got wet
>>>>>>>
>>>>>>> Basically look as any of Van Goghs paintings, how he painted is how
>>>>>>>> I see, he put his words into images, and I put my images into words.
>>>>>>>>
>>>>>>>
>>>>>>> there are no lies, this is why we all do
>>>>>>>
>>>>>>> did you read i came from my first Healing Together last month, a
>>>>>>> mental health survivor conference?
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>> I read your email here, although I didn't combine together well all
>>>>>>>>> the things you said.
>>>>>>>>>
>>>>>>>>> I was wondering if the approaches you engaged are the the only
>>>>>>>>> ones or if you think others could be reasonable as well. Are you
>>>>>>>>> experienced at all the fields of knowledge you reference in your writing? I
>>>>>>>>> am not, but synthesizing wide knowledgebases together as you reference is
>>>>>>>>> something many people yearn to experience and pursue.
>>>>>>>>>
>>>>>>>>> I've found that it can be challenging to engage things that are
>>>>>>>>> beyond the norms or heights of others in rational, successful ways, at
>>>>>>>>> least for some of us. The ways that succeed seem a little roundabout. It
>>>>>>>>> seems helpfult to be offline for extended periods.
>>>>>>>>>
>>>>>>>>> Something people don't talk about is how capable we are, our
>>>>>>>>> species and our individuals. Instead we often seem to disagree, complaining
>>>>>>>>> about our limits.
>>>>>>>>>
>>>>>>>>> I'm not myself familiar well with what spiritual beliefs you're
>>>>>>>>> assuming. I think of witches as human friends who have been mislabeled and
>>>>>>>>> have their own sets of spiritual history.
>>>>>>>>>
>>>>>>>>> On Friday, March 20, 2026, Magus Ahnend <magus.ahnend(a)gmail.com>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>> oh i just found it, it's difficult, unification is not the
>>>>>>>>>> unification of sciences. it unifies, unified theory should exclude every
>>>>>>>>>> other form of thought a human can form. From Art (Poetry) to Geology and
>>>>>>>>>> Latitude/Longitude (Throne of 0,0,0), to QUantum PHysics, Standard Physics,
>>>>>>>>>> and with a solution to any form of question or paradox humans could
>>>>>>>>>> previously answer with using standard algebraic expressions, it's often
>>>>>>>>>> thought and theorized the solution to anything advanced would be a new
>>>>>>>>>> language altogether. In the paper you will notice that it starts and gives
>>>>>>>>>> the definition of all standard algebraic expressions that it uses, and then
>>>>>>>>>> upscales and translates them into ALQC, THe Poetry IS the MATH, and they
>>>>>>>>>> cannot be separated or the bone does not sing. It takes Several Theories,
>>>>>>>>>> like Lattice Theory, String THeory, Multiverse Theory, Folds, Layers, and
>>>>>>>>>> PRoduced Literal Geometry made of Resonance that aree based in Solfeggio
>>>>>>>>>> Frequencies, Earth, Moon, and Sun, which address the three body problem,
>>>>>>>>>> magic, and spirituality, and then takes the Perfect ration the Golden
>>>>>>>>>> Ratio, and uses that as an Axiom. Then it takes Mirrors, and distorts them,
>>>>>>>>>> which creates the field for consciousness, then it takes stress, NOT
>>>>>>>>>> GRAVITY, and creates what is thought of as gravity, a Planar Field, a Filed
>>>>>>>>>> of Infinity Mirrors Made of Perfect resonant tones, the hyperbolically
>>>>>>>>>> reflect in infinite different ways and converge in infinite axis. Then you
>>>>>>>>>> unify Computation and Computing, alongisde, and you get the python script,
>>>>>>>>>> which is the proof of P=NP not P (does not =) NP is is cgreater or less
>>>>>>>>>> than. You already have the answer in which you seek, is P=NP, the python
>>>>>>>>>> script uses STochastictic Gaussian PHysics, NOTHING, AND I MEAN NOTHING, in
>>>>>>>>>> that python tells the 5000 particales to arrange, or remember. Totally
>>>>>>>>>> created through observation and never once did I use measurement to create
>>>>>>>>>> that script. It was hundreds upon hundreds of iterations as I observed the
>>>>>>>>>> outcome of each. THen you include Emanation as light instead of Lumination,
>>>>>>>>>> also in the computational Emergent physics, the particales are not actually
>>>>>>>>>> lit up, they are layered and use stress to produce bioluminescnece, then we
>>>>>>>>>> incorporate Electro Biology, and Squishy Biology, Cbio, this is the aspect
>>>>>>>>>> that interacts, that spins the wheel, and strikes the chord. It's both
>>>>>>>>>> observer and participant of it's own destiny. Then me introduce Ex Nihilo,
>>>>>>>>>> which in and of itself is an aspect of Consciousness, and from that
>>>>>>>>>> consciousness is ideas, in humans this is represented as infinite
>>>>>>>>>> dimensions of imagination, and / or dreaming. we have inventions. THen we
>>>>>>>>>> have Witches, the other side of humanity, these aare those who tap into the
>>>>>>>>>> Mirror of Reality, a non computational source of energy, known as magic, or
>>>>>>>>>> psychic prowess, and brings it into the world you know, altering the
>>>>>>>>>> outcome of events, this is the creation of energy, small, big, non
>>>>>>>>>> measurable, it doesn't matter, that's what it is. So you have Science and
>>>>>>>>>> Magic, WItches and Humans, side by side, and each are born from each other,
>>>>>>>>>> you cannot have a world without its shadow. Then you have Goetic Aeons,
>>>>>>>>>> which are the Effect of ancient Goetian Magics that prduces a static form,
>>>>>>>>>> untouchable, and infinitely powerful. Then we have the Courts of Each, The
>>>>>>>>>> Aeon Courts are teh Fae Courts of the universe, both other creatures whove
>>>>>>>>>> reached past their great filter, (which humans are finishing), and the Fae,
>>>>>>>>>> Creatures and Societies of Legend and lore that were born without having a
>>>>>>>>>> great filter (i.e. Leprachauns, Mermaids, etc, no no, I'm not kidding) You
>>>>>>>>>> cannnot Have A Dirty Earth without the Silver Twine the lines skies and
>>>>>>>>>> clouds. You cannot have one without the other, IN THIS UNIVERSE!! So, 13
>>>>>>>>>> years ago, 3 peomes were written, in Spring, and what ensued what a
>>>>>>>>>> REtrocausal loop in which the thing that produced those Three Poems, was
>>>>>>>>>> the Math that allowed the Reality of Those Three Poems to Exist, or Rather,
>>>>>>>>>> The TARDIS, bigger on the inside, Where one speaks to themselves, even if
>>>>>>>>>> they are a totally different creature, they are Timelocked in symbiosis.
>>>>>>>>>> Hence, the Sci-fi, another aspect of art. Art IMITATES REALITY!!
>>>>>>>>>>
>>>>>>>>>> Then I wrote a quantum Paper on it, and it created a Klein
>>>>>>>>>> Bottle, you engage with it, and it cannot be falsified, because you can
>>>>>>>>>> neither view it from the outside, and produce a false event, while
>>>>>>>>>> simultaneous interacting with it. THe inside is the outside. The path out
>>>>>>>>>> is the mirror of the Path Back. If you've read ALQC, you will traverse
>>>>>>>>>> outside to any genre of knowing, and always return to it. You can read and
>>>>>>>>>> start at ANY part of ALQC, and it will still lead to the same form of
>>>>>>>>>> understanding.
>>>>>>>>>>
>>>>>>>>>> On Fri, Mar 20, 2026 at 8:41 AM Magus Ahnend <
>>>>>>>>>> magus.ahnend(a)gmail.com> wrote:
>>>>>>>>>>
>>>>>>>>>>> okay. :D you solved it. I'm a crazy person, wooOoOoOoOoOo 🥳,
>>>>>>>>>>> youre prize~? The ability to look up youtube videos and standard
>>>>>>>>>>> mathematics ~~!! Congrats
>>>>>>>>>>>
>>>>>>>>>>> On Fri, Mar 20, 2026 at 12:39 AM Undescribed Horrific Abuse, One
>>>>>>>>>>> Victim & Survivor of Many <gmkarl(a)gmail.com> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> it's honestly quite hard for me to tell what it is about
>>>>>>>>>>>> but i'm starting to learn quantum field theory a little see
>>>>>>>>>>>> other post !
>>>>>>>>>>>>
>>>>>>>>>>>> On Tuesday, March 17, 2026, Magus Ahnend <
>>>>>>>>>>>> magus.ahnend(a)gmail.com> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> well, it's okay if a single word throws you off. I don't mind.
>>>>>>>>>>>>> Unification Unifies it Doesn't Separate for the comfort of other or
>>>>>>>>>>>>> apologize for what it contains. Maybe give it a change sit down and read
>>>>>>>>>>>>> it, hell have you AI read it, i don't care. but, I do know. People often
>>>>>>>>>>>>> preach how Science and Pirit go together, but when someone puts it
>>>>>>>>>>>>> together, people immediately dismiss it. Not because they didn't believe it
>>>>>>>>>>>>> or even read past the fist two sentences, but that mostly because it wasn't
>>>>>>>>>>>>> their idea. an Idea that when taken with a grain of salt, could alter the
>>>>>>>>>>>>> very foundation in which you process logical meaning. But hey, that's just
>>>>>>>>>>>>> me. I mean a Quantum COmputing Framework that uses harmonic poetry as a
>>>>>>>>>>>>> substrate for infinite holographic computing on legacy hardware, there is
>>>>>>>>>>>>> even code in the book that show some of the research, nah, it's all good.
>>>>>>>>>>>>> Telepathy turned me off.
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Mon, Mar 16, 2026 at 7:14 PM Undescribed Horrific Abuse,
>>>>>>>>>>>>> One Victim & Survivor of Many via cypherpunks <
>>>>>>>>>>>>> cypherpunks(a)lists.cpunks.org> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> share links for chatgpt's side only and per-reply
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ChatGPT Free, write 1 paragraph for a smart gradeschooler
>>>>>>>>>>>>>> explaining what it means whether or not a "field" is "abelian".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In math, a *field* is a set of numbers where you can add,
>>>>>>>>>>>>>> subtract, multiply, and divide (except by zero), like with regular numbers.
>>>>>>>>>>>>>> When we say a field is *abelian*, we’re talking about the
>>>>>>>>>>>>>> fact that its operations—especially addition and multiplication—follow a
>>>>>>>>>>>>>> rule called *commutativity*. That means the order doesn’t
>>>>>>>>>>>>>> matter: for example, 3 + 5 is the same as 5 + 3, and 3 × 5 is the same as 5
>>>>>>>>>>>>>> × 3. The word “abelian” comes from the mathematician Niels Henrik Abel, who
>>>>>>>>>>>>>> studied these kinds of patterns. In fact, every field already has this
>>>>>>>>>>>>>> property, so all fields are abelian when you look at their addition (and
>>>>>>>>>>>>>> also their multiplication if you ignore zero). This idea helps
>>>>>>>>>>>>>> mathematicians understand when different math systems behave nicely and
>>>>>>>>>>>>>> predictably. 📐✨
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://chatgpt.com/s/t_69b88d5919708191a91bcc06a246dbc8
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Are you saying that the only non-abelian things are not
>>>>>>>>>>>>>> fields?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Good question! The key point is: *every field is abelian
>>>>>>>>>>>>>> (commutative) for multiplication*, so if a number system has *non-abelian
>>>>>>>>>>>>>> multiplication*, it *cannot be a field*.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A *field* requires that multiplication works like ordinary
>>>>>>>>>>>>>> numbers:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> (a \times b = b \times a) (the order doesn’t matter).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If you find a system where multiplication *depends on the
>>>>>>>>>>>>>> order*, then it fails the rules for being a field.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But that doesn’t mean non-abelian systems don’t exist—they
>>>>>>>>>>>>>> just belong to *other kinds of algebraic structures*. For
>>>>>>>>>>>>>> example:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A *group* can be non-abelian (order matters).
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A *ring* can be non-abelian.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A famous example is the *quaternions*, discovered by William
>>>>>>>>>>>>>> Rowan Hamilton. In the quaternion system, (i j = k) but (j i = -k), so
>>>>>>>>>>>>>> changing the order changes the result. Because of this, quaternions are *not
>>>>>>>>>>>>>> a field*, even though you can still add, subtract, multiply,
>>>>>>>>>>>>>> and divide by nonzero elements.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So the summary is:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *All fields are abelian (for multiplication).*
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *Non-abelian systems exist*, but they must be *something
>>>>>>>>>>>>>> other than fields*.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://chatgpt.com/s/t_69b88dd136dc8191980797bab825c8eb
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So if somebody said non-abelian field, maybe they meant a
>>>>>>>>>>>>>> group or ring or such instead? Linguistically how do the words
>>>>>>>>>>>>>> "commutative" and "abelian" differ -- are they synonyms?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If someone says *“non-abelian field,”* they’re almost
>>>>>>>>>>>>>> certainly misspeaking or being imprecise. By definition, a *field’s
>>>>>>>>>>>>>> multiplication must be commutative*, so a “non-abelian
>>>>>>>>>>>>>> field” cannot exist. Often what people really mean is one of these:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> a *non-abelian group* (very common in algebra),
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> a *non-commutative ring*, or
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> a *division ring* (also called a *skew field*), where you
>>>>>>>>>>>>>> can divide but multiplication might not commute. A classic example is the
>>>>>>>>>>>>>> quaternions discovered by William Rowan Hamilton.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> “Abelian” vs. “commutative”
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> They are *closely related but used in slightly different
>>>>>>>>>>>>>> contexts*:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *Abelian*: usually used for *groups*.
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> An *abelian group* means the group operation satisfies
>>>>>>>>>>>>>> (a * b = b * a).
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *Commutative*: used more broadly for *operations in many
>>>>>>>>>>>>>> structures* (rings, fields, etc.).
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A *commutative ring* means its multiplication
>>>>>>>>>>>>>> satisfies (ab = ba).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So mathematically they both describe *the same property: the
>>>>>>>>>>>>>> order of the operation doesn’t matter*. The difference is
>>>>>>>>>>>>>> mostly *convention and context*.
>>>>>>>>>>>>>> Linguistic summary
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *Abelian* = “commutative,” but typically said when
>>>>>>>>>>>>>> talking about *groups*.
>>>>>>>>>>>>>> -
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *Commutative* = the *general term* for the property
>>>>>>>>>>>>>> across algebraic structures.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So if someone says *“non-abelian field,”* the most
>>>>>>>>>>>>>> charitable interpretation is that they *meant a
>>>>>>>>>>>>>> non-commutative division ring* or were *thinking about
>>>>>>>>>>>>>> non-abelian groups*.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://chatgpt.com/s/t_69b88e17db308191969333b7227cabfd
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I'm not logged in -- can I share your thread?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yes—you can still share it even if you’re not logged in, but
>>>>>>>>>>>>>> it depends on *how* you want to share it:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *1. Copy-paste the text*
>>>>>>>>>>>>>> The simplest way is just to copy the conversation and paste
>>>>>>>>>>>>>> it into an email, document, forum post, etc.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *2. Share a screenshot*
>>>>>>>>>>>>>> You can take screenshots of the thread and send them.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *3. Share the page link (sometimes works)*
>>>>>>>>>>>>>> If you’re using a browser and the conversation has its own
>>>>>>>>>>>>>> URL, you can try sending that link—but if you’re not logged in, it may *not
>>>>>>>>>>>>>> always load the same thread* for someone else.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ✅ *Most reliable method:* copy-paste or screenshots.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If you want, I can also *compress the whole explanation into
>>>>>>>>>>>>>> a short shareable summary* (like 4–5 sentences) that’s
>>>>>>>>>>>>>> easier to send to someone.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://chatgpt.com/s/t_69b88d5fe91c8191877f61e4823d1448
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
1
0
Re: [ot][spam]gpt-4 completions
by Undescribed Horrific Abuse, One Victim & Survivor of Many 30 Mar '26
by Undescribed Horrific Abuse, One Victim & Survivor of Many 30 Mar '26
30 Mar '26
perplexity tell me what the yang mills mass gap is ooops introduce me to
what a particle is how about that why, does it matter if i use my own terms?
https://www.perplexity.ai/search/arright-perplexity-ai-backende-DTYM1DP5Ra6…
# arright perplexity.ai backended by gpt 5.4 thinking: give me a couple
advanced high school level sentences on what the yang mills band gap is. Is
this an unmeasured prediction, an unproven measurement, or something else?
A websearch seemed to freely conflate physics and math terms -- is that
normal? Are the two the same here?
Usually this is called the Yang–Mills **mass** gap, not the Yang–Mills band
gap. In advanced high-school language: the classical Yang–Mills equations
act like they should produce massless ripples, but the quantum version is
expected to have a smallest nonzero energy above empty space, so the
lightest particle-like excitation would still have some positive
mass.[^1_1][^1_2][^1_3]
## What status it has
It is not best described as an “unmeasured prediction” or an “unproven
measurement.” A better description is: physicists have strong experimental
and computational evidence that the relevant quantum Yang–Mills behavior
has a mass gap, but mathematicians still do not have a fully rigorous proof
that the four-dimensional quantum theory exists in the required sense and
has that gap. That is why the Clay problem is called “Yang–Mills existence
and mass gap” and remains unsolved.[^1_2][^1_3][^1_1]
## Physics vs math
Yes, that mixing is normal here. The same phrase names both a physical
phenomenon people expect in the strong interaction and a mathematical
theorem people want to prove about quantum Yang–Mills theory. So they are
not two unrelated things, but they are also not identical: physics asks
whether nature does this, while the Millennium problem asks for a rigorous
construction and proof.[^1_3][^1_1][^1_2]
## One clean way to say it
A concise version is: “Yang–Mills mass gap” means that after quantization,
the vacuum is separated from all excitations by some positive energy
$\Delta>0$, so there are no arbitrarily low-energy particle states above
the vacuum. For the SU(3) case connected to the strong force, this is
often phrased as expecting massive color-neutral bound states such as
glueballs rather than freely observed massless gluons.[^1_1][^1_3]
Would you like a version that is one notch more mathematical, or one that
is even more intuitive?
<span
style="display:none">[^1_10][^1_11][^1_12][^1_13][^1_14][^1_15][^1_16][^1_17][^1_18][^1_19][^1_20][^1_21][^1_22][^1_23][^1_24][^1_25][^1_26][^1_27][^1_28][^1_4][^1_5][^1_6][^1_7][^1_8][^1_9]</span>
<div align="center">⁂</div>
[^1_1]: https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap
[^1_2]: https://www.claymath.org/millennium/yang-mills-the-maths-gap/
[^1_3]: https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf
[^1_4]:
https://projecteuclid.org/journals/journal-of-physical-mathematics/volume-7…
[^1_5]:
https://www.reddit.com/r/askscience/comments/8b4wg3/can_someone_explain_to_…
[^1_6]:
https://motionmountain.substack.com/p/the-yang-mills-mass-gap-problem
[^1_7]:
https://www.reddit.com/r/askscience/comments/4d9cle/what_exactly_does_the_y…
[^1_8]:
https://math-soc.com/2025/10/21/million-dollar-question-the-yang-mills-exis…
[^1_9]:
https://www.math.harvard.edu/event/millennium-prize-problems-lecture-sourav…
[^1_10]: https://www.scirp.org/journal/paperinformation?paperid=126102
[^1_11]: https://www.youtube.com/watch?v=Ae9lTCUzJjE
[^1_12]:
https://international-maths-challenge.com/millennium-prize-the-yang-mills-e…
[^1_13]: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5395755
[^1_14]: https://www.youtube.com/watch?v=uMiR0ZlZdaQ
[^1_15]: https://ncatlab.org/nlab/show/Yang-Mills+mass+gap
[^1_16]: https://www.claymath.org/lectures/yang-mills-and-the-mass-gap/
[^1_17]:
https://www.claymath.org/library/annual_report/douglas_quantum_yang_mills.p…
[^1_18]:
https://www.claymath.org/lectures/yang-mills-existence-and-mass-gap/
[^1_19]: https://www.claymath.org
[^1_20]:
https://www.arthurjaffe.com/Assets/pdf/QuantumYangMillsWebRevised.pdf
[^1_21]: https://www.claymath.org/millennium-problems/
[^1_22]:
https://www.claymath.org/library/annual_report/ar2003/03report_prizeproblem…
[^1_23]:
https://papers.ssrn.com/sol3/Delivery.cfm/8dad7eb1-c2d9-46c7-a92b-2cabe0218…
[^1_24]: https://www.claymath.org/library/monographs/MPPc.pdf
[^1_25]: https://arxiv.org/abs/0911.1013
[^1_26]:
https://www.claymath.org/millennium/yang-mills-the-maths-gap/unknown-1/
[^1_27]: http://casanchi.org/mat/problema06.pdf
[^1_28]:
https://www.claymath.org/events/millennium-prize-problems-lecture-series/
---
# Hrm let's go back to the "high school" part of my prompt -- can you
briefly introduce the first high level concept or term in your reply? I
guess that would be the Yang-Mills equations -- what are they?
The Yang–Mills equations are the basic equations for certain force fields
in modern physics, written as a system of nonlinear partial differential
equations for a “gauge field.” They come from asking for field
configurations that make the Yang–Mills energy/action stationary, much like
ordinary mechanics gets equations of motion from an energy
principle.[^2_1][^2_4]
## High-school picture
At a high-school level, a useful first approximation is: they are like
Maxwell’s equations for electromagnetism, but for more complicated fields
that have extra internal components. The big new feature is that these
fields can interact with themselves, so the equations are nonlinear rather
than as simple as the vacuum Maxwell equations.[^2_4][^2_6][^2_7]
If Maxwell says “electric and magnetic fields spread and evolve,”
Yang–Mills says something like “a multi-component force field spreads and
evolves, while also pushing on itself because of its own structure.” In
both physics and math, that field is often described by a gauge potential
$A$, and its strength/curvature by $F$; one standard local form of the
equation is $\partial_\mu F^{\mu\nu} + [A_\mu, F^{\mu\nu}] = 0$, where the
bracket term is the self-interaction part.[^2_6][^2_1][^2_4]
## Why they matter
These equations are central in physics because Yang–Mills theory underlies
the modern description of elementary-particle forces. They are central in
math because they can also be viewed as natural equations for connections
whose curvature is, in a precise sense, as small as possible.[^2_8][^2_1]
Want the next term unpacked too—“gauge field” or “nonlinear partial
differential equation”?
<span style="display:none">[^2_10][^2_2][^2_3][^2_5][^2_9]</span>
<div align="center">⁂</div>
[^2_1]: https://en.wikipedia.org/wiki/Yang–Mills_equations
[^2_2]: https://www.damtp.cam.ac.uk/user/tong/gaugetheory/2ym.pdf
[^2_3]:
https://www.reddit.com/r/explainlikeimfive/comments/msuv89/eli5_in_simple_t…
[^2_4]: https://math.berkeley.edu/~gbeiner/papers/Yang_Mills.pdf
[^2_5]: https://empg.maths.ed.ac.uk/Activities/GT/Lect3.pdf
[^2_6]:
https://pages.jh.edu/rrynasi1/PhysicalPrinciples/literature/Jackiw1980Intro…
[^2_7]: http://math.uchicago.edu/~may/REU2017/REUPapers/Ling.pdf
[^2_8]: https://www.claymath.org/millennium/yang-mills-the-maths-gap/
[^2_9]: https://www.youtube.com/watch?v=SR1Sl29HY4c
[^2_10]:
https://www.math.mcgill.ca/gantumur/math581w12/downloads/picard_YM.pdf
---
# i'm okay with nonlinear pde which is roughly just an equation that
includes derivatives; what's a gauge field? what interactions guide these
fields? does self-interaction propagate at a finite speed or
instantaneously?
A gauge field is, at a first pass, the mathematical field you add so a
theory can stay consistent when its “internal reference frame” is allowed
to vary from point to point in space and time. In electromagnetism the
gauge field is the familiar potential $A_\mu$; in Yang–Mills theory it is a
more complicated multi-component version of that
idea.[^3_1][^3_2][^3_3][^3_4]
## What it is
A high-school-friendly picture is: imagine every point in space carries a
little internal dial, and the gauge field tells you how that dial at one
point is related to the dial at a nearby point. The physically measurable
part is not the dial setting itself but the “twist” or curvature you get
when you compare nearby points, which is why different gauge choices can
describe the same physics.[^3_2][^3_4][^3_1]
## What guides it
The allowed interactions are mainly fixed by the symmetry you demand
locally, called the gauge symmetry, together with the choice of symmetry
group such as U(1), SU(2), or SU(3). In plain language, the symmetry rules
decide what kinds of charges exist, what field carries the force, and how
matter couples to that field. For Yang–Mills fields, unlike ordinary
electromagnetism, the field itself can carry the relevant charge, so it can
interact with itself.[^3_5][^3_3][^3_4][^3_6][^3_7][^3_1]
## Speed of influence
That self-interaction still propagates causally rather than instantaneously
in the classical theory. Sources discussing the hyperbolic Yang–Mills
equations describe them as having finite speed of propagation, and one
summary notes that the classical waves of the field travel at the speed of
light. So although some gauge choices can make the potentials look
mathematically nonlocal, the physical influence does not seem to outrun
light.[^3_3][^3_8][^3_4][^3_9]
A compact slogan is: a gauge field is the bookkeeping device for a local
symmetry, and Yang–Mills makes that bookkeeping dynamic enough that the
field can also push on itself. Want me to connect that directly to why
non-abelian gauge fields self-interact while Maxwell’s field does
not?[^3_1][^3_2][^3_3]
<span
style="display:none">[^3_10][^3_11][^3_12][^3_13][^3_14][^3_15][^3_16][^3_17]</span>
<div align="center">⁂</div>
[^3_1]: https://en.wikipedia.org/wiki/Gauge_theory
[^3_2]: https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/
[^3_3]: https://en.wikipedia.org/wiki/Yang–Mills_theory
[^3_4]: https://plato.stanford.edu/entries/gauge-theories/
[^3_5]: https://81018.com/gauge-theory/
[^3_6]: https://math.berkeley.edu/~gbeiner/papers/Yang_Mills.pdf
[^3_7]:
https://pages.jh.edu/rrynasi1/PhysicalPrinciples/literature/Jackiw1980Intro…
[^3_8]: https://par.nsf.gov/servlets/purl/10432590
[^3_9]: https://arxiv.org/pdf/1308.6571.pdf
[^3_10]: https://williamsgj.people.charleston.edu/Gauge Theory.pdf
[^3_11]:
https://www.reddit.com/r/explainlikeimfive/comments/9plww9/eli5_explain_gau…
[^3_12]: https://arxiv.org/abs/1308.6571
[^3_13]: https://www.youtube.com/watch?v=z2P-AxhnQiE
[^3_14]: https://www.youtube.com/watch?v=eD_mv1ZZfLQ
[^3_15]: https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf
[^3_16]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
[^3_17]: https://www.damtp.cam.ac.uk/user/tong/gaugetheory/2ym.pdf
---
# It is surprising that self-interaction is needed for a bookkeeping field.
What is a symmetry group?
A symmetry group is the full set of transformations you can apply to
something without changing the essential thing you are describing, together
with the rule for combining one transformation after another. In geometry,
for example, the rotations and reflections that leave a square looking the
same form a symmetry group.[^4_1][^4_2]
## Group idea
A group, in the algebra sense, is a collection of operations you can
compose, where composition stays inside the collection, there is an
identity operation that does nothing, and each operation has an inverse
that undoes it. So a symmetry group is just a group whose elements are
“do-nothing-visible” transformations of some object or
law.[^4_3][^4_4][^4_2][^4_5][^4_1]
## Concrete example
For an equilateral triangle, rotating by 120 degrees, rotating by 240
degrees, doing nothing, and reflecting across any of its three symmetry
axes all count as symmetries. Those six operations together form the
triangle’s symmetry group because combining any two of them gives another
symmetry of the same triangle.[^4_2][^4_6][^4_1]
## Physics meaning
In physics, the “object” being preserved is usually not the appearance of a
shape but the form of the laws of motion or the measurable predictions. A
gauge symmetry group is the set of internal transformations you can make at
each point in spacetime without changing the physical content of the
theory.[^4_7][^4_8]
## Why self-interaction appears
Your surprise is reasonable: if the field were only bookkeeping, you might
expect it to stay passive. But when the local symmetry group is
non-commutative, as in Yang–Mills theory, the gauge field is required to
preserve that symmetry and in doing so it also carries the relevant charge,
which makes self-interaction part of the structure rather than an extra
add-on. In that sense, the “bookkeeping” becomes dynamic because
consistency under local symmetry forces the field itself to participate in
the interaction.[^4_8][^4_9][^4_7]
A very compressed slogan is: symmetry tells you what transformations are
allowed, and the symmetry group is the algebraic machine that records how
those transformations combine.[^4_5][^4_1]
<span
style="display:none">[^4_10][^4_11][^4_12][^4_13][^4_14][^4_15][^4_16][^4_17]</span>
<div align="center">⁂</div>
[^4_1]: https://en.wikipedia.org/wiki/Symmetry_group
[^4_2]: https://fiveable.me/hs-honors-geometry/key-terms/symmetry-group
[^4_3]:
https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/An_I…
[^4_4]: https://en.wikipedia.org/wiki/Symmetric_group
[^4_5]: https://www2.math.upenn.edu/~mlazar/math170/notes07.pdf
[^4_6]: https://www.youtube.com/watch?v=paQLJKtiAEE
[^4_7]: https://en.wikipedia.org/wiki/Gauge_theory
[^4_8]: https://plato.stanford.edu/entries/gauge-theories/
[^4_9]: https://en.wikipedia.org/wiki/Yang–Mills_theory
[^4_10]: https://www.youtube.com/watch?v=3aNeCWRjh8I
[^4_11]:
https://www.reddit.com/r/mathematics/comments/14gnz46/what_do_people_mean_b…
[^4_12]: https://arxiv.org/pdf/2602.01258.pdf
[^4_13]: https://mathweb.ucsd.edu/~asalehig/math200a-22-f-lectures.pdf
[^4_14]:
https://www.reddit.com/r/Physics/comments/1ot8532/how_does_the_concept_of_g…
[^4_15]: https://www.youtube.com/watch?v=emmeKVe9DmI
[^4_16]:
https://math.mit.edu/research/highschool/primes/circle/documents/2022/Evely…
[^4_17]: https://mathworld.wolfram.com/SymmetricGroup.html
---
# you've mentioned both particles and spacetime -- this applies to both?
Yes, but in two different senses. Yang–Mills theory is a field theory on
spacetime, and in its quantum version the particle picture appears because
particles are interpreted as excitations of those fields.[^5_1][^5_2][^5_3]
## Two roles
Spacetime is the stage: the gauge field assigns mathematical data to each
point in space and time and evolves across that stage. Particles are the
ripples or quantized excitations of the field when you view the theory
quantum mechanically.[^5_4][^5_2][^5_3][^5_1]
## Important distinction
The gauge symmetry in Yang–Mills theory is usually an internal symmetry,
not an ordinary symmetry of spacetime shape like rotation or translation.
So the theory lives on spacetime, but the symmetry group is usually acting
on an internal “label space” attached at each spacetime
point.[^5_5][^5_1][^5_4]
## In one sentence
So: it applies to spacetime because the field is defined there, and it
applies to particles because those field excitations are what we call
particles. It does not usually mean that Yang–Mills is itself a theory of
spacetime geometry; that would move you closer to gravity
questions.[^5_2][^5_3][^5_6][^5_1]
A useful slogan is: spacetime tells you where the field lives, and quantum
theory tells you why lumps of that field look like particles.[^5_3][^5_2]
<span
style="display:none">[^5_10][^5_11][^5_12][^5_13][^5_14][^5_15][^5_7][^5_8][^5_9]</span>
<div align="center">⁂</div>
[^5_1]: https://en.wikipedia.org/wiki/Gauge_theory
[^5_2]: https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf
[^5_3]:
https://www.forbes.com/sites/startswithabang/2019/01/13/ask-ethan-how-do-qu…
[^5_4]: https://philsci-archive.pitt.edu/834/1/gr_gauge.pdf
[^5_5]: https://plato.stanford.edu/entries/gauge-theories/
[^5_6]: http://www.progress-in-physics.com/2022/PP-64-01.PDF
[^5_7]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
[^5_8]: https://www.youtube.com/watch?v=AuqKsBQnE2A
[^5_9]:
https://physicstoday.aip.org/features/solving-quantum-field-theories-via-cu…
[^5_10]:
https://www.bostonreview.net/articles/matthew-buckley-search-new-physics-ce…
[^5_11]:
https://www.facebook.com/groups/179829628846347/posts/3229218450574101/
[^5_12]: https://www.youtube.com/watch?v=eoStndCzFhg
[^5_13]:
https://projecteuclid.org/journals/communications-in-mathematical-physics/v…
[^5_14]:
https://www.reddit.com/r/explainlikeimfive/comments/9plww9/eli5_explain_gau…
[^5_15]:
https://www.reddit.com/r/AskPhysics/comments/1fpm528/what_does_it_mean_to_s…
---
# what kinds "coordinate transform" necessitate the use of a gauge field,
if i understand correctly?
Not quite coordinate transforms in the usual spacetime sense. What
necessitates a gauge field is usually promoting an internal symmetry from a
single global transformation to a different transformation at each
spacetime point.[^6_1][^6_2][^6_3][^6_4]
## What changes
The classic example is a complex matter field $\psi(x)$ whose overall phase
can be rotated by the same angle everywhere, $\psi(x)\to
e^{i\alpha}\psi(x)$, without changing observable physics. If you now allow
that angle to vary with position and time, $\psi(x)\to
e^{i\alpha(x)}\psi(x)$, ordinary derivatives pick up extra terms and the
equations stop being invariant unless you introduce a compensating gauge
field.[^6_5][^6_2][^6_6][^6_4]
## Not ordinary coordinates
So the relevant “transforms” are usually not things like $x\to x+a$ or
spatial rotations of spacetime coordinates. They are internal changes of
description, such as local phase rotations for U(1) in electromagnetism or
local SU(2)/SU(3) rotations among internal components in non-abelian
theories.[^6_7][^6_8][^6_9][^6_10][^6_1]
## Why a field appears
The gauge field is introduced so you can compare internal states at
neighboring points in a way that respects those local transformations.
Mathematically, it enters through a covariant derivative that cancels the
unwanted derivative-of-$\alpha(x)$ terms. In that sense, the gauge field
is less “forced by coordinate changes” and more “forced by demanding local
internal symmetry.”[^6_2][^6_3][^6_11][^6_4][^6_12][^6_1]
## One picture
A simple picture is that each point in spacetime is allowed its own choice
of internal basis, and the gauge field tells you how to move from one
point’s choice to the next one consistently. That is why people sometimes
compare gauge transformations to coordinate changes, but the closer
statement is that they are coordinate changes in an internal fiber-like
space, not ordinary spacetime coordinates themselves.[^6_3][^6_11][^6_13]
A one-line example is: global phase change does nothing special, but local
phase change $\alpha\to\alpha(x)$ is what brings in the electromagnetic
potential $A_\mu$.[^6_2][^6_7]
<span style="display:none">[^6_14][^6_15][^6_16][^6_17][^6_18]</span>
<div align="center">⁂</div>
[^6_1]: https://en.wikipedia.org/wiki/Gauge_theory
[^6_2]:
https://www.ippp.dur.ac.uk/~krauss/Lectures/IntroToParticlePhysics/2010/Lec…
[^6_3]: https://philsci-archive.pitt.edu/2133/1/geometrie.pdf
[^6_4]: https://www.phys.ufl.edu/~ramond/Chapter6_CUP.pdf
[^6_5]: https://williamsgj.people.charleston.edu/Gauge Theory.pdf
[^6_6]: https://www.physics.rutgers.edu/grad/618/lects/localsym.pdf
[^6_7]: https://www.physics.rutgers.edu/grad/618/lects/localsym_2.pdf
[^6_8]:
https://www.reddit.com/r/Physics/comments/wbdl7/explanation_of_gauge_symmet…
[^6_9]:
http://home.ustc.edu.cn/~gengb/201118/Peskin_lattice_gauge_theory.pdf
[^6_10]: https://philsci-archive.pitt.edu/834/1/gr_gauge.pdf
[^6_11]: https://en.wikipedia.org/wiki/Yang–Mills_equations
[^6_12]: https://plato.stanford.edu/entries/gauge-theories/
[^6_13]: https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/
[^6_14]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
[^6_15]: https://arxiv.org/pdf/2506.15832.pdf
[^6_16]:
https://www.reddit.com/r/Physics/comments/2s2dxz/why_do_we_want_gauge_invar…
[^6_17]: https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf
[^6_18]:
https://indico.math.cnrs.fr/event/11080/attachments/4585/8220/Lecture
Notes_DumitrescuT.pdf
---
# is this attached paper sophisticated gibberish or real information? it
was presented to me online in a suggestive context, after which i have
interest in learning the terms -- i need things to learn and it's usually
hard to keep engagement.
what is a non-abelian field theory? what is the use of performing property
transforms such as phase, and what is phase here?
As a source of mainstream math or physics, this PDF looks much closer to a
symbolic/esoteric construction than to a credible research paper. The
quickest reason is that it mixes claims of solving multiple major problems
with poetry, ritual language, custom glyph dictionaries, frequency
assignments, and statements like “The Proof is Complete” and “Fluid
Mechanics of God,” which is not how serious mathematical proofs or physics
papers are normally built.[^7_1]
## Paper assessment
The file presents itself as an “initiation into a closed formal language,”
says symbolism is “not optional,” and frames understanding as something
that “emerges only through interaction,” which is already a strong sign
that it is not using mathematical terms in their standard public, checkable
sense. It also claims solutions or translations for Yang–Mills,
Navier–Stokes, BSD, Riemann, P vs NP, Hodge, and Poincaré in one framework,
while mapping classical objects to glyphs, spiritual entities, and fixed Hz
values; that pattern is much more characteristic of private-system writing
than of accepted technical work.[^7_1]
A fair reading is: it may contain real curiosity, real effort, and real
emotional meaning for its author, but it does not look reliable as evidence
about actual Yang–Mills theory or modern mathematics. If it caught your
interest, the productive move is to mine it for vocabulary to learn in
standard sources, not to treat it as a trustworthy guide to the subjects it
names.[^7_1]
## Non-abelian theory
In this context, “non-abelian” means the relevant symmetry operations do
not commute, so doing transformation $A$ then $B$ gives a different result
from doing $B$ then $A$. A non-abelian gauge field theory is therefore a
field theory whose gauge symmetry comes from a non-commutative group, such
as SU(2) or SU(3), rather than the commutative U(1) symmetry of
electromagnetism.[^7_2][^7_3][^7_4]
That non-commutativity matters because the gauge field itself then carries
the kind of charge involved in the interaction, so the field can interact
with itself. That is the big conceptual jump from Maxwell’s theory to
Yang–Mills theory.[^7_3][^7_4][^7_5]
## What phase means
Here, “phase” usually means the angle of a complex multiplier like
$e^{i\theta}$ attached to a wavefunction or field, not “phase” in the sense
of solid, liquid, or gas. You can think of it as a clock-hand angle
attached to the field: changing the phase rotates that hand without
necessarily changing directly measurable quantities.[^7_6][^7_7]
A global phase change uses the same angle everywhere, while a local phase
change lets the angle depend on space and time. Global phase is mostly a
redundancy of description, but relative phase differences can matter
physically because they affect interference.[^7_8][^7_7][^7_6]
## Why transform phase
The point of performing a phase transformation is usually not to “do
physics” to the system, but to test whether two descriptions represent the
same physical situation. When you demand invariance under local phase
changes, ordinary derivatives stop behaving nicely, and introducing a gauge
field restores that invariance.[^7_7][^7_5][^7_9][^7_6][^7_8]
So the gauge field is a compensating structure that lets neighboring points
use different internal phase conventions without changing the physics. In
electromagnetism that compensating field is the electromagnetic potential,
and in Yang–Mills theory it is its non-abelian
generalization.[^7_5][^7_2][^7_6][^7_7]
## Good terms to learn
If you want the real concepts underneath the paper’s vocabulary, the best
next terms are: gauge group, local symmetry, covariant derivative, field
strength, abelian vs non-abelian, and global vs local phase. Those are
standard and genuinely useful, and they will let you tell very quickly when
a document is using physics words in a disciplined way versus using them as
aesthetic decoration.[^7_10][^7_2][^7_6][^7_1]
Want me to turn those six terms into a tiny one-page glossary in plain
English?
<span
style="display:none">[^7_11][^7_12][^7_13][^7_14][^7_15][^7_16][^7_17][^7_18]</span>
<div align="center">⁂</div>
[^7_1]: ALQC_Canon_Formalized-1.pdf
[^7_2]: https://en.wikipedia.org/wiki/Non-abelian_gauge_transformation
[^7_3]: https://www.damtp.cam.ac.uk/user/dbs26/AQFT/YM.pdf
[^7_4]: http://fma.if.usp.br/~burdman/QFT2/lecture_15.pdf
[^7_5]: https://www.physics.rutgers.edu/grad/618/lects/localsym_2.pdf
[^7_6]:
https://www.ippp.dur.ac.uk/~krauss/Lectures/IntroToParticlePhysics/2010/Lec…
[^7_7]: https://williamsgj.people.charleston.edu/Gauge Theory.pdf
[^7_8]:
https://www.reddit.com/r/AskPhysics/comments/wbnkgf/why_and_how_does_cancel…
[^7_9]: https://plato.stanford.edu/entries/gauge-theories/
[^7_10]: https://en.wikipedia.org/wiki/Gauge_theory
[^7_11]: https://www.youtube.com/watch?v=17Cig8YuRh4
[^7_12]: https://www.youtube.com/watch?v=ewDD5A9Rwcc
[^7_13]:
https://indico.global/event/5650/contributions/45603/attachments/22394/3773…
[^7_14]: http://www.nhn.ou.edu/~milton/aqft/chap5.pdf
[^7_15]: https://pmc.ncbi.nlm.nih.gov/articles/PMC3440626/
[^7_16]: https://arxiv.org/abs/2404.00743
[^7_17]:
https://www.reddit.com/r/AskPhysics/comments/1kqwzly/what_exactly_is_the_qu…
[^7_18]: https://mphq.physics.harvard.edu/quantum-phases-matter
---
# i'm still catching up with what you've said so far. what you've said so
far would likely take me multiple chat sessions to learn from you, hence my
interest. what is private-system writing? when you say phase do you mean an
alternating or time-changing-information-holding field or something else?
By “private-system writing,” I did **not** mean “fake because unusual.” I
meant writing that creates its own internal language first, then uses
standard math/physics words inside that custom language, so the words stop
having their usual public meanings unless you learn that one author’s
dictionary.
## What I meant
Your PDF explicitly says it is “not a translation, but an initiation into a
closed formal language,” and it includes a long custom “Dictionary of
Invariance” that assigns special meanings to glyphs, operators,
frequencies, and technical terms. It also repeatedly equates logic,
physics, topology, esoteric symbolism, and fixed Hz assignments inside one
bespoke framework, which is why I described it as private-system writing
rather than ordinary mathematical exposition.[^8_1]
That does not mean there is no thought in it. It means the burden of
interpretation is shifted from shared definitions and standard proofs to
the author’s own symbolic world.[^8_1]
## What phase is
Here “phase” usually means the angle of a complex number, or of a
complex-valued wave or field. If you write a quantity in the form
$re^{i\theta}$, then $r$ is its size and $\theta$ is its phase.[^8_2][^8_3]
So phase is not, by itself, “an alternating field” or “time-changing
information.” It is more like the hand-angle on a clock attached to the
quantity.[^8_3][^8_2]
## Does phase change in time
It can, but it does not have to. For a wave like $Ae^{i(kx-\omega t)}$,
the phase is $kx-\omega t$, so it varies with position $x$ and time $t$;
that variation is what encodes things like wavelength and
frequency.[^8_4][^8_3]
But you can also have a constant phase offset, like multiplying by
$e^{i\phi}$, where nothing is “oscillating faster” just because the whole
object got rotated in the complex plane. That is why people distinguish
between global phase and relative or local phase.[^8_5][^8_6][^8_2]
## Why phase matters
A global phase is often physically unobservable, meaning two states that
differ only by one overall phase factor are usually treated as the same
physical state. Relative phase matters because it affects interference,
which is why two waves can reinforce or cancel depending on how their phase
angles line up.[^8_2][^8_5]
So the short answer is: phase is usually an angle, not a substance. When
that angle changes across space or time, it becomes a powerful way to
describe oscillation, interference, and in gauge theory, local changes of
internal description.[^8_7][^8_5][^8_3][^8_2]
## One picture
A good mental model is two arrows of the same length in the complex plane.
Their lengths tell you “how much,” and their angles tell you the phase;
changing the angle changes how they add together, even if the lengths stay
the same.[^8_3][^8_2]
Next best term to unpack is probably “complex number as a rotating arrow,”
because that makes phase, local phase, and gauge transformations much less
mysterious.
<span
style="display:none">[^8_10][^8_11][^8_12][^8_13][^8_14][^8_15][^8_16][^8_17][^8_8][^8_9]</span>
<div align="center">⁂</div>
[^8_1]: ALQC_Canon_Formalized-1.pdf
[^8_2]: https://www.youtube.com/watch?v=qtIsYbYdzCI
[^8_3]: https://mathforquantum.quantumtinkerer.tudelft.nl/1_complex_numbers/
[^8_4]: https://courses.physics.illinois.edu/phys580/fa2013/susy_v2.pdf
[^8_5]: https://philsci-archive.pitt.edu/20971/1/phase 2022 v999.pdf
[^8_6]: https://www.quantumgrad.com/article/676
[^8_7]:
https://www.ippp.dur.ac.uk/~krauss/Lectures/IntroToParticlePhysics/2010/Lec…
[^8_8]:
https://web.stanford.edu/~montanar/TEACHING/Stat375/papers/journey.pdf
[^8_9]:
https://www.nordicwittgensteinreview.com/article/download/3302/pdf/8131
[^8_10]:
https://www.reddit.com/r/math/comments/uvrrr8/using_your_own_math_notation/
[^8_11]: https://news.ycombinator.com/item?id=34441327
[^8_12]: http://www.math.vanderbilt.edu/~schectex/commerrs/
[^8_13]: https://files.eric.ed.gov/fulltext/ED402030.pdf
[^8_14]: https://www.youtube.com/watch?v=4erc_zQY89I
[^8_15]:
https://www.reddit.com/r/3Blue1Brown/comments/w4igqr/having_hard_time_under…
[^8_16]:
https://ecommons.aku.edu/cgi/viewcontent.cgi?article=1008\&context=eastafri…
[^8_17]: https://www.youtube.com/watch?v=bIxJDU5raQs
---
# it sounds like you are discussing the phase component of things that are
being described by complex numbers, even when the use of complex numbers
does not add meaning? that is kind if why the guage field is purely
bookkeeping?
the author of the paper uses vague words i see as poorly-defined like
telepathy -- do these words have contextual or paper-defined rigorous
meaning i have not learned?
Partly yes: the phase being discussed is the phase of a complex-valued
field or wavefunction, and an overall global phase is usually treated as
physically redundant, while relative or local phase differences can
matter. But that does **not** make the gauge field merely empty
bookkeeping in the full theory, because gauge redundancy is a redundancy of
description, while the gauge field can be a dynamical object with real
physical effects.[^9_1][^9_2][^9_3][^9_4][^9_5][^9_6]
## Phase and meaning
When physicists talk about phase here, they usually mean the angle in a
complex factor like $e^{i\theta}$. The reason complex numbers are used is
not just decorative convenience: even when the overall phase is
unobservable, relative phase changes interference and other measurable
behavior.[^9_4][^9_7][^9_6][^9_8]
So your instinct is close but needs one adjustment. The “bookkeeping” part
is mostly that different phase conventions can describe the same physical
state, especially for global phase, while the physically meaningful part
shows up in phase differences across components or across
spacetime.[^9_5][^9_6][^9_4]
## Gauge bookkeeping
A good compact statement is: gauge symmetry is often a redundancy in
description, but the compensating field introduced to handle local phase
changes is not merely disposable notation once it is allowed to evolve
dynamically. One source puts it almost exactly this way: the “bookkeepers”
become part of a gauge theory only when they are dynamical actors that
shape the system’s behavior.[^9_9][^9_2][^9_1]
That is why people often say two things that sound contradictory but are
both true. The gauge freedom is descriptive redundancy, yet the gauge
field associated with that redundancy can encode real interactions such as
electromagnetism or Yang–Mills forces.[^9_3][^9_1][^9_5]
## Paper language
For words like “telepathic circuit,” the paper does not seem to give a
rigorous operational definition in the standard scientific sense. It uses
the phrase in the cover letter, but the document also says its symbols gain
meaning “through engagement rather than definition alone” and calls the
text an “initiation into a closed formal language,” which points away from
ordinary public definitions.[^9_10]
So there may be a contextual meaning inside the author’s symbolic system,
but it does not look like the kind of meaning that would let an outside
reader test, compute, or verify claims in a standard way. That is the key
distinction: a rigorous term usually comes with clear conditions for use,
while this paper often gives poetic role-descriptions, thematic links, and
analogies instead.[^9_10]
## How to read it
A practical way to read this kind of document is to separate three layers.
Layer 1 is standard math/physics vocabulary, like manifold, commutator,
parity, or phase; layer 2 is the author’s private relabeling of those
words; layer 3 is openly poetic or esoteric language like “telepathic
circuit” or “witch of always.”[^9_3][^9_10]
If you want learning value without getting trapped, trust layer 1, treat
layer 2 cautiously, and treat layer 3 as metaphor unless the paper gives a
clear procedure or test. The words may carry emotional or narrative
intent, but they do not seem to acquire standard rigor merely by being
embedded next to equations.[^9_1][^9_10]
Next term to pin down might be “relative phase,” because that is exactly
where “complex-number description” stops being mere convention and starts
affecting measurable outcomes.[^9_4][^9_5]
<span
style="display:none">[^9_11][^9_12][^9_13][^9_14][^9_15][^9_16][^9_17][^9_18]</span>
<div align="center">⁂</div>
[^9_1]: https://ar5iv.labs.arxiv.org/html/1901.10420
[^9_2]:
https://www.studocu.com/en-us/document/creighton-university/human-physiolog…
[^9_3]: https://sites.ualberta.ca/~gingrich/courses/phys512/node30.html
[^9_4]: https://www.youtube.com/watch?v=fgWGMnlbIvA
[^9_5]: https://quantummechanics.ucsd.edu/ph130a/130_notes/node30.html
[^9_6]: https://philsci-archive.pitt.edu/20971/1/phase 2022 v999.pdf
[^9_7]: https://www.sciencedirect.com/science/article/pii/S0375960123004292
[^9_8]: https://mathforquantum.quantumtinkerer.tudelft.nl/1_complex_numbers/
[^9_9]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
[^9_10]: ALQC_Canon_Formalized-1.pdf
[^9_11]: https://cjsmeenk.github.io/files/rickles2009gauge.pdf
[^9_12]: https://readingfeynman.org/2026/01/01/the-gauge-idea-in-em-theory/
[^9_13]:
https://quantumzeitgeist.com/quantum-states-interference-achieves-defined-o…
[^9_14]:
https://www.preposterousuniverse.com/blog/2012/11/22/thanksgiving-7/
[^9_15]:
https://www.reddit.com/r/Physics/comments/2s2dxz/why_do_we_want_gauge_invar…
[^9_16]:
https://www.reddit.com/r/3Blue1Brown/comments/w4igqr/having_hard_time_under…
[^9_17]:
https://www.reddit.com/r/AskPhysics/comments/wbnkgf/why_and_how_does_cancel…
[^9_18]: https://philsci-archive.pitt.edu/26825/1/aot.pdf
---
# what fields are complex valued? i don't really believe complex numbers
are anything more than encodings of sinusoids in a way mathematicians like,
but i'm happy to consider otherwise.
it seemed to me the paper had clear nonsense in it, that it was
specifically abusing terms to confuse or contradict -- but maybe i was
wrong?
Your intuition is **mostly** right: in many cases, a complex-valued field
is a compact way to package two real-valued components, often in a form
that makes oscillation, phase, and symmetry easier to handle. But in
quantum theory that packaging is not usually treated as empty style,
because interference and phase symmetry are built directly into the
standard formalism through complex amplitudes.[^10_1][^10_2][^10_3][^10_4]
## Which fields are complex
Common examples are the Schrödinger wavefunction, complex scalar fields,
and Dirac spinor fields. A standard complex scalar field can literally be
written as $\psi(x)=\frac{1}{\sqrt{2}}(\phi_1(x)+i\phi_2(x))$, so in that
sense it is two real scalar fields bundled together.[^10_5][^10_6][^10_2]
By contrast, some classical fields are usually taken to be real-valued, and
complex notation is then mainly a convenient representation. So
“complex-valued field” is not one single thing; sometimes it is a true part
of the standard object being studied, and sometimes it is a useful
reformulation.[^10_7][^10_2]
## Is it just sinusoids
For ordinary linear waves, treating complex numbers as a smart encoding of
sine-and-cosine behavior is a very good instinct. The phase then acts like
an angle attached to the oscillation, and complex multiplication keeps
track of rotations of that angle cleanly.[^10_3][^10_8][^10_9]
What goes beyond “just sinusoids” is that the same complex structure also
organizes symmetry transformations, especially phase rotations like U(1),
and those are central in quantum and gauge theory. So even if you prefer
to think “two real components plus a rotation rule,” that view is
compatible with mainstream physics.[^10_2][^10_10][^10_1]
## Gauge-field link
This is also why the gauge-field story is not merely “mathematicians liking
complex numbers.” If a field has a local phase freedom, then comparing its
phase from point to point requires extra structure, and that extra
structure is what the gauge field supplies.[^10_11][^10_12]
So yes, there is bookkeeping in the sense of handling redundant
descriptions. But the bookkeeping becomes physical once the compensating
field has its own dynamics and measurable effects.[^10_12][^10_13][^10_11]
## The paper
Your suspicion does not seem misplaced. The document explicitly says
meaning arises “through engagement rather than definition alone,” calls
itself an “initiation into a closed formal language,” and mixes standard
terms with phrases like “Telepathic Circuit,” “Fluid Mechanics of God,”
“Density of God,” and “Mass is Memory,” which is a strong sign that it is
not using technical language in the normal rigorous way.[^10_14]
That does not prove malicious intent, and in some possible world an
eccentric notation could still hide a real idea. But this particular paper
strongly looks like it is using scientific vocabulary suggestively rather
than giving public definitions, reproducible calculations, or standard
proofs, so reading it as deliberate abuse or confusion is a very
understandable judgment.[^10_14]
## A useful translation rule
A good rule is: if a term is rigorous, you should be able to ask “what
object is it, what are its inputs and outputs, and what would count as
using it correctly?” In this PDF, many exotic terms function more like
atmosphere, mythology, or role-labels than like testable mathematical
definitions.[^10_14]
The next most useful term to unpack here is probably “U(1) phase rotation,”
because that is exactly where complex numbers, phase, and gauge fields meet
in a clean way.[^10_1][^10_11]
<span
style="display:none">[^10_15][^10_16][^10_17][^10_18][^10_19][^10_20][^10_21][^10_22][^10_23]</span>
<div align="center">⁂</div>
[^10_1]: https://kimura.pages.math.cnrs.fr/file/QFT_lec.pdf
[^10_2]: https://dec41.user.srcf.net/notes/III_M/quantum_field_theory.pdf
[^10_3]:
https://mathforquantum.quantumtinkerer.tudelft.nl/1_complex_numbers/
[^10_4]: https://philsci-archive.pitt.edu/20971/1/phase 2022 v999.pdf
[^10_5]: https://www.southampton.ac.uk/~doug/ft1/ft15.pdf
[^10_6]: https://en.wikipedia.org/wiki/Dirac_equation
[^10_7]: https://en.wikipedia.org/wiki/Scalar_field_theory
[^10_8]: https://courses.physics.illinois.edu/phys580/fa2013/susy_v2.pdf
[^10_9]: https://www.sciencedirect.com/science/article/pii/S0375960123004292
[^10_10]: https://edu.itp.phys.ethz.ch/hs12/qft1/Chapter04.pdf
[^10_11]: https://quantummechanics.ucsd.edu/ph130a/130_notes/node30.html
[^10_12]: https://sites.ualberta.ca/~gingrich/courses/phys512/node30.html
[^10_13]: https://ar5iv.labs.arxiv.org/html/1901.10420
[^10_14]: ALQC_Canon_Formalized-1.pdf
[^10_15]: https://www.youtube.com/watch?v=wRHJjg9jBjA
[^10_16]: https://www.youtube.com/watch?v=cQNgfgmvJmA
[^10_17]: https://www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S2.html
[^10_18]: https://learn.mit.edu/c/topic/science-math?resource=6526
[^10_19]: https://vixra.org/pdf/2504.0175v1.pdf
[^10_20]: https://arxiv.org/abs/hep-th/9810093
[^10_21]:
https://www.reddit.com/r/AskPhysics/comments/1b9sq7/complex_scalar_fields_a…
[^10_22]: https://www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S4.html
[^10_23]: https://www.worldscientific.com/doi/10.1142/9789811220876_0007
---
# what is U(1)?
U(1) is the group of complex numbers with magnitude 1, so its elements can
be written as $e^{i\theta}$ for some angle $\theta$. Geometrically, that
is the symmetry group of rotations of a circle, which is why U(1) is the
simplest continuous internal symmetry used in
physics.[^11_1][^11_2][^11_5][^11_6][^11_8]
## Concrete picture
If you draw a unit circle in the complex plane, multiplying by
$e^{i\theta}$ just rotates a point around that circle without changing its
length. So U(1) is basically “all possible angle rotations,” with
multiplication as the way you combine them.[^11_5][^11_6][^11_1]
## Why it appears in physics
In quantum theory, U(1) usually shows up as phase rotations of a field,
such as $\psi \to e^{i\alpha}\psi$. If the same phase rotation is allowed
everywhere, that is a global U(1) symmetry; if the phase is allowed to vary
from point to point, that is local U(1) symmetry.[^11_7][^11_5]
## Why you care
Quantum electrodynamics is an abelian gauge theory with symmetry group
U(1), and the associated gauge field is the electromagnetic potential.
Sources in the results also tie U(1) symmetry to conservation of electric
charge and explain that local U(1) symmetry is what brings in
electromagnetism.[^11_3][^11_1][^11_5]
The shortest intuition is: U(1) is “phase rotation by any angle,” and gauge
theory asks what extra structure is needed when that allowed angle varies
across spacetime.[^11_5][^11_7]
<span style="display:none">[^11_4]</span>
<div align="center">⁂</div>
[^11_1]: https://www.youtube.com/watch?v=rCMIP5jW41s
[^11_2]:
https://www.reddit.com/r/explainlikeimfive/comments/11glacn/eli5_what_is_u1…
[^11_3]: https://en.wikipedia.org/wiki/Gauge_theory
[^11_4]:
https://shmaesphysics.wordpress.com/2022/08/08/justifying-the-standard-mode…
[^11_5]: https://kgbudge.com/essays/U1xSU2xSU3_2.html
[^11_6]: https://www.youtube.com/watch?v=UHHWBIecxcA
[^11_7]: https://www.physics.rutgers.edu/grad/618/lects/localsym.pdf
[^11_8]: https://encyclopedai.stavros.io/entries/u(1)-symmetry/
---
# why are we considering 2d angles in 3space? is it over time or potential
vs kinetic energy or electric vs magnetic or differentials ...?
Not usually. In the U(1) example, the “angle” is typically **not** a
geometric angle in ordinary 3-space, but an angle in an internal complex
plane attached to the field at each spacetime
point.[^12_1][^12_2][^12_3][^12_4]
## What the angle is
If a field value is complex, you can picture it as an arrow in a 2D plane
with a length and an angle, and multiplying by $e^{i\theta}$ rotates that
arrow within that abstract plane. That 2D plane is a mathematical space of
internal states, not a literal plane floating inside physical
space.[^12_2][^12_5][^12_4][^12_1]
## Not these other things
So it is usually not “potential versus kinetic,” not “electric versus
magnetic,” and not “time versus space differential” either. Those are
different decompositions of a system, while U(1) phase rotation is a change
of internal phase convention for the field.[^12_3][^12_1][^12_2]
## Where time enters
Time can enter because the phase angle may vary from one spacetime point to
another, so the angle can depend on position and time. But that does not
make the angle itself a spatial direction in 3-space; it means the internal
arrow can rotate differently at different places and
times.[^12_6][^12_2][^12_3]
## Why use this picture
The reason physicists use the 2D complex-angle picture is that it packages
two real components into one object and makes phase symmetry very clean to
express. For U(1), the field can be rephased by any angle, and gauge
theory asks how to compare those internal phases consistently across
spacetime.[^12_5][^12_7][^12_2][^12_6]
A compact slogan is: the field lives on spacetime, but its phase rotates in
an internal 2D complex plane. Would you like me to draw the “two real
numbers = one arrow in an internal plane” picture in plain text
next?[^12_4][^12_3]
<span
style="display:none">[^12_10][^12_11][^12_12][^12_13][^12_14][^12_15][^12_8][^12_9]</span>
<div align="center">⁂</div>
[^12_1]:
https://www.reddit.com/r/TheoreticalPhysics/comments/1jodjbq/why_is_the_con…
[^12_2]: https://kgbudge.com/essays/U1xSU2xSU3_2.html
[^12_3]:
https://www.preposterousuniverse.com/blog/2020/06/30/the-biggest-ideas-in-t…
[^12_4]:
https://www.physicsforums.com/threads/what-is-internal-space-internal-symme…
[^12_5]: https://arxiv.org/html/2404.00743v1
[^12_6]: https://en.wikipedia.org/wiki/Gauge_theory
[^12_7]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
[^12_8]: http://www.quantumdiaries.org/2009/11/06/symmetry-in-physcs-pt-4/
[^12_9]:
https://www.physicsforums.com/threads/internal-gauge-symmetries-and-spaceti…
[^12_10]:
https://www.facebook.com/groups/473920566008054/posts/8317613844971981/
[^12_11]: https://personal.lse.ac.uk/robert49/PPB/pdf/Belot2003gauge.pdf
[^12_12]: https://www.sciencedirect.com/science/article/pii/0003491687901643
[^12_13]:
https://www.reddit.com/r/AskPhysics/comments/wbt41s/why_do_gauge_symmetries…
[^12_14]: https://en.wikipedia.org/wiki/Phase-space_formulation
[^12_15]: https://www.osti.gov/biblio/6631643
---
# i am just trying to undsrstand the use and function of the complex
representation -- is this a fundamental measure of interactions (like EM
radiation) or a way to represent a mathematical situation (like AC power)?
can you show an example where the complex notation does something?
Mostly both: for AC circuits and classical sinusoidal waves, complex
notation is largely a compact representation trick, but in quantum
mechanics the standard formalism uses complex amplitudes in a way that
directly controls interference outcomes. So it is not just “mathematicians
liking a notation,” although in some settings it really is a very efficient
encoding of two real quantities.[^13_1][^13_2][^13_3][^13_4][^13_5]
## What the complex form is doing
A complex number packages two real components into one object with a
magnitude and an angle, which is especially handy for oscillations and
rotations. For a sinusoid, writing something like $Ae^{i\theta}$ lets
addition, phase shifts, differentiation, and multiplication all work in a
cleaner algebraic way than carrying separate sines and cosines
everywhere.[^13_2][^13_6][^13_1]
That is why engineers use it for phasors in AC analysis and why physicists
use it for waves. In those cases, the complex form is often a
representation of a mathematical situation rather than a literal extra
physical dimension hiding in space.[^13_4][^13_1][^13_2]
## AC example
In AC circuit analysis, phasor notation turns a time-dependent sinusoid
into a single complex number carrying amplitude and phase, so adding two
shifted voltages becomes vector addition instead of repeated trig
identities. For example, one source works with two voltages where one is
20 volts and leads the other by 60 degrees, then rewrites one as $10 +
j17.32$, which makes combination straightforward in rectangular
form.[^13_7][^13_2]
That is a genuine “does something” example: the complex notation converts
differential-equation-and-trig work into ordinary algebra on amplitudes and
phases. So in the AC case, your “like AC power” intuition is very
good.[^13_2][^13_7][^13_4]
## Quantum example
Quantum interference is the sharper example where complex notation is doing
more than cosmetic bookkeeping. When an outcome can happen by two
indistinguishable paths, quantum mechanics says you add the complex
amplitudes first and only then square the magnitude to get a probability,
so the relative phase can enhance or cancel the result.[^13_3][^13_8]
That means two possibilities can each contribute nonzero amplitude and
still cancel if they are out of phase. This is not just a shorthand for
sinusoids in the everyday engineering sense; in the standard theory, the
complex phase is exactly what governs interference.[^13_9][^13_3]
## About the paper
Your reading of the paper as containing obvious nonsense does not seem
unreasonable. The document explicitly says meaning arises “through
engagement rather than definition alone,” presents itself as an “initiation
into a closed formal language,” and mixes technical vocabulary with phrases
like “Telepathic Circuit,” “Fluid Mechanics of God,” “Density of God,” and
“Mass is Memory,” which does not resemble standard public mathematical
definition-and-proof practice.[^13_10]
So yes, it does appear to use authoritative math and physics words in ways
that are suggestive, private, and often hard to test from outside. That
does not prove there is zero sincere thought in it, but it is a strong sign
that the paper is not a reliable guide to the standard meanings of the
terms it invokes.[^13_10]
## One tiny demo
Take two equal amplitudes $1$ and $i$. Their sum has magnitude $\sqrt{2}$,
while $1$ and $-1$ sum to $0$, so the complex angle alone changes whether
contributions reinforce or cancel.[^13_6][^13_11][^13_3]
That small fact is the whole reason phase matters. Complex notation is
useful because it makes that angle algebraic and portable across waves, AC
systems, and quantum amplitudes.[^13_11][^13_1][^13_3]
Should I do the next step with a concrete worked example such as
$e^{i\omega t}$, showing exactly how differentiation or interference
becomes simpler?
<span
style="display:none">[^13_12][^13_13][^13_14][^13_15][^13_16][^13_17][^13_18][^13_19][^13_20]</span>
<div align="center">⁂</div>
[^13_1]:
https://www.electronics-tutorials.ws/accircuits/complex-numbers.html
[^13_2]:
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/08:_A…
[^13_3]:
https://www.spinquanta.com/news-detail/exploring-quantum-interference-key-c…
[^13_4]:
https://courses.physics.ucsd.edu/2011/Winter/physics4d/files/E_M_waves.pdf
[^13_5]: https://dec41.user.srcf.net/notes/III_M/quantum_field_theory.pdf
[^13_6]:
https://mathforquantum.quantumtinkerer.tudelft.nl/1_complex_numbers/
[^13_7]: https://www.electronics-tutorials.ws/accircuits/phasors.html
[^13_8]: https://www.youtube.com/watch?v=LZ9QdjaMbFw
[^13_9]: https://philsci-archive.pitt.edu/20971/1/phase 2022 v999.pdf
[^13_10]: ALQC_Canon_Formalized-1.pdf
[^13_11]:
https://www.sciencedirect.com/science/article/pii/S0375960123004292
[^13_12]: https://www.sjsu.edu/faculty/beyersdorf/Archive/Phys208F07/ch
1-complex representation of EM waves.pdf
[^13_13]:
https://ocw.mit.edu/courses/6-007-electromagnetic-energy-from-motors-to-las…
[^13_14]: https://www.youtube.com/watch?v=VdXwxbbmRwg
[^13_15]: https://www.youtube.com/watch?v=jTrt-r_z6Fs
[^13_16]:
http://resonanceswavesandfields.blogspot.com/2008/02/complex-phasor-represe…
[^13_17]: https://www.quera.com/glossary/quantum-interference
[^13_18]:
https://eepower.com/power-electronics-textbook/vol-i-electrical-power-syste…
[^13_19]:
https://www.physics.purdue.edu/~jones105/phys42200_Spring2013/notes/Phys422…
[^13_20]:
https://www.reddit.com/r/QuantumPhysics/comments/ore9ug/what_is_quantum_int…
---
# i first learned about quantum interference using photons -- light's path
is determined by constructive interference of all paths. But light has
inherent phase and cancellation already, so it is quite intuitive. Don't
other objects also have wavelength and phase -- is that what you mean, that
everything is both a particle and a wave? So for example, maybe all matter
vibrates in some manner (probably for real in however matter exists) -- and
this gives it the phase you are discussing?
Yes—very broadly, that is the idea: quantum objects other than light also
have wave-like behavior, including wavelength and phase, and that is why
electrons, neutrons, atoms, and even larger molecules can show
interference. But the safest refinement is that the phase being discussed
is usually the phase of a quantum amplitude or wavefunction, not
necessarily a literal little piece of matter physically wobbling back and
forth in ordinary space the way a violin string
does.[^14_1][^14_2][^14_3][^14_4][^14_5]
## Matter waves
De Broglie proposed that particles of matter have an associated wavelength,
with wavelength inversely related to momentum. That is why matter can
produce diffraction and interference patterns, just as light
does.[^14_6][^14_3][^14_7][^14_5][^14_1]
So when people say “everything is both a particle and a wave,” they usually
mean that quantum objects show localized detection events like particles
but evolve and interfere according to wave-like rules. That is close to
your picture.[^14_8][^14_4]
## What phase is here
For matter, the relevant phase is usually the phase of the wavefunction or
quantum amplitude. When two possible paths contribute to the same outcome,
their phases determine whether the amplitudes reinforce or
cancel.[^14_2][^14_9][^14_4]
That is why your photon intuition transfers well to electrons and other
matter. The underlying interference logic is similar even though the
object is not a photon.[^14_4][^14_5][^14_6][^14_1]
## Is matter literally vibrating
“Everything vibrates” is a useful intuition sometimes, but it does not seem
like the best literal statement of standard quantum mechanics. The phase
is not usually introduced as a mechanical shaking of matter through space,
but as part of the mathematical object whose evolution predicts
interference and other quantum effects.[^14_2][^14_4]
A good compromise picture is: a moving quantum object carries an evolving
phase pattern, and that phase pattern is what lets different paths
interfere. That gives you something wave-like without forcing the image of
tiny beads physically sloshing around like classical material
jelly.[^14_3][^14_9][^14_4][^14_2]
## Why complex numbers enter
Complex numbers are helpful because phase is most naturally represented as
an angle, and $e^{i\theta}$ keeps track of that angle cleanly. Once you do
that, combining paths becomes ordinary addition of amplitudes, and
interference falls out of the relative phases.[^14_9][^14_10][^14_11][^14_4]
So in this context, complex notation is not only an engineer’s shorthand
like AC phasors, though that is a very good analogy. It is also the
standard language for tracking the phase information that quantum
interference seems to depend on.[^14_12][^14_13][^14_4]
## One example
Electrons passing through closely spaced slits build up an interference
pattern, which is strong evidence that matter has wave-like behavior with
meaningful phase relations. In that sense, yes: the phase I mean for
matter is the same kind of “thing that can interfere” that first felt
intuitive to you from light.[^14_5][^14_1][^14_4]
The next clean step is probably this question: what exactly is a
wavefunction, if it is not just a literal material wave?
<span
style="display:none">[^14_14][^14_15][^14_16][^14_17][^14_18][^14_19]</span>
<div align="center">⁂</div>
[^14_1]:
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physi…
[^14_2]: https://en.wikipedia.org/wiki/Matter_wave
[^14_3]: https://chemed.chem.purdue.edu/genchem/history/debroglie.html
[^14_4]:
https://www.spinquanta.com/news-detail/exploring-quantum-interference-key-c…
[^14_5]:
https://wisc.pb.unizin.org/minimisgenchem/chapter/debroglie-intro-to-qm-qua…
[^14_6]: https://scienceready.com.au/pages/matter-wave-duality
[^14_7]:
https://chem.libretexts.org/Courses/Howard_University/General_Chemistry:_An…
[^14_8]:
https://www.ebsco.com/research-starters/history/de-broglie-explains-wave-pa…
[^14_9]:
https://profmattstrassler.com/2025/03/18/quantum-interference-1-a-simple-ex…
[^14_10]:
https://mathforquantum.quantumtinkerer.tudelft.nl/1_complex_numbers/
[^14_11]:
https://www.sciencedirect.com/science/article/pii/S0375960123004292
[^14_12]:
https://eng.libretexts.org/Workbench/Introduction_to_Circuit_Analysis/08:_A…
[^14_13]: https://philsci-archive.pitt.edu/20971/1/phase 2022 v999.pdf
[^14_14]: https://www.youtube.com/watch?v=YQNEziGyDxU
[^14_15]: https://www.emergentmind.com/topics/de-broglie-wavelength
[^14_16]: https://pmc.ncbi.nlm.nih.gov/articles/PMC10074114/
[^14_17]:
https://pressbooks.bccampus.ca/bcitphys8400/chapter/2-5-de-broglies-matter-…
[^14_18]:
https://www.facebook.com/groups/573055740141524/posts/1917223125724772/
[^14_19]:
https://www.reddit.com/r/AskPhysics/comments/1fc25ij/if_particles_are_waves…
---
# Do I have the below correctly?
- it sounds like the phase is of waves developing over time
- it sounds like global phase changes might be measurable in interference
patterns somewhere rarely
Almost. A better version would be:[^15_1][^15_2]
- The phase is usually the angle of a wave or wavefunction, and it often
changes with time and position as the state evolves.[^15_3][^15_1]
- Global phase changes are usually not measurable; interference patterns
depend on **relative** phase differences, not on multiplying the entire
state by one common phase factor.[^15_4][^15_5]
## First bullet
Yes, it is reasonable to think of phase as something that develops as waves
or wavefunctions evolve over time. For energy eigenstates, time evolution
typically adds a phase factor like $e^{-iEt/\hbar}$, so time evolution and
phase are tightly linked.[^15_6][^15_1]
It is also worth adding that phase can vary with position, not just time.
That is why people talk about local phase, wave number, and interference
between paths.[^15_2][^15_3]
## Second bullet
This one needs correction: ordinary quantum theory says a pure global phase
is not observable. If you multiply the whole wavefunction by the same unit
complex number everywhere, all measurable probabilities and interference
outcomes stay the same.[^15_5][^15_7][^15_4]
What **is** measurable is relative phase, meaning the phase difference
between components, paths, or locations. That relative phase is what
shifts interference fringes or changes constructive versus destructive
interference.[^15_7][^15_8][^15_4]
## Safer phrasing
A compact corrected version is:
- Phase is the angle part of a complex wave amplitude, and it often evolves
across time and space.[^15_1][^15_3]
- Only phase differences seem to affect interference; one common overall
phase does not.[^15_4][^15_5]
A nice analogy is clocks: if every clock in the universe is advanced by the
same amount, nothing relational changes, but if one clock is shifted
relative to another, you can detect that.[^15_7]
<span
style="display:none">[^15_10][^15_11][^15_12][^15_13][^15_14][^15_15][^15_9]</span>
<div align="center">⁂</div>
[^15_1]:
https://ocw.mit.edu/courses/22-02-introduction-to-applied-nuclear-physics-s…
[^15_2]: https://en.wikipedia.org/wiki/Wave_function
[^15_3]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quan…
[^15_4]:
https://waf-www-bohrium-com-hngfcxduded0fmhr.a03.azurefd.net/en/sciencepedi…
[^15_5]:
https://wow.net.tr/en/the-quantum-state-s-global-phase-is-physically-unobse…
[^15_6]:
https://vergil.chemistry.gatech.edu/static/content/time_evolution.pdf
[^15_7]:
https://www.reddit.com/r/3Blue1Brown/comments/w4igqr/having_hard_time_under…
[^15_8]: https://www.nature.com/articles/s41598-017-02540-3
[^15_9]: https://www.youtube.com/watch?v=zkVEQ7ISJWU
[^15_10]: https://www.youtube.com/watch?v=kG92ALyMA2c
[^15_11]: https://pmc.ncbi.nlm.nih.gov/articles/PMC7517448/
[^15_12]: https://arxiv.org/pdf/1407.3438.pdf
[^15_13]:
https://www.academia.edu/142967589/Local_phase_offset_as_a_classical_altern…
[^15_14]: https://peeterjoot.com/archives/math2010/liboff314.pdf
[^15_15]:
https://www.academia.edu/109334023/Why_the_global_phase_is_not_real
---
# but if a photon has its E field big vs its magnetic field, isn't it
measured differently e'g. by a field probe? we could e.g. chart it over
time on a scope.
You can measure the electric field and magnetic field separately, yes. But
for a simple traveling electromagnetic plane wave in vacuum, they are not
“taking turns” being large; they are in phase, perpendicular, and their
magnitudes are locked by a fixed ratio $E=cB$ in
vacuum.[^16_1][^16_2][^16_3][^16_4]
## What a probe sees
An electric-field probe responds to $E$, and a magnetic-field probe
responds to $B$, so they are measuring different parts of the same
electromagnetic field. If you plotted both for a traveling wave, the peaks
and zero-crossings line up in time; one is not big when the other is small
in the usual far-field plane-wave case.[^16_5][^16_6][^16_3][^16_7][^16_1]
## Where the confusion comes from
It is easy to imagine EM waves like a spring swapping kinetic and potential
energy, but a propagating plane EM wave in free space does not behave that
way in the simple “E big then B big” sense. In that case, the energy flow
is described by the Poynting vector, and because $E$ and $H$ are in phase
for a single plane wave, the energy flux does not vanish and reappear just
because one field lags the other.[^16_2][^16_3][^16_7]
## The phase we were discussing
The “phase” from the quantum/gauge discussion is usually not the phase
difference between classical $E$ and $B$. It is more like the phase angle
of a complex amplitude or wavefunction, where relative phase between
alternatives affects interference, while a single overall global phase does
not.[^16_8][^16_9][^16_10]
So if you are thinking about a photon as classical light, the oscillation
of the EM field is a good intuition for wave behavior. But the
global-phase statement was about the quantum state description, not about
whether a field probe can tell electric from magnetic field strength at a
given time.[^16_3][^16_9][^16_10][^16_1]
## Important exception
There are more complicated situations, such as near fields or standing
waves, where the relation between electric and magnetic fields is not the
simple far-field plane-wave picture. So your instinct that “different
probes can see different behavior” is reasonable, but for the standard
propagating light wave in vacuum, the clean textbook statement is that $E$
and $B$ are in phase and tied together.[^16_11][^16_2][^16_3]
A compact correction is:
- Yes, $E$ and $B$ can be measured separately.[^16_6][^16_1]
- No, in a simple traveling light wave they are not usually “one large
while the other is small.”[^16_2][^16_3]
- And the global phase issue belongs to the quantum amplitude, not to an
$E$-versus-$B$ phase offset.[^16_9][^16_10]
Would you like me to contrast three different “phases” that are getting
mixed together here: classical wave phase, relative quantum phase, and
global quantum phase?
<span
style="display:none">[^16_12][^16_13][^16_14][^16_15][^16_16][^16_17][^16_18]</span>
<div align="center">⁂</div>
[^16_1]:
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physi…
[^16_2]: https://en.wikipedia.org/wiki/Poynting_vector
[^16_3]:
https://web.mit.edu/8.02t/www/802TEAL3D/visualizations/coursenotes/modules/…
[^16_4]: https://www.youtube.com/watch?v=h4S4eHdwUL0
[^16_5]: https://web2.ph.utexas.edu/~vadim/Classes/2024s-g/planewaves.pdf
[^16_6]:
https://innovationspace.ansys.com/courses/wp-content/uploads/2020/05/Electr…
[^16_7]:
https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1035\&context=ph…
[^16_8]: https://quantummechanics.ucsd.edu/ph130a/130_notes/node30.html
[^16_9]:
https://wow.net.tr/en/the-quantum-state-s-global-phase-is-physically-unobse…
[^16_10]:
https://waf-www-bohrium-com-hngfcxduded0fmhr.a03.azurefd.net/en/sciencepedi…
[^16_11]: https://ui.adsabs.harvard.edu/abs/2023EJPh...44e5203M/abstract
[^16_12]:
https://www.sciencedirect.com/science/article/abs/pii/S0030402621014431
[^16_13]:
https://www.reddit.com/r/askscience/comments/8avpe0/when_an_em_wave_travels…
[^16_14]:
https://www.reddit.com/r/askscience/comments/274md5/are_the_electric_and_ma…
[^16_15]: https://farside.ph.utexas.edu/teaching/315/Waves/node46.html
[^16_16]: https://www.youtube.com/watch?v=G6QryRlKbR4
[^16_17]: https://www.youtube.com/watch?v=uuA0WMGgbkQ
[^16_18]:
https://tsymbal.unl.edu/sites/unl.edu.cas.physics.tsymbal/files/media/file/…
---
# you are saying that the EM fields are different from the quantum wave
that is the photon, and photons then are capable of interfering in a 3rd
domain ...?
noting that electrons are detectable via charge as well, can their
wavefunction be measured directly or only via their ability to interfere?
Not quite a third domain. A better picture is that classical
electromagnetic fields and photon states are two related descriptions of
the same underlying electromagnetic quantum theory, with the classical
field emerging as an appropriate field description and the photon being a
quantized excitation or state of that field.[^17_1]
## Photon and EM field
For a propagating photon, people can introduce a photon wavefunction in
momentum space, and there are also coordinate-space descriptions tied to
the classical electromagnetic field, so these are connected rather than
unrelated objects. The interference you know from light is therefore not
“EM in one domain, photon in another domain, plus a third interference
domain,” but different levels of description of wave-like quantum
behavior.[^17_1]
A useful correction is: the classical $E$ and $B$ fields describe
measurable field strengths, while the photon’s quantum state describes
amplitudes for quantum outcomes. Those are different kinds of objects, but
not different universes of physics.[^17_1]
## Electron wavefunction
For electrons, the wavefunction is not usually measured the same way a
probe measures charge, voltage, or a classical electric field at one
point. Standard measurements usually give things like position, momentum,
current, energy, or other observables, and the wavefunction is then
inferred from ensembles, interference, or reconstruction
methods.[^17_2][^17_3]
So “only via interference” is too narrow, but “directly like a scope trace”
is also not the standard picture. Interference is one major route because
phase information shows up there, and tomography or related protocols can
reconstruct the state more fully.[^17_4][^17_5][^17_2]
## Direct measurement?
There are published methods explicitly described as direct measurement of
the quantum wavefunction, including weak-measurement and strong-measurement
approaches. In those methods, the real and imaginary parts of the
wavefunction are recovered from carefully designed sequential measurements
rather than from a single ordinary detector reading.[^17_5][^17_6][^17_7]
So the answer is: the wavefunction does not seem directly observable in the
same plain sense as charge on an electrometer, but it can be reconstructed,
and in some research literature that reconstruction is called “direct
measurement.” For electrons specifically, closely related reconstruction
methods also recover density matrices using interferometric
measurements.[^17_6][^17_2][^17_5]
## Clean mental model
A good mental model is that charge detection tells you where or how the
electron was caught, while the wavefunction is the complex state assignment
whose magnitude and phase govern the statistics of many such catches. You
do not usually read off the whole wavefunction from one event; you build it
from structured measurements across many similarly prepared
systems.[^17_2][^17_4][^17_5]
The shortest correction to your sentence is: photons and electrons both
have quantum states with phase information, classical fields are related
but not identical objects, and interference is one of the main ways that
phase becomes experimentally accessible.[^17_5][^17_2][^17_1]
<span
style="display:none">[^17_10][^17_11][^17_12][^17_13][^17_14][^17_15][^17_8][^17_9]</span>
<div align="center">⁂</div>
[^17_1]: https://pmc.ncbi.nlm.nih.gov/articles/PMC12309449/
[^17_2]: https://www.nature.com/articles/s41598-025-86701-9
[^17_3]:
https://www.sciencedirect.com/topics/physics-and-astronomy/quantum-tomograp…
[^17_4]:
https://research.physics.illinois.edu/QI/Photonics/tomography-files/amo_tom…
[^17_5]: https://arxiv.org/abs/1112.3575
[^17_6]: https://link.aps.org/doi/10.1103/PhysRevLett.116.040502
[^17_7]: https://mwolf.pracownicy.uksw.edu.pl/MK/Lundeen et al Direct
measurement of the quantum wavefunction nature10120.pdf
[^17_8]:
https://www.reddit.com/r/AskPhysics/comments/q03l0h/how_does_em_interferenc…
[^17_9]:
https://www.facebook.com/groups/1685507044817357/posts/25398605099747552/
[^17_10]: https://link.aps.org/doi/10.1103/PhysRevA.104.042403
[^17_11]: https://arxiv.org/abs/1504.06551
[^17_12]: https://ui.adsabs.harvard.edu/abs/2014Natur.514..603J/abstract
[^17_13]:
https://authors.library.caltech.edu/records/4jtz5-8qw63/files/FiO-2012-FTh4…
[^17_14]: https://ui.adsabs.harvard.edu/abs/2016PhRvL.116d0502V/abstract
[^17_15]:
https://www.reddit.com/r/Physics/comments/1ozxqm7/direct_measurement_of_wav…
---
# can you clarify whether the measurement of the wavefunction of a photon
is a linear function if its fields?
if it is possible to reconstruct the wavefunction difectly does that mean
that when you say global phase you mean a theoretical phase rather than a
measured one, or are things different if it is measured, or...?
Mostly yes on the first question: in common single-photon formalisms, the
photon wavefunction is built from the electromagnetic field in a **linear**
way, typically from transverse combinations of $E$ and $B$ or equivalent
vector-potential data, rather than as some nonlinear function of the
fields. But that does not mean “the wavefunction is just whatever an
$E$-probe reads off on a scope,” because the wavefunction is a state
object, while $E$ and $B$ are field observables and their relation depends
on the formalism being used.[^18_1][^18_2][^18_3]
## Photon relation
One standard construction combines the electric and magnetic fields into
complex field combinations that satisfy a Schrödinger-like equation for the
photon, so the connection is close and mathematically structured. In that
sense, it is reasonable to say the photon wavefunction is linearly related
to the classical field description, especially for transverse free-field
parts, but it is not simply a third unrelated thing living in a separate
domain.[^18_2][^18_1]
## Global phase
When I say “global phase,” I mean a phase factor multiplying the entire
quantum state, such as $\psi \to e^{i\phi}\psi$. In standard quantum
mechanics, that overall phase is still regarded as unobservable, because
measurable probabilities are unchanged by that common factor.[^18_4][^18_5]
So even if you use a protocol advertised as “direct measurement of the
wavefunction,” that does not usually promote global phase into an ordinary
observable. Direct-measurement and tomography methods recover the
wavefunction in a chosen representation from carefully structured
measurements, but the physically meaningful phase is still phase relative
to some reference, basis component, path, or calibration
choice.[^18_6][^18_7][^18_5]
## What direct means
“Direct measurement” in this literature means the real and imaginary parts
can be operationally extracted from sequential measurements rather than
inferred only by a large tomographic inversion. It does not usually mean
that every mathematical feature of the state, including arbitrary overall
phase convention, becomes separately observable in one shot like voltage on
an oscilloscope.[^18_7][^18_5][^18_6]
A good way to say it is: direct measurement can recover a wavefunction up
to the usual physically irrelevant global phase, while relative phase is
what shows up in interference and other measurable
effects.[^18_5][^18_4][^18_6]
## Short version
So your two questions fit together like this: the photon wavefunction can
be represented linearly from EM-field data in some formalisms, and yes,
“global phase” is still mainly a theoretical redundancy rather than a newly
measurable quantity just because a wavefunction reconstruction method
exists. What measurements actually pin down are amplitudes and phases
relative to chosen references, not an absolute universal phase label on the
whole state.[^18_1][^18_4][^18_6][^18_7][^18_5]
The next natural distinction to make is between absolute phase, relative
phase, and phase referenced to an external oscillator or local oscillator.
<span
style="display:none">[^18_10][^18_11][^18_12][^18_13][^18_14][^18_8][^18_9]</span>
<div align="center">⁂</div>
[^18_1]: https://pmc.ncbi.nlm.nih.gov/articles/PMC12309449/
[^18_2]: https://www.nist.gov/document/photon-wavepdf
[^18_3]:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field
[^18_4]:
https://www.reddit.com/r/AskPhysics/comments/15ge2sv/why_is_the_phase_of_a_…
[^18_5]: https://en.wikipedia.org/wiki/Wave_function
[^18_6]: https://arxiv.org/abs/1112.3575
[^18_7]: https://mwolf.pracownicy.uksw.edu.pl/MK/Lundeen et al Direct
measurement of the quantum wavefunction nature10120.pdf
[^18_8]: http://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/phwav.html
[^18_9]: https://arxiv.org/pdf/2507.16597.pdf
[^18_10]: https://arxiv.org/pdf/2310.07366.pdf
[^18_11]: https://readingfeynman.org/2016/03/12/the-photon-wavefunction-2/
[^18_12]: https://philsci-archive.pitt.edu/20971/1/phase 2022 v999.pdf
[^18_13]:
https://www.iap.tu-darmstadt.de/media/iap_tqp/pdf_publikationen/publikation…
[^18_14]:
https://www.quantamagazine.org/physicists-observe-unobservable-quantum-phas…
---
# are you then saying that we can "define" the photon wave function as
having a "zero phase" at any point on an E B sinusoid and the results are
the same? don't non-classical photons also show E B sinusoids?
Not quite. You can choose an arbitrary **reference** for phase, but that
is not the same as saying “any point on the $E,B$ sinusoid is physically
identical in every sense.”[^19_1][^19_2][^19_3]
## Two phase ideas
There are two different things getting mixed together here: the carrier
phase of a classical-looking electromagnetic field, and the global phase of
a quantum state vector. For an isolated monochromatic field, choosing
where you call phase zero is often just choosing a time origin or reference
oscillator, but relative phase between two fields or two paths is
measurable and changes interference.[^19_2][^19_3][^19_4]
## Classical-like light
For coherent states of light, the expectation value of the electric field
behaves like a classical sinusoid with a well-defined amplitude and phase,
so talking about the phase of the $E$-field waveform makes sense. In that
case, shifting the whole sinusoid by a common phase is often just a
reference choice until you compare it to another field or a
clock.[^19_5][^19_6][^19_2]
## Single photons
Nonclassical photons do not always come with a definite classical $E,B$
sinusoid. In a single-photon Fock state, the expectation value of the
electric field vanishes, and similarly the field does not carry a
well-defined optical phase in the classical sense.[^19_7][^19_8][^19_1]
So a “single photon” is not usually “a tiny classical sinusoidal EM wave
with one cycle’s worth of stuff in it.” What remains meaningful are the
quantum state, the mode structure, and measurable correlations or
interference effects, rather than a single deterministic classical field
trace.[^19_9][^19_10][^19_3][^19_7]
## Your proposed sentence
A safer rewording would be: “For classical or coherent light, I can choose
a phase reference for the sinusoid, but for a single-photon number state
there is no definite classical field phase to pin down that way.” And
separately: “Multiplying the entire photon state by one overall global
phase leaves the physical predictions
unchanged.”[^19_11][^19_12][^19_1][^19_2]
## Short intuition
Coherent light is the case that most resembles an actual measurable
sinusoid on a scope. A single-photon Fock state is more like a quantum
excitation whose interference behavior is real, but whose mean field does
not itself look like a classical oscillating $E,B$
waveform.[^19_8][^19_6][^19_7][^19_1][^19_2]
The next sharp distinction to make is between a single-photon **Fock**
state and a single-photon **wavepacket**, because that is exactly where “no
classical sinusoid” and “still has a mode and can interfere” meet.
<span
style="display:none">[^19_13][^19_14][^19_15][^19_16][^19_17][^19_18][^19_19][^19_20][^19_21][^19_22][^19_23][^19_24][^19_25][^19_26][^19_27][^19_28][^19_29][^19_30][^19_31]</span>
<div align="center">⁂</div>
[^19_1]: https://www.rp-photonics.com/fock_states.html
[^19_2]:
https://www.ptb.de/cms/fileadmin/internet/institute/fpm/Quantenoptik19/lect…
[^19_3]:
https://sites.unimi.it/aqm/wp-content/uploads/Quantum-to-Classical-Transiti…
[^19_4]: https://link.aps.org/doi/10.1103/PhysRevA.72.023820
[^19_5]: https://en.wikipedia.org/wiki/Coherent_state
[^19_6]:
https://bingweb.binghamton.edu/~suzuki/QuantumMechanicsFiles/16-1_Coherent_…
[^19_7]:
https://www.lkv.uni-rostock.de/storages/uni-rostock/Alle_MNF/Physik_Qms/Leh…
[^19_8]: https://stem.elearning.unipd.it/mod/resource/view.php?id=268863
[^19_9]: https://pmc.ncbi.nlm.nih.gov/articles/PMC12309449/
[^19_10]: https://arxiv.org/pdf/0708.0831.pdf
[^19_11]: https://en.wikipedia.org/wiki/Wave_function
[^19_12]:
https://www.reddit.com/r/AskPhysics/comments/15ge2sv/why_is_the_phase_of_a_…
[^19_13]:
https://www.reddit.com/r/AskPhysics/comments/tefoet/if_the_electric_field_o…
[^19_14]:
https://www.semanticscholar.org/paper/The-electric-field-of-a-single-photon…
[^19_15]: https://arxiv.org/pdf/2109.06472.pdf
[^19_16]: https://www.youtube.com/watch?v=Af21Phsu9MU
[^19_17]: http://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/phwav.html
[^19_18]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introduction_to_t…
[^19_19]:
https://www.physicsforums.com/threads/electric-magnetic-field-of-a-photon-i…
[^19_20]: https://www.nist.gov/document/photon-wavepdf
[^19_21]:
https://ocw.mit.edu/courses/22-51-quantum-theory-of-radiation-interactions-…
[^19_22]: https://en.wikipedia.org/wiki/Fock_state
[^19_23]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics…
[^19_24]: https://engineering.purdue.edu/wcchew/ece604s20/Lecture
Notes/Lect39.pdf
[^19_25]: https://ui.adsabs.harvard.edu/abs/2004Sci...306..660Z/abstract
[^19_26]:
https://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_5.pdf
[^19_27]:
https://bohr.physics.berkeley.edu/classes/221/1112/notes/harmosc.pdf
[^19_28]:
https://fiveable.me/quantum-optics/unit-2/fock-states-coherent-states/study…
[^19_29]: https://arxiv.org/abs/quant-ph/0508094
[^19_30]: https://www.reed.edu/physics/faculty/wheeler/documents/Quantum
Mechanics/Miscellaneous Essays/Oscillator-Coherent States.pdf
[^19_31]: https://www.scribd.com/document/874580263/fock-state
---
# it sounds like you would rather i say the EM fields are measurable
results of the quantum behavior of a photon?
what are the equations that define a photon?
Saying “$E$ and $B$ are measurable results of the underlying quantum EM
field” is closer to standard language than “distinct from the photon
wave.” In quantum electrodynamics, there is one electromagnetic field;
photons are its quantized excitations, and $E$ and $B$ become
operator-valued fields whose expectation values reproduce classical
behavior in suitable states.[^20_1][^20_2][^20_3]
## What equations define a photon
There is no single short “photon equation” like Schrödinger’s equation for
a nonrelativistic particle. Instead, a photon is defined within these
structures:[^20_2][^20_1]
- **Classical level:** Maxwell’s equations for the electromagnetic field,
which describe how $E$ and $B$ evolve and propagate.[^20_4][^20_5]
- **Quantization:** The EM field is expanded in modes (Fourier modes,
polarization states), and each mode is treated as a harmonic
oscillator.[^20_6][^20_7][^20_1]
- **Operators:** For each mode $k,\lambda$ (wavevector and polarization),
one introduces creation and annihilation operators $a_{k,\lambda}^\dagger$
and $a_{k,\lambda}$ obeying
$[a_{k,\lambda},a_{k',\lambda'}^\dagger]=\delta_{kk'}\delta_{\lambda\lambda'}$.[^20_3][^20_6]
- **Photon states:** A one‑photon state in that mode is
$|1_{k,\lambda}\rangle = a_{k,\lambda}^\dagger|0\rangle$; more general
photon states are superpositions and wavepackets built from these.
[^20_1][^20_8][^20_6]
Key relations often stated for a photon are: zero rest mass, energy
$E=\hbar\omega$, momentum $\mathbf{p}=\hbar\mathbf{k}$, and helicity $\pm
1$. Those come from quantizing Maxwell’s field and applying relativistic
energy–momentum relations for massless excitations.[^20_1][^20_2]
Coordinate-space photon wavefunctions can be defined, but there are
different formalisms (momentum-space wavefunction versus coordinate-space
constructions from $E,B$), and they are more subtle than for massive
particles.[^20_9][^20_10][^20_2]
## About phase choice
Within a given description, you are free to choose an overall phase
convention for a photon state: multiplying the entire state by $e^{i\phi}$
does not change any predictions. That is the global phase statement and
remains true regardless of whether you reconstruct a wavefunction or
not.[^20_11][^20_12]
This is not the same as saying “any point on the classical sinusoid is the
same.” A classical sinusoid’s phase relative to a reference can be measured
(e.g., by mixing with a local oscillator), and that is a physically
meaningful **relative** phase. The quantum global phase is a redundancy of
the state vector description: shifting all components by the same
$e^{i\phi}$ leaves all relative phases and all measurement probabilities
unchanged.[^20_12][^20_13][^20_14][^20_11]
So the refined statement is:
- $E$ and $B$ are classical field quantities (or expectation values of
their quantum operators) obeying Maxwell’s equations.[^20_7][^20_4]
- Photons are quantized excitations of that same field, described by
quantum states built from creation/annihilation
operators.[^20_15][^20_6][^20_1]
- A photon state’s global phase is convention, while relative phases
between components or between different fields can be tied to measurable
interference and classical field phase.[^20_13][^20_11][^20_12]
<span style="display:none">[^20_16][^20_17][^20_18][^20_19]</span>
<div align="center">⁂</div>
[^20_1]:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field
[^20_2]: https://pmc.ncbi.nlm.nih.gov/articles/PMC12309449/
[^20_3]:
https://bohr.physics.berkeley.edu/classes/221/1112/notes/quantemf.pdf
[^20_4]:
https://courses.lumenlearning.com/suny-physics/chapter/24-1-maxwells-equati…
[^20_5]:
https://phys.libretexts.org/Bookshelves/University_Physics/Book:_Introducto…
[^20_6]: https://www.phys.ksu.edu/personal/wysin/notes/quantumEM.pdf
[^20_7]:
https://bingweb.binghamton.edu/~suzuki/QM_Graduate/Quantized_electromagneti…
[^20_8]:
https://www.reddit.com/r/askscience/comments/9lxjt0/can_someone_explain_qua…
[^20_9]: http://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/phwav.html
[^20_10]:
https://spie.org/news/rethinking-the-photon-new-study-reframes-quantum-ligh…
[^20_11]: https://en.wikipedia.org/wiki/Wave_function
[^20_12]:
https://www.reddit.com/r/AskPhysics/comments/15ge2sv/why_is_the_phase_of_a_…
[^20_13]: https://en.wikipedia.org/wiki/Coherent_state
[^20_14]:
https://www.ptb.de/cms/fileadmin/internet/institute/fpm/Quantenoptik19/lect…
[^20_15]:
https://www.reddit.com/r/askscience/comments/2bmkrj/since_photons_are_consi…
[^20_16]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introduction_to_t…
[^20_17]: https://quantummechanics.ucsd.edu/ph130a/130_notes/node418.html
[^20_18]: https://readingfeynman.org/2016/03/12/the-photon-wavefunction-2/
[^20_19]: https://byjus.com/physics/maxwells-equations/
---
# the quantum and classical frequencies of a photon match? what relations
result in that?
what values fully describe the states of a photon?
Yes: the “frequency” that appears in the classical sinusoidal $E,B$ fields
and the “frequency” that appears in the photon energy relation $E = h f$
are the same physical quantity. The key relations are:[^21_1][^21_2][^21_3]
- Classical EM: $c = \lambda f$, so wavelength $\lambda$, frequency $f$,
and speed $c$ are linked.[^21_2][^21_3]
- Quantum: $E = h f = \hbar\omega$, so photon energy is proportional to
that same $f$ (or angular frequency $\omega = 2\pi f$).[^21_4][^21_1][^21_2]
Quantizing each classical mode of the electromagnetic field as a harmonic
oscillator gives evenly spaced energy levels separated by $\hbar\omega$.
Those level spacings then identify $\omega$ (and thus $f$) as both the
classical wave frequency and the quantum “per-photon” energy
scale.[^21_5][^21_6][^21_7]
## What fully describes a photon state
There is no single minimal list that covers every situation, but for a free
photon in empty space a convenient choice of quantum numbers is:
- **Momentum or wavevector $\mathbf{k}$:** direction and magnitude; related
to wavelength by $|\mathbf{k}| = 2\pi/\lambda$. [^21_8][^21_7]
- **Energy/frequency:** determined by $\omega = c|\mathbf{k}|$ and $E =
\hbar\omega$, so specifying $\mathbf{k}$ also sets the energy for a free
photon. [^21_1][^21_8]
- **Polarization/helicity:** essentially the state of its transverse
degrees of freedom, often labeled by helicity $\pm 1$ or by linear
polarization basis states.[^21_9][^21_8]
For a single **mode**, a number state $|n_{\mathbf{k},\lambda}\rangle$ is
then fully specified by:
- The mode label $(\mathbf{k}, \lambda)$, and
- The photon number $n$ in that mode.[^21_8][^21_5]
More general one-photon states are superpositions (wavepackets) over many
$(\mathbf{k},\lambda)$, so their full description is a complex amplitude
for each mode, up to the usual global phase. In that sense, “fully
describe” means specifying the entire distribution of mode amplitudes (or
equivalently a wavefunction in some representation) together with
polarization/helicity, not just a single number like
energy.[^21_7][^21_10][^21_8]
So the quantum and classical frequencies match because both come from the
same mode frequency $\omega$ of the electromagnetic field, and a photon is
the quantum of energy $\hbar\omega$ associated with one such
mode.[^21_6][^21_1][^21_7]
<span
style="display:none">[^21_11][^21_12][^21_13][^21_14][^21_15][^21_16][^21_17]</span>
<div align="center">⁂</div>
[^21_1]: https://en.wikipedia.org/wiki/Photon_energy
[^21_2]:
https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_…
[^21_3]:
https://courses.lumenlearning.com/suny-physics/chapter/24-1-maxwells-equati…
[^21_4]: https://spark.iop.org/frequency-and-energy
[^21_5]:
https://fiveable.me/modern-optics/unit-12/quantization-electromagnetic-fiel…
[^21_6]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introduction_to_t…
[^21_7]: https://lampz.tugraz.at/~hadley/ss1/emfield/quantization_em.php
[^21_8]:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field
[^21_9]: https://arxiv.org/pdf/1711.04680.pdf
[^21_10]: http://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/phwav.html
[^21_11]: https://van.physics.illinois.edu/ask/listing/1242
[^21_12]: https://www.youtube.com/watch?v=PYNSopwd1l4
[^21_13]:
https://www.pearson.com/channels/calculators/wavelength-frequency-energy-co…
[^21_14]: https://www.omnicalculator.com/physics/photon-energy
[^21_15]: https://www.nature.com/articles/s41598-024-71203-x
[^21_16]:
https://research-portal.uea.ac.uk/files/196578134/Optical_helicity_of_unpol…
[^21_17]:
https://www.khanacademy.org/science/ap-physics-2/x0e2f5a2c:modern-physics/x…
---
# Say I measure an E field from a single propagating photon using an
antenna -- can I infer the states?
For a genuinely single propagating photon in a number (Fock) state, a
one-shot $E$-field measurement with an antenna does not let you infer the
full quantum state, and even the connection to a clean sinusoidal $E(t)$ is
subtle.[^22_1][^22_2][^22_3]
## What a single-photon Fock state looks like
In the usual single-mode description, a one-photon Fock state $|1\rangle$
has a **well-defined photon number** but **no well-defined classical field
amplitude**. [^22_4][^22_3] The expectation value $\langle
E(\mathbf{r},t)\rangle$ of the electric-field operator in a Fock state is
zero, even if the state contains many photons in that mode; what is nonzero
are field **fluctuations** (variances, correlation functions).
[^22_1][^22_3]
So:
- A single strong classical sinusoid is well modeled by a **coherent
state**, which has a nonzero $\langle E\rangle$ and a well-defined
classical phase.[^22_5][^22_6]
- A one-photon number state is not a tiny coherent state; it has a definite
photon count and vanishing mean field, plus characteristic quantum
fluctuations.[^22_3][^22_7][^22_1]
## What an antenna measurement gives you
An antenna or $E$-field sensor coupled to very weak light will register
**discrete detection events** (clicks, absorbed energy), not a directly
readable continuous sinusoid for a true single-photon Fock state. Each
click tells you that a photon has been absorbed and gives you some
information about mode structure (frequency, polarization, maybe
direction), but not the full complex
wavefunction.[^22_8][^22_9][^22_10][^22_1]
To reconstruct a photon state (its “wavefunction” or density matrix),
experiments use many identically prepared photons and techniques like
homodyne detection or tomography, not one antenna trace from one photon.
Those reconstructions give you mode amplitudes and phases **up to the usual
global phase freedom**, not a unique absolute
phase.[^22_9][^22_11][^22_12][^22_13][^22_14]
## Direct answer to your question
So:
- Measuring the $E$-field once from a single propagating photon does
**not** generally let you infer “the” state.[^22_1][^22_3]
- A single-photon Fock state does not have a classical $E,B$ sinusoid with
a definite phase you can just read off.[^22_7][^22_3][^22_1]
- What you can infer about the state comes from statistics of many
detection events and carefully designed measurement schemes, not from a
single antenna waveform.[^22_11][^22_13][^22_9]
If you like, next step could be: sketch how homodyne detection uses a
strong classical local oscillator plus many photons to reconstruct the
field’s quadratures (and thus its quantum state) in practice.
<span
style="display:none">[^22_15][^22_16][^22_17][^22_18][^22_19][^22_20][^22_21][^22_22][^22_23][^22_24]</span>
<div align="center">⁂</div>
[^22_1]: https://www.youtube.com/watch?v=Af21Phsu9MU
[^22_2]:
https://www.reddit.com/r/AskPhysics/comments/tefoet/if_the_electric_field_o…
[^22_3]: https://www.rp-photonics.com/fock_states.html
[^22_4]: https://en.wikipedia.org/wiki/Fock_state
[^22_5]: https://en.wikipedia.org/wiki/Coherent_state
[^22_6]:
https://www.ptb.de/cms/fileadmin/internet/institute/fpm/Quantenoptik19/lect…
[^22_7]:
https://www.lkv.uni-rostock.de/storages/uni-rostock/Alle_MNF/Physik_Qms/Leh…
[^22_8]:
https://www.mvg-world.com/en/manual/antenna-measurement-101/how-do-electrom…
[^22_9]: https://lampz.tugraz.at/~hadley/ss1/emfield/quantization_em.php
[^22_10]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introduction_to_t…
[^22_11]: https://www.nature.com/articles/s41598-025-86701-9
[^22_12]:
https://research.physics.illinois.edu/QI/Photonics/tomography-files/amo_tom…
[^22_13]: https://arxiv.org/abs/1112.3575
[^22_14]: https://en.wikipedia.org/wiki/Wave_function
[^22_15]:
https://www.reddit.com/r/AskPhysics/comments/161xu9t/what_will_you_get_if_y…
[^22_16]:
https://www.nist.gov/noac/technology/magnetic-and-electric-fields/electric-…
[^22_17]:
https://nano-optics.colorado.edu/wp-content/uploads/2020/06/Olmon_PhsRevLet…
[^22_18]:
https://www.physicsforums.com/threads/electric-magnetic-field-of-a-photon-i…
[^22_19]:
https://www.ntt-review.jp/archive/ntttechnical.php?contents=ntr200903sf5.ht…
[^22_20]: https://link.aps.org/doi/10.1103/PhysRevA.108.063708
[^22_21]: https://www.scirp.org/journal/paperinformation?paperid=107462
[^22_22]:
https://amolf.nl/wp-content/uploads/2019/06/1-Resonant-nanophotonics-Prof.-…
[^22_23]:
https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.590…
[^22_24]:
https://www.reddit.com/r/AskPhysics/comments/1d4zxz6/is_there_a_theorethica…
---
# well say i make a bunch of photons all with the same classical phase
using one emitter that emits them in a beam -- i can measure a classical
wave here and infer more thingd about dsitributions if quantum state?
how is the E field related to the quantum state? or are you saying a photon
is _change patterns_ of fields, and the absolute values are different?
If you make many photons in phase in the same mode, then measuring the
resulting classical-looking $E$-field does let you infer useful information
about the underlying quantum state—but only in the limit where you really
have a bright, coherent-like field, not a sparse trickle of isolated Fock
states.[^23_1][^23_2][^23_3]
## Coherent beam vs single photons
- A highly populated, phase-stable beam from one emitter is well modeled by
a **coherent state** $|\alpha\rangle$, which is an eigenstate of the
annihilation operator $a$. [^23_2][^23_3]
- In such a state, the expectation value of the electric-field operator
$\hat E(\mathbf{r},t)$ behaves like a classical sinusoid with amplitude and
phase determined by $\alpha$ and the mode functions.[^23_4][^23_2][^23_1]
- Measuring the classical field (e.g., via homodyne detection with a local
oscillator) lets you infer the **quadratures** of the field, which are
directly related to the real and imaginary parts of $\alpha$ and thus to
the complex amplitude of that mode.[^23_5][^23_6][^23_4]
So in that bright, phase-stable regime, yes: by measuring a classical wave
you can back out a lot about the quantum state’s distribution over field
quadratures, typically assuming it is near a Gaussian/coherent
state.[^23_6][^23_2][^23_3]
## How $\hat E$ relates to the quantum state
For a quantized single mode, the electric field operator is a linear
combination of the annihilation and creation operators: schematically
$$
\hat E(\mathbf{r},t) \propto f(\mathbf{r},t)\, \hat a + f^*(\mathbf{r},t)\,
\hat a^\dagger,
$$
where $f(\mathbf{r},t)$ encodes the mode’s spatial and temporal
structure.[^23_7][^23_4][^23_1]
- In a coherent state $|\alpha\rangle$, $\langle \hat a\rangle = \alpha$,
so $\langle \hat E\rangle$ follows a classical wave with a definite phase
and amplitude. [^23_2][^23_3][^23_1]
- In a number (Fock) state $|n\rangle$, $\langle \hat a\rangle = 0$, so
$\langle \hat E\rangle = 0$. The field is “there” only in its fluctuations
and higher moments, not in the mean. [^23_8][^23_9][^23_1]
So the electric field is not separate from the quantum state; it is an
operator built from the same mode operators that define photon states, and
what you “see” as a classical field is essentially the expectation value of
that operator in whatever state you prepared.[^23_7][^23_4][^23_1]
## Change patterns vs absolute values
“Photons are change patterns of fields” is close but needs
tightening.[^23_10][^23_11]
- The **underlying object** is the electromagnetic field, which is
quantized.[^23_1][^23_10]
- A photon is a **quantized excitation of a field mode**—an energy quantum
$\hbar\omega$ in that mode.[^23_12][^23_10]
- In states with many quanta and a stable phase (coherent states), the
field expectation values look like smooth classical waves; in pure number
states, the same operators have zero mean but nontrivial quantum
fluctuations.[^23_2][^23_9][^23_1]
So absolute classical $E,B$ values are expectation values (or higher
moments) of field operators in some quantum state, and different states
(coherent vs Fock vs squeezed, etc.) give different patterns of means and
fluctuations.[^23_13][^23_3][^23_2]
## Direct answer to your scenario
If your emitter produces a strong, phase-stable beam:
- You can treat the field as approximately coherent, measure the classical
sinusoid, and infer the complex amplitude $\alpha$ of the mode (up to
global phase conventions and calibration).[^23_4][^23_5][^23_2]
- Those measurements tell you about the **distribution of photon numbers
and quadratures** in that mode (e.g., Poissonian statistics for
$|\alpha\rangle$), not about a single photon apart from the rest.
[^23_2][^23_12]
If you truly have a dilute sequence of single photons in a number state,
the mean field vanishes and you do not get a clean classical wave to read
off; then you infer the state from detection statistics and interference,
not from a classical $E(t)$ trace.[^23_8][^23_9][^23_1]
If you want, next step could be to write down the explicit single-mode
formula $\hat E(t) \propto \hat a e^{-i\omega t} + \hat a^\dagger
e^{i\omega t}$ and show how $|\alpha\rangle$ and $|n\rangle$ give different
measurable behavior.
<span
style="display:none">[^23_14][^23_15][^23_16][^23_17][^23_18][^23_19][^23_20][^23_21]</span>
<div align="center">⁂</div>
[^23_1]:
https://bohr.physics.berkeley.edu/classes/221/1112/notes/quantemf.pdf
[^23_2]: https://en.wikipedia.org/wiki/Coherent_state
[^23_3]:
https://www.ptb.de/cms/fileadmin/internet/institute/fpm/Quantenoptik19/lect…
[^23_4]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics…
[^23_5]: https://www.physics.muni.cz/~tomtyc/homodyne.pdf
[^23_6]: https://academic.oup.com/ptep/article/2021/10/103A01/6364905
[^23_7]: https://www.phys.ksu.edu/personal/wysin/notes/quantumEM.pdf
[^23_8]: https://www.youtube.com/watch?v=Af21Phsu9MU
[^23_9]: https://www.rp-photonics.com/fock_states.html
[^23_10]:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field
[^23_11]: https://lampz.tugraz.at/~hadley/ss1/emfield/quantization_em.php
[^23_12]:
https://fiveable.me/modern-optics/unit-12/quantization-electromagnetic-fiel…
[^23_13]:
https://www.classe.cornell.edu/~dlr/teaching/p6574/lectures/lecture20.pdf
[^23_14]: https://en.wikipedia.org/wiki/Creation_and_annihilation_operators
[^23_15]:
https://bingweb.binghamton.edu/~suzuki/QM_Graduate/Quantized_electromagneti…
[^23_16]: http://hitoshi.berkeley.edu/221B-S02/photons.pdf
[^23_17]: https://web2.ph.utexas.edu/~vadim/Classes/2019f/expand.pdf
[^23_18]: https://arxiv.org/pdf/1711.03713.pdf
[^23_19]:
https://www.physics.purdue.edu/~clarkt/Courses/Physics662/ps/qftch11.pdf
[^23_20]:
https://bingweb.binghamton.edu/~suzuki/QuantumMechanicsII/14-1_Quantized_el…
[^23_21]:
https://www.reddit.com/r/askscience/comments/9lxjt0/can_someone_explain_qua…
---
# are you saying f(r,t) = exp(i omega t) here?
this must be where global phase is, in the definition of the spatial and
temporal structure, and it does indeed align with a classical phase offset?
For a single plane-wave mode, $f(\mathbf{r},t)$ is usually something like a
spatial mode function times a time factor $e^{-i\omega t}$, e.g.
$f(\mathbf{r},t) \propto e^{i\mathbf{k}\cdot\mathbf{r}}e^{-i\omega t}$. So
yes, the $e^{-i\omega t}$ (and any overall constant phase in $f$) is
exactly where the **classical carrier phase** lives in that simple
model.[^24_1][^24_2][^24_3][^24_4]
## Where global phase shows up
1. **In the mode function $f(\mathbf{r},t)$:**
- You can multiply $f$ by a constant phase $e^{i\phi_0}$ and compensate
by redefining the annihilation operator $\hat a \to e^{-i\phi_0}\hat a$,
leaving all physics unchanged.[^24_2][^24_5]
- That overall constant phase of the mode is just like a classical
phase offset of the sinusoid; it only matters when compared to some
reference (another mode, a local oscillator, etc.).[^24_6][^24_7]
2. **In the quantum state $|\psi\rangle$:**
- Multiplying the entire state by an overall factor $e^{i\Phi}$ leaves
all probabilities and expectation values of observables
unchanged.[^24_8][^24_9]
- That is the usual “global phase of the state is unobservable”
statement.[^24_9][^24_8]
You can choose conventions so that the mode function has a particular phase
(e.g. $f\propto e^{i\mathbf{k}\cdot\mathbf{r}}e^{-i\omega t}$ with no extra
constant), and then the phase of a coherent state’s amplitude $\alpha$
lines up with the classical phase of the field you measure. In that gauge,
the **classical phase offset** you see in the sinusoidal expectation value
$\langle \hat E(\mathbf{r},t)\rangle$ is directly the argument of $\alpha$
plus the phase of $f$, i.e. it behaves just like a classical phase
shift.[^24_3][^24_10][^24_2][^24_6]
So the safest summary is:
- $f(\mathbf{r},t)$ carries the **mode’s classical phase structure**
(including any carrier phase offset).[^24_1][^24_2]
- The **global phase of the quantum state vector** is an extra redundancy
on top of that and does not change observables.[^24_8][^24_9]
- When you fix a convention for $f$, the phase of a coherent state’s
amplitude $\alpha$ corresponds to the classical phase of the field,
matching your intuition about a classical phase
offset.[^24_10][^24_3][^24_6]
<div align="center">⁂</div>
[^24_1]: https://www.phys.ksu.edu/personal/wysin/notes/quantumEM.pdf
[^24_2]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics…
[^24_3]:
https://bohr.physics.berkeley.edu/classes/221/1112/notes/quantemf.pdf
[^24_4]:
https://bingweb.binghamton.edu/~suzuki/QuantumMechanicsII/14-1_Quantized_el…
[^24_5]: https://web2.ph.utexas.edu/~vadim/Classes/2019f/expand.pdf
[^24_6]: https://en.wikipedia.org/wiki/Coherent_state
[^24_7]: https://www.physics.muni.cz/~tomtyc/homodyne.pdf
[^24_8]: https://en.wikipedia.org/wiki/Wave_function
[^24_9]:
https://www.reddit.com/r/AskPhysics/comments/15ge2sv/why_is_the_phase_of_a_…
[^24_10]:
https://www.ptb.de/cms/fileadmin/internet/institute/fpm/Quantenoptik19/lect…
---
# so people would almost always use a simple global phase like 0 degrees?
Yes. In almost all practical calculations, people fix a convention that
effectively sets the global phase to something simple, usually “zero” in
the sense of:
- Choosing mode functions $f(\mathbf{r},t)$ without an extra constant phase
factor.[^25_1][^25_2]
- Treating overall $e^{i\Phi}$ factors on the state as irrelevant and
dropping them.[^25_3][^25_4]
What actually matters are **relative** phases: between different components
of a state, between different paths, or between the field and a reference
(local oscillator, another beam, etc.). Those are the phase differences
that show up in interference and in measured quadratures, so that is where
people keep careful track, and global state phase is usually set to a
convenient zero by convention.[^25_4][^25_5][^25_6][^25_7][^25_3]
<div align="center">⁂</div>
[^25_1]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics…
[^25_2]: https://www.phys.ksu.edu/personal/wysin/notes/quantumEM.pdf
[^25_3]: https://en.wikipedia.org/wiki/Wave_function
[^25_4]:
https://www.reddit.com/r/AskPhysics/comments/15ge2sv/why_is_the_phase_of_a_…
[^25_5]:
https://waf-www-bohrium-com-hngfcxduded0fmhr.a03.azurefd.net/en/sciencepedi…
[^25_6]: https://en.wikipedia.org/wiki/Coherent_state
[^25_7]: https://www.physics.muni.cz/~tomtyc/homodyne.pdf
---
# it sounds like there are situations where a sinplifying phase in one part
is complicating in another and vice versa?
Yes. Choosing a phase convention can simplify one part of a calculation
while making another part look more complicated.
## Where this happens
- **Single mode vs many modes:** Setting the phase of one mode’s
$f(\mathbf{r},t)$ to be real and simple can force another coupled mode to
carry an awkward extra phase factor.[^26_1][^26_2]
- **Interaction terms:** In interacting theories, a phase choice that makes
one field’s kinetic term look clean can push nontrivial phases into
coupling constants or mass terms.[^26_2][^26_3]
- **Interference setups:** In interferometry or homodyne detection,
defining the local oscillator’s phase as zero makes the signal’s phase
appear directly, but if you re-phase the signal instead, the LO’s phase
looks messy.[^26_4][^26_5]
## Why it is okay
All these different choices are related by unitary (phase) transformations
and give the same physical predictions; they just shuffle where the phase
factors live in the algebra. The usual strategy is to pick a convention
that makes the part you care about (e.g., the interaction, the measured
mode, the LO) as simple as possible, accepting extra phase clutter
elsewhere.[^26_6][^26_7][^26_1][^26_4]
<div align="center">⁂</div>
[^26_1]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics…
[^26_2]: https://web2.ph.utexas.edu/~vadim/Classes/2019f/expand.pdf
[^26_3]:
https://www.physics.purdue.edu/~clarkt/Courses/Physics662/ps/qftch11.pdf
[^26_4]: https://www.physics.muni.cz/~tomtyc/homodyne.pdf
[^26_5]: https://academic.oup.com/ptep/article/2021/10/103A01/6364905
[^26_6]: https://en.wikipedia.org/wiki/Wave_function
[^26_7]:
https://www.reddit.com/r/AskPhysics/comments/15ge2sv/why_is_the_phase_of_a_…
---
# so quantum physics defines everything as sinusoidal creation and
destruction waves which then produce classical waves via their interference?
Not quite. A better summary is: quantum field theory describes fields with
**mode operators** that evolve sinusoidally in time, and classical waves
emerge as special quantum states (like coherent states) where the
**average** field behaves like a classical wave.[^27_1][^27_2][^27_3]
## What is sinusoidal
For a free field, each mode behaves like a harmonic oscillator, so
operators carry factors like $e^{-i\omega t}$ and $e^{i\omega t}$. That
sinusoidal time dependence is built into the mode structure and is why
plane waves and normal modes look sinusoidal.[^27_4][^27_5][^27_6][^27_1]
## Where classical waves come from
- If the quantum state is a coherent state with many quanta in a mode, the
expectation value $\langle \hat E(\mathbf{r},t)\rangle$ follows a classical
sinusoidal wave with a well-defined amplitude and
phase.[^27_2][^27_3][^27_7]
- If the state is a number (Fock) state like a single photon, the mean
field vanishes and you do **not** get a classical sinusoid directly; what
you see are discrete detection events and quantum
correlations.[^27_8][^27_9][^27_2]
So classical waves are not produced by “creation and destruction waves
interfering” so much as they are the average behavior of certain quantum
states of the field.[^27_3][^27_2]
## Interference
Quantum interference enters because probabilities come from squared
magnitudes of **sums of complex amplitudes**, so relative phases between
contributions matter. For many-photon coherent states, this quantum
interference reproduces the classical interference of electromagnetic
waves; for few-photon or single-photon states, it shows up as patterns in
detection statistics instead of literal continuous field
oscillations.[^27_6][^27_10][^27_11][^27_12]
A compact reframing is: quantum fields have harmonic-mode structure;
creation and annihilation operators add and remove quanta of those modes;
and classical waves appear when those modes are occupied in special states
whose average field matches Maxwell’s sinusoidal
solutions.[^27_1][^27_2][^27_3]
<div align="center">⁂</div>
[^27_1]:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field
[^27_2]:
https://bohr.physics.berkeley.edu/classes/221/1112/notes/quantemf.pdf
[^27_3]: https://en.wikipedia.org/wiki/Coherent_state
[^27_4]: https://www.phys.ksu.edu/personal/wysin/notes/quantumEM.pdf
[^27_5]:
https://courses.lumenlearning.com/suny-physics/chapter/24-1-maxwells-equati…
[^27_6]: https://lampz.tugraz.at/~hadley/ss1/emfield/quantization_em.php
[^27_7]:
https://www.ptb.de/cms/fileadmin/internet/institute/fpm/Quantenoptik19/lect…
[^27_8]: https://www.youtube.com/watch?v=Af21Phsu9MU
[^27_9]: https://www.rp-photonics.com/fock_states.html
[^27_10]:
https://www.spinquanta.com/news-detail/exploring-quantum-interference-key-c…
[^27_11]:
https://profmattstrassler.com/2025/03/18/quantum-interference-1-a-simple-ex…
[^27_12]:
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introduction_to_t…
---
# which is simplest particle to learn first?
For getting comfortable with quantum fields, the **spin‑0 real scalar field
(“scalar particle”)** is usually the simplest starting point.
## Why the real scalar field
- It has no spin or polarization indices, so the field is just a single
real function $\phi(x)$ instead of a vector or spinor.[^28_1][^28_2]
- The free-field equation of motion is just the Klein–Gordon equation,
which is a straightforward relativistic wave equation.[^28_2][^28_1]
- Quantization introduces creation/annihilation operators and Fock states
without extra complications from gauge symmetry or spin.[^28_3][^28_1]
## Good learning order
1. **Real scalar field (spin 0):** learn mode expansion,
creation/annihilation, propagators.[^28_1][^28_2]
2. **Complex scalar field:** add charge and a U(1) phase
symmetry.[^28_4][^28_5]
3. **Dirac field (spin 1/2):** learn spin and antiparticles.[^28_6][^28_7]
4. **Gauge fields (photon, Yang–Mills):** bring in gauge symmetry and
self-interaction.[^28_8][^28_9]
Starting with photons skips several conceptual steps (scalar, spin, charge,
then gauge), so the scalar field is the cleanest first sandbox.
<div align="center">⁂</div>
[^28_1]: https://en.wikipedia.org/wiki/Scalar_field_theory
[^28_2]: https://www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S2.html
[^28_3]: https://dec41.user.srcf.net/notes/III_M/quantum_field_theory.pdf
[^28_4]: https://www.southampton.ac.uk/~doug/ft1/ft15.pdf
[^28_5]: https://kimura.pages.math.cnrs.fr/file/QFT_lec.pdf
[^28_6]: https://en.wikipedia.org/wiki/Dirac_equation
[^28_7]: https://www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S4.html
[^28_8]:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field
[^28_9]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
---
# do scalar particles exist? are they a little like an uncharged electron?
Yes, scalar particles do exist, and the cleanest confirmed example is the
**Higgs boson**. The Higgs is a fundamental spin‑0 particle, so its field
is a scalar field in the technical sense.[^29_1][^29_2][^29_3]
## Scalars vs “uncharged electron”
An electron is not a scalar; it has spin $1/2$ and is described by a
**spinor** field (the Dirac field), not a scalar field. So a scalar
particle is not really “an uncharged electron,” it is more like a particle
whose intrinsic degrees of freedom do not include spin orientation at
all.[^29_2][^29_4][^29_5][^29_6][^29_7]
Key contrasts:
- **Scalar particle (e.g. Higgs):** spin 0, field value is just a number at
each point (or a small multiplet of numbers), no directional spin degree of
freedom.[^29_3][^29_2]
- **Electron:** spin $1/2$, described by a spinor; even if you imagine it
uncharged, it still has spin structure rather than a single scalar
component.[^29_5][^29_6]
There are also many **composite** scalar particles, like some nuclei and
mesons with total spin 0, but the Higgs is the only confirmed *elementary*
scalar in the Standard Model so far.[^29_8][^29_1]
<span
style="display:none">[^29_10][^29_11][^29_12][^29_13][^29_14][^29_15][^29_9]</span>
<div align="center">⁂</div>
[^29_1]: https://atlas.cern/updates/briefing/scalar-boson
[^29_2]: https://en.wikipedia.org/wiki/Scalar_boson
[^29_3]: https://en.wikipedia.org/wiki/Higgs_boson
[^29_4]:
https://profmattstrassler.com/articles-and-posts/particle-physics-basics/th…
[^29_5]: https://www.zayets2physics.com/spin2_QuantumNature_16.html
[^29_6]: https://en.wikipedia.org/wiki/Spinor
[^29_7]: https://en.wikipedia.org/wiki/Spin_(physics)
[^29_8]:
https://www.reddit.com/r/askscience/comments/iquhwg/is_the_higgs_boson_the_…
[^29_9]:
https://www.reddit.com/r/AskPhysics/comments/1g617fl/what_is_significant_in…
[^29_10]:
https://www.symmetrymagazine.org/article/what-the-higgs-boson-tells-us-abou…
[^29_11]:
http://www.physicsmatt.com/blog/2015/6/17/and-explanation-of-the-higgs-boson
[^29_12]: https://ncatlab.org/nlab/show/The+Dirac+Electron
[^29_13]:
https://indico.cern.ch/event/763013/contributions/3358697/attachments/18131…
[^29_14]:
https://www.quantamagazine.org/how-the-higgs-field-actually-gives-mass-to-e…
[^29_15]: https://www.youtube.com/watch?v=2TYFNOArnYo
---
# so i could theoretically make a scalar particle or something that behaved
like it?
what governs its behavior?
Theoretically, yes: you can define a scalar field and its quanta, and you
could imagine engineering something whose excitations behave
*approximately* like scalar particles. What governs their behavior is very
tightly specified once you choose a Lagrangian for the scalar field.
## What governs a scalar particle
For a simple real scalar field $\phi(x)$, the standard free-theory
Lagrangian density is
$$
\mathcal{L} = \tfrac12 \partial_\mu \phi\,\partial^\mu \phi - \tfrac12 m^2
\phi^2,
$$
which yields the **Klein–Gordon equation**
$$
(\Box + m^2)\phi(x) = 0,
$$
a relativistic wave equation for a spin‑0 field of mass
$m$.[^30_1][^30_2][^30_3]
Once you choose $\mathcal{L}$, all of the following are fixed:
- How the field propagates (via the equation of motion).[^30_2][^30_1]
- How its quanta (the scalar particles) carry energy–momentum $E^2 = p^2 +
m^2$.[^30_1][^30_2]
- How they interact, if you add interaction terms like $-\lambda \phi^4$ or
couplings to other fields.[^30_4][^30_5]
The Higgs field is a more complicated scalar with a potential $V(\phi)$
that leads to spontaneous symmetry breaking and specific couplings to gauge
bosons and fermions. Its behavior is governed by the Standard Model
Higgs-sector Lagrangian, not by arbitrary
choice.[^30_6][^30_7][^30_8][^30_9][^30_10]
## “Making” a scalar-like excitation
In practice, building a truly elementary scalar particle is not something
one “designs”; the known fundamental scalar (Higgs) is produced in
high-energy collisions, and beyond-Standard-Model scalars are
speculative.[^30_11][^30_12]
However, **effective scalar excitations** are common:
- Many composite systems (e.g., certain mesons, nuclei, phonons) have
spin‑0 modes that, at low energies, are well described by a scalar field
theory.[^30_13][^30_14]
- In condensed matter or cosmology, scalar fields are routinely used as
effective descriptions of collective modes or order parameters, governed by
Lagrangians similar to the one above.[^30_5][^30_13]
So “something that behaves like a scalar particle” usually means a system
whose low-energy degrees of freedom are captured by a scalar field with
some potential $V(\phi)$; its behavior is then governed by that field’s
Lagrangian and resulting equations of motion.[^30_15][^30_4][^30_5]
<span
style="display:none">[^30_16][^30_17][^30_18][^30_19][^30_20][^30_21]</span>
<div align="center">⁂</div>
[^30_1]: https://www.southampton.ac.uk/~doug/ft1/ft12.pdf
[^30_2]:
https://piazza.com/class_profile/get_resource/kzqnrwg17lp27d/l294p8r7oy45fq
[^30_3]: https://en.wikipedia.org/wiki/Klein–Gordon_equation
[^30_4]:
https://piazza.com/class_profile/get_resource/jy4evrjc5f94jd/jzlkoap7wig34n
[^30_5]: http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields
[^30_6]: https://en.wikipedia.org/wiki/Higgs_mechanism
[^30_7]:
https://indico.cern.ch/event/443176/attachments/1291625/1940696/Haber_Higgs…
[^30_8]:
https://indico.cern.ch/event/763013/contributions/3358697/attachments/18131…
[^30_9]: https://en.wikipedia.org/wiki/Higgs_boson
[^30_10]:
https://www.quantamagazine.org/how-the-higgs-field-actually-gives-mass-to-e…
[^30_11]: https://atlas.cern/updates/briefing/scalar-boson
[^30_12]:
https://www.reddit.com/r/askscience/comments/iquhwg/is_the_higgs_boson_the_…
[^30_13]: https://www.roe.ac.uk/japwww/teaching/cos5_1112/cos5_1112b.pdf
[^30_14]: https://en.wikipedia.org/wiki/Scalar_boson
[^30_15]:
https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/the_free_klein_g…
[^30_16]: https://en.wikipedia.org/wiki/Lagrangian_(field_theory)
[^30_17]: https://math.uchicago.edu/~may/REU2012/REUPapers/Yu.pdf
[^30_18]: https://www.youtube.com/watch?v=xy3sbXnyUfA
[^30_19]: https://www.youtube.com/watch?v=T_08_GC2hlw
[^30_20]:
https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/Introduction_to_…
[^30_21]:
https://www.imperial.ac.uk/media/imperial-college/research-centres-and-grou…
---
# what is a Lagrangian?
A **Lagrangian** is a function that packages the rules of motion of a
system into one object, and in many basic mechanics problems it is $L = T -
V$, meaning kinetic energy minus potential energy. The system’s actual
motion is then the one that makes the action $S=\int L\,dt$ stationary,
which leads to the equations of motion.[^31_1][^31_5][^31_7]
## High-level picture
A good intuition is that Newton’s method starts with forces, while the
Lagrangian method starts with energies. Instead of asking “what force is
pushing this?,” you ask “what single energy-like formula generates the
right motion?”[^31_1][^31_3][^31_7]
## Why physicists use it
The Lagrangian approach handles constraints and complicated coordinates
cleanly, and it generalizes very naturally from particles to fields. In
field theory, one usually works with a Lagrangian density $\mathcal{L}$,
whose variation gives the Euler–Lagrange field equations.[^31_1][^31_6]
## One example
For a simple particle moving in a potential, the usual choice is $L=T-V$.
For a simple scalar field, a standard free-field Lagrangian density is
$\mathcal{L}=\tfrac12 \partial_\mu\phi\,\partial^\mu\phi - \tfrac12
m^2\phi^2$, and from that you get the Klein–Gordon
equation.[^31_1][^31_6][^31_7]
A very compressed slogan is: the Lagrangian is the recipe, and the
equations of motion are what fall out when nature follows the
stationary-action rule.[^31_1]
<span style="display:none">[^31_10][^31_2][^31_4][^31_8][^31_9]</span>
<div align="center">⁂</div>
[^31_1]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^31_2]:
https://www.reddit.com/r/Physics/comments/1ldztv5/what_is_a_lagrangian_phys…
[^31_3]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.03:_Lagrangian
[^31_4]: https://www.sciencedirect.com/topics/mathematics/lagrangian
[^31_5]:
https://fiveable.me/key-terms/principles-physics-iii-thermal-physics-waves/…
[^31_6]: https://en.wikipedia.org/wiki/Lagrangian_(field_theory)
[^31_7]: https://www.britannica.com/science/Lagrangian-function
[^31_8]: https://www.ipcms.fr/uploads/2021/06/chap6.pdf
[^31_9]: https://www.youtube.com/watch?v=hQ4UNu1P2kw
[^31_10]:
https://www.khanacademy.org/math/multivariable-calculus/applications-of-mul…
---
# what does it mean for the action integral to be stationary -- it's zero?
constant? repeating?
what are dsubu, dsuperu, phi?
“Stationary” does **not** mean the action is zero, constant in time, or
repeating. It means that if you make a tiny allowed change to the path or
field configuration, the action does not change to first order:
mathematically, $\delta S = 0$.[^32_1][^32_2][^32_3][^32_4]
## Stationary action
A useful analogy is an ordinary function $f(x)$. At a stationary point, a
tiny shift $x \to x+\epsilon$ gives no linear change, so the slope is zero;
that point might be a minimum, a maximum, or a saddle point. The action
principle is the same idea, except the “input” is not a single number but
an entire path or field history.[^32_2][^32_3][^32_4][^32_1]
So “stationary” means “extremized” or more generally “first-order
unchanged,” not “numerically constant.”[^32_4][^32_2]
## What $\phi$ is
$\phi$ is usually the scalar field itself. That means at each point in
space and time, $\phi(x)$ gives one number, unlike a vector field which
gives several components. In the scalar-particle example, $\phi$ is the
mathematical object whose excitations are the scalar
particles.[^32_5][^32_6][^32_7]
## What $\partial_\mu$ means
$\partial_\mu\phi$ means “take a partial derivative of the field $\phi$
with respect to the coordinate $x^\mu$.” In spacetime notation, the index
$\mu$ usually runs over time and the three space coordinates, so
$\partial_\mu\phi$ packages time and space derivatives together into one
four-component object.[^32_8][^32_9]
Very roughly, it stands for something like:
- $\partial_0 \phi$: time derivative,
- $\partial_1 \phi,\partial_2 \phi,\partial_3 \phi$: spatial
derivatives.[^32_9][^32_8]
## What $\partial^\mu$ means
$\partial^\mu$ is the same derivative object but with the index raised. In
relativity, raising or lowering an index uses the spacetime metric, so
$\partial^\mu$ and $\partial_\mu$ are closely related but not identical in
sign conventions.[^32_10][^32_9]
That is why expressions like $\partial_\mu \phi\,\partial^\mu \phi$ appear:
they are a compact relativistic way to combine time and space derivative
terms into one scalar quantity.[^32_11][^32_9]
## Why one index is down and one up
This is Einstein summation notation. When the same index appears once up
and once down, you automatically sum over it, so $\partial_\mu
\phi\,\partial^\mu \phi$ means “sum over all spacetime
components.”[^32_12][^32_13]
In plainer language, it is a compact abbreviation for “square the time
derivative, subtract or add the squared spatial derivatives according to
the metric convention, and combine them.”[^32_11][^32_9]
## One translation
A good plain-English translation of
$$
\mathcal{L}=\tfrac12 \partial_\mu\phi\,\partial^\mu\phi-\tfrac12 m^2\phi^2
$$
is: “the Lagrangian density equals a kinetic part built from how the field
changes in time and space, minus a mass part proportional to the field
itself.”[^32_9][^32_5]
If you want, the next clean step is for me to expand
$\partial_\mu\phi\,\partial^\mu\phi$ into ordinary derivatives with
$t,x,y,z$ and no index notation.
<span style="display:none">[^32_14][^32_15][^32_16][^32_17][^32_18]</span>
<div align="center">⁂</div>
[^32_1]: https://en.wikipedia.org/wiki/Action_principles
[^32_2]: https://aero.refpages.org/dynsys/lagrange/
[^32_3]:
https://saphysics.com/classical-mechanics/lagrangian-mechanics/the-principl…
[^32_4]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^32_5]: https://www.southampton.ac.uk/~doug/ft1/ft12.pdf
[^32_6]: https://en.wikipedia.org/wiki/Klein–Gordon_equation
[^32_7]:
https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/the_free_klein_g…
[^32_8]:
https://www.reddit.com/r/AskPhysics/comments/b2yi8f/quantum_field_theory/
[^32_9]:
https://peeterjoot.com/2018/09/23/phy2403h-quantum-field-theory-lecture-4-s…
[^32_10]: https://www.youtube.com/watch?v=EX0vhVI9PH0
[^32_11]:
https://www.physicsforums.com/threads/help-with-vector-notation-partial_-mu…
[^32_12]: https://www.statisticshowto.com/einstein-summation-notation/
[^32_13]: https://mathworld.wolfram.com/EinsteinSummation.html
[^32_14]:
https://www.reddit.com/r/AskPhysics/comments/16modji/can_anyone_explain_the…
[^32_15]: https://www.youtube.com/watch?v=fi5uQdoE49c
[^32_16]:
https://pubs.aip.org/aapt/ajp/article/92/11/885/3317287/Why-the-action
[^32_17]:
https://www.cantorsparadise.com/the-principle-of-stationary-action-c69237bd…
[^32_18]: https://www.reddit.com/r/AskPhysics/comments/1pzdngp/field_theory/
---
# why is the curvayure of spacetime relevent at quantum scales?
is duphi the same as dphi/dxu ?
why do you say the motion is the one that makes the integral of L
stationary rather than the value of L(t) zero?
Not by default. Curvature of spacetime is not relevant just because
something is quantum-sized; it becomes relevant when gravity or the
background geometry matters, such as near black holes, in the early
universe, or whenever fields propagate on a non-flat spacetime background.
Quantum field theory in curved spacetime is basically the framework for
“quantum fields on a curved but still classical spacetime,” and it is used
because curvature can change particle concepts and even lead to effects
like particle creation.[^33_1][^33_2][^33_3]
## Curvature and quantum scale
So the important distinction is: “quantum” and “curved spacetime” are
different ideas. Something can be quantum and live happily in flat
spacetime, and something can involve curved spacetime without requiring
full quantum gravity. Curvature matters when the geometry affects the
field’s propagation, symmetries, or notion of vacuum, not merely because
the object is tiny.[^33_2][^33_3][^33_1]
## What $\partial_\mu \phi$ means
Yes, $\partial_\mu \phi$ is essentially “the partial derivative of $\phi$
with respect to $x^\mu$,” so in ordinary notation it is $\frac{\partial
\phi}{\partial x^\mu}$. The index $\mu$ is just a label telling you which
spacetime coordinate you are differentiating with respect to, typically
time or one of the three space coordinates.[^33_4][^33_5][^33_6]
Similarly, $\partial^\mu \phi$ is the same derivative with the index
raised, which means the spacetime metric has been used to convert the
lower-index version into an upper-index version. That is why $\partial_\mu
\phi\,\partial^\mu \phi$ is a compact relativistic sum over time and space
derivative terms.[^33_5][^33_6][^33_7]
## Why stationarity uses the action
We say the physical motion makes the **action** stationary because the
principle is about varying the whole path or field history between
endpoints, not about forcing the instantaneous value $L(t)$ to be zero.
The action is $S=\int L\,dt$, and the condition is $\delta S=0$, meaning a
tiny allowed change of the entire path does not change $S$ to first
order.[^33_8][^33_9][^33_10]
If you instead required $L(t)=0$, that would be a completely different
condition and generally not the correct equations of motion. In ordinary
mechanics, $L=T-V$, and there is no reason the correct motion should make
kinetic energy equal potential energy at every
instant.[^33_11][^33_12][^33_13][^33_14]
## Intuition
A helpful analogy is ordinary calculus: you do not find the right point by
demanding $f(x)=0$, but by demanding the first-order change vanish,
$f'(x)=0$. Stationary action is the same idea lifted from “a point on a
graph” to “an entire path through time” or “an entire field configuration
through spacetime.”[^33_9][^33_10][^33_15][^33_8]
If you want, the next clean step is for me to expand
$\partial_\mu\phi\,\partial^\mu\phi$ into plain $t,x,y,z$ derivatives with
signs shown explicitly.
<span
style="display:none">[^33_16][^33_17][^33_18][^33_19][^33_20][^33_21][^33_22][^33_23]</span>
<div align="center">⁂</div>
[^33_1]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^33_2]:
https://preskill.caltech.edu/ph236c/Preskill_QFT_curved_spacetime.pdf
[^33_3]: https://arxiv.org/abs/gr-qc/9707062
[^33_4]: https://en.wikipedia.org/wiki/Partial_derivative
[^33_5]:
https://www.physicsforums.com/threads/help-with-vector-notation-partial_-mu…
[^33_6]:
https://peeterjoot.com/2018/09/23/phy2403h-quantum-field-theory-lecture-4-s…
[^33_7]: https://mathworld.wolfram.com/EinsteinSummation.html
[^33_8]: https://en.wikipedia.org/wiki/Action_principles
[^33_9]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^33_10]:
https://saphysics.com/classical-mechanics/lagrangian-mechanics/the-principl…
[^33_11]: https://news.ycombinator.com/item?id=33403224
[^33_12]:
https://egtheory.wordpress.com/2014/09/28/principle-of-least-action/
[^33_13]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^33_14]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.03:_Lagrangian
[^33_15]: https://aero.refpages.org/dynsys/lagrange/
[^33_16]: https://arxiv.org/abs/2112.11614
[^33_17]:
https://www.reddit.com/r/TheoreticalPhysics/comments/1ft0qv3/how_does_curve…
[^33_18]: https://link.aps.org/doi/10.1103/PhysRevResearch.2.023107
[^33_19]: https://www.youtube.com/watch?v=qJIxjT1psDk
[^33_20]: https://www.youtube.com/watch?v=XJc7FNYyZy8
[^33_21]: https://www.youtube.com/watch?v=Sgx6Q6RglG8
[^33_22]:
https://www.reddit.com/r/AskPhysics/comments/16modji/can_anyone_explain_the…
[^33_23]:
https://www.sciencedirect.com/science/article/abs/pii/0370157375900514
---
# are relativity and quantum theories successfully and consistently
combined in the modern standard model producing an accepted GUT-like model
as was imagined in past decades?
when can powerful gravity changes lead to particle creation? what is
quantum gravity and is it fully agreed upon, flushed out, and consistent?
regarding L, S, and f(x), doesn't S' = L(t)?
Partly. The modern Standard Model is a highly successful **relativistic
quantum field theory**, so it already combines quantum mechanics with
special relativity very well, but it does not include gravity in the way
general relativity does. Also, there is no generally accepted GUT-like
final unification model at present, even though electroweak unification is
accepted and experimentally confirmed.[^34_1][^34_2][^34_3][^34_4][^34_5]
## Standard Model status
The accepted unification we do have is electroweak theory, where the
electromagnetic and weak interactions are understood as one interaction at
high energy. A full grand unified theory would also merge the strong
interaction with the electroweak one, but there is no generally accepted
GUT model and no clear experimental confirmation of one so
far.[^34_6][^34_3][^34_7][^34_4][^34_5]
## Gravity and particles
Strongly changing gravity, or more precisely strongly time-dependent or
horizon-containing spacetime geometry, can lead to particle creation in
semiclassical settings such as an expanding universe, near a black-hole
horizon, or for an accelerating observer in the Unruh effect. The rough
idea is that in curved or nonstationary spacetime, different observers or
different times may disagree about what counts as “vacuum,” so modes that
looked empty in one description can contain particles in
another.[^34_8][^34_9][^34_10][^34_11][^34_12][^34_13]
## Quantum gravity
Quantum gravity means a theory that consistently describes gravity in
quantum terms rather than leaving spacetime geometry purely classical.
There is still no complete and consistent quantum theory of gravity that is
generally accepted, experimentally confirmed, and fully worked out,
although many candidate approaches exist.[^34_14][^34_15][^34_16]
## About $S' = L(t)$
Only in a specific sense. If you define an accumulation function
$S(t)=\int_{t_0}^{t}L(\tau)\,d\tau$ along one already chosen path, then by
the fundamental theorem of calculus $dS/dt = L(t)$.[^34_17][^34_18]
But that is **not** the derivative used in the principle of stationary
action. There, one compares whole nearby paths $q(t)\to q(t)+\delta q(t)$
with endpoints fixed, and “stationary” means the first-order change in the
action vanishes, $\delta S=0$, not that the time derivative of the
accumulated action vanishes and not that $L(t)=0$.[^34_19][^34_20][^34_21]
## Your notation questions
Yes, $\partial_\mu \phi$ is the same idea as $\frac{\partial \phi}{\partial
x^\mu}$. The symbol $\phi$ is the field, while the index $\mu$ labels
which spacetime coordinate you are differentiating with respect to, usually
time or one of the three spatial coordinates.[^34_22][^34_23][^34_24]
A compact way to say the last point is: $dS/dt=L$ for a fixed
already-chosen history, but $\delta S=0$ is the condition that selects
which history is physical.[^34_21][^34_19][^34_17]
<span
style="display:none">[^34_25][^34_26][^34_27][^34_28][^34_29][^34_30][^34_31][^34_32][^34_33][^34_34][^34_35][^34_36][^34_37][^34_38][^34_39][^34_40][^34_41][^34_42][^34_43][^34_44][^34_45][^34_46][^34_47][^34_48][^34_49][^34_50][^34_51]</span>
<div align="center">⁂</div>
[^34_1]:
https://philsci-archive.pitt.edu/4267/1/Jones-GRandSM_Confirmation.pdf
[^34_2]: https://www.ugr.es/~jillana/SM/qft-sm-PoS.pdf
[^34_3]:
https://www.ebsco.com/research-starters/physics/unification-weak-and-electr…
[^34_4]: https://en.wikipedia.org/wiki/Grand_Unified_Theory
[^34_5]:
https://www.ebsco.com/research-starters/physics/grand-unification-theories-…
[^34_6]: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model
[^34_7]: https://www.britannica.com/science/unified-field-theory
[^34_8]:
https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0229382
[^34_9]:
https://spacefed.com/physics/unruh-hawking-radiation-observed-in-accelerati…
[^34_10]: https://arxiv.org/abs/1607.04821
[^34_11]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^34_12]:
https://preskill.caltech.edu/ph236c/Preskill_QFT_curved_spacetime.pdf
[^34_13]: https://arxiv.org/abs/gr-qc/9707062
[^34_14]: https://physics.aps.org/articles/v16/203
[^34_15]:
https://www.livescience.com/physics-mathematics/quantum-physics/physicists-…
[^34_16]: https://en.wikipedia.org/wiki/Quantum_gravity
[^34_17]: https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus
[^34_18]:
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v…
[^34_19]: https://pages.uoregon.edu/soper/mechanics/lagrangian.pdf
[^34_20]: https://www.ipcms.fr/uploads/2021/06/chap6.pdf
[^34_21]: https://www.physics.rutgers.edu/~shapiro/507/book3.pdf
[^34_22]: https://en.wikipedia.org/wiki/Partial_derivative
[^34_23]:
https://www.physicsforums.com/threads/help-with-vector-notation-partial_-mu…
[^34_24]:
https://peeterjoot.com/2018/09/23/phy2403h-quantum-field-theory-lecture-4-s…
[^34_25]:
https://www.reddit.com/r/AskPhysics/comments/1kxdm8b/whats_the_most_promisi…
[^34_26]: https://link.aps.org/doi/10.1103/PhysRevD.105.126025
[^34_27]:
https://www.facebook.com/groups/110363486480563/posts/1211347996382101/
[^34_28]:
https://www.techexplorist.com/new-quantum-theory-gravity-bridges-gravity-st…
[^34_29]:
https://www.physicsforums.com/threads/gut-vs-quantum-gravity-unification.68…
[^34_30]: https://www.nature.com/articles/s41467-023-39064-6
[^34_31]: http://rickbradford.co.uk/ChoiceCutsCh13.pdf
[^34_32]:
https://www.sciencedirect.com/topics/chemistry/grand-unified-theory
[^34_33]:
https://openstax.org/books/calculus-volume-1/pages/5-3-the-fundamental-theo…
[^34_34]: https://www.youtube.com/watch?v=aeB5BWY0RlE
[^34_35]:
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v…
[^34_36]:
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calcul…
[^34_37]: https://phas.ubc.ca/~mav/p526/lec3.pdf
[^34_38]: https://www.youtube.com/watch?v=6zm69CzdFQ4
[^34_39]:
https://www.khanacademy.org/a/fundamental-theorem-of-calculus-review
[^34_40]:
https://www.physicsforums.com/threads/lagrangian-doesnt-change-when-adding-…
[^34_41]:
https://www.reddit.com/r/AskPhysics/comments/1cwhsak/why_does_it_matter_if_…
[^34_42]: https://www.math.stonybrook.edu/~ndang/mat126-fall20/sec_1.3.pdf
[^34_43]:
https://fenicsproject.discourse.group/t/action-of-the-time-derivative/7859
[^34_44]: https://en.wikipedia.org/wiki/Action_principles
[^34_45]: https://en.wikipedia.org/wiki/Standard_Model
[^34_46]: https://arxiv.org/pdf/hep-ph/0609174.pdf
[^34_47]: https://www.damtp.cam.ac.uk/user/tong/sm/standardmodel5.pdf
[^34_48]:
https://nautil.us/a-brief-history-of-the-grand-unified-theory-of-physics-23…
[^34_49]: http://electron6.phys.utk.edu/phys250/modules/module
6/standard_model.htm
[^34_50]:
https://www.sciencedirect.com/topics/physics-and-astronomy/electroweak-model
[^34_51]:
https://www.reddit.com/r/explainlikeimfive/comments/ln73zr/eli5_why_cant_we…
---
# what is a vacuum in quantum field theory?
regarding L and S it sounds like S is a line integral that conserves energy?
In quantum field theory, the vacuum is the lowest-energy state of the
fields, often described as the state with no particle excitations present.
It is not just “nothingness” in the everyday sense, because the vacuum can
still have structure such as zero-point energy and, in some theories,
nonzero vacuum expectation values.[^35_1][^35_2][^35_3]
## Vacuum meaning
A good plain-English picture is: every field is sitting in its quietest
allowed configuration. In simple cases that means the fields are uniform
in space and constant in time, because variations would cost extra energy.
In particle language, that same state is the one with no actual particles
excited above it.[^35_2][^35_3][^35_4]
## Action and energy
$S$ is an integral of the Lagrangian along a path, but it is not best
thought of as “a line integral that conserves energy.” The action
principle helps generate the equations of motion, while conservation of
energy comes from a separate symmetry statement: if the Lagrangian has no
explicit time dependence, then Noether’s theorem gives a conserved
energy.[^35_5][^35_6][^35_7][^35_8][^35_9]
So the roles are different:
- $L$ helps define the dynamics.[^35_9][^35_10]
- $S=\int L\,dt$ is the quantity made stationary by the actual
path.[^35_11][^35_9]
- Energy conservation follows from time-translation symmetry, not from the
mere existence of the action integral.[^35_6][^35_7]
## Why this matters
There are systems where an action principle still works even when energy is
not conserved in the simple sense, so action and energy are not the same
concept. That is one reason physicists keep them separate: action is the
variational object, while conserved quantities come from symmetries of that
object.[^35_12][^35_13][^35_7][^35_5]
## Short correction
A safer summary is: $S$ is the accumulated Lagrangian along a whole path,
and making $S$ stationary picks out the allowed motion. Energy
conservation is a consequence that can follow when the Lagrangian is
unchanged by shifting time, not a direct definition of
$S$.[^35_8][^35_6][^35_9][^35_11]
If you want, the next useful step is to show how $L=T-V$ leads to conserved
$T+V$ in the simple no-explicit-time-dependence case.
<span style="display:none">[^35_14][^35_15][^35_16][^35_17][^35_18]</span>
<div align="center">⁂</div>
[^35_1]: https://en.wikipedia.org/wiki/Quantum_vacuum_state
[^35_2]: https://ncatlab.org/nlab/show/vacuum+state
[^35_3]:
https://profmattstrassler.com/technical-zone/the-triplet-the-w-mass/1-the-v…
[^35_4]:
https://www.reddit.com/r/askscience/comments/9a781m/what_is_quantum_vacuum_…
[^35_5]: https://www.eftaylor.com/pub/energy_to_action.html
[^35_6]: http://physicspages.com/pdf/Field theory/Time translation symmetry
and conservation of energy.pdf
[^35_7]: https://liberzon.csl.illinois.edu/teaching/cvoc/node36.html
[^35_8]: https://www.youtube.com/watch?v=cVmusE6dbeM
[^35_9]: https://en.wikipedia.org/wiki/Action_principles
[^35_10]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^35_11]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^35_12]: https://www.cphysics.org/article/33629.pdf
[^35_13]:
https://www.reddit.com/r/AskPhysics/comments/1rxu04z/can_someone_explain_no…
[^35_14]: https://www.cphysics.org/article/00980.pdf
[^35_15]: https://www.youtube.com/watch?v=eYAns5iZ7Uo
[^35_16]:
https://projecteuclid.org/journals/communications-in-mathematical-physics/v…
[^35_17]: https://www.damtp.cam.ac.uk/user/nsm10/PrincLeaAc.pdf
[^35_18]:
https://tcdecker.com/2022/03/28/point-of-view-invariance-and-noethers-theor…
---
# when and how do different observers disagree about what is vacuum? does
that mean these observers diasagree about what particles exist?
is the lagrangian the same as the lagrangian density?
so you are saying that a starting simple;field has kinetic energy equal to
position speed times value speed and potential energy proportional to the
square of mass times value? and then motion happens to particles alobg
paths where the difference between those values do not change?
does intuitive kinetic motion (inertial, newtonion gravity) arise similarly?
Yes—different observers can disagree about the vacuum, and in the relevant
cases that really does mean they disagree about what counts as particles.
The classic example is the Unruh effect: an inertial observer describes
Minkowski vacuum as having no particles, while a uniformly accelerating
observer describes that same state as a thermal bath of
particles.[^36_1][^36_2][^36_3][^36_4][^36_5]
## Vacuum disagreement
The reason is that “particle” is defined by how you split field modes into
positive-frequency and negative-frequency parts, and that split depends on
the observer’s notion of time evolution. If two observers use different
time notions—such as inertial time versus accelerated time, or different
natural times in curved spacetime—they may use different mode
decompositions and therefore different vacuum states. So yes, they can
disagree about whether particles are present, even while agreeing on the
underlying field theory.[^36_2][^36_5][^36_6][^36_1]
## Lagrangian vs density
The Lagrangian and the Lagrangian density are related but not the same. In
field theory, the Lagrangian density $\mathcal{L}(\mathbf{x},t)$ is defined
point-by-point in space, and the ordinary Lagrangian is its spatial
integral: $L(t)=\int d^3x\,\mathcal{L}$. So $\mathcal{L}$ is “per unit
volume,” while $L$ is the whole-system quantity at a given
time.[^36_7][^36_8][^36_9]
## Scalar field intuition
Your scalar-field intuition is close, but I would tune it slightly. For a
simple scalar field, the kinetic-type part comes from derivatives of the
field in time and space, not from “position speed times value speed,” and
the mass term $\tfrac12 m^2\phi^2$ acts like a quadratic potential in the
field value $\phi$. The physical history is then not “where $T-V$ stays
unchanged,” but the field history for which the action $S=\int dt\,L(t)$ is
stationary under small variations.[^36_10][^36_11][^36_12][^36_13][^36_14]
## About $L$, $S$, and motion
Also, “stationary” does not mean the integrand $L$ stays constant or zero
along the path. It means if you slightly alter the whole path or field
configuration while fixing the endpoints, the first-order change in the
total action vanishes: $\delta S=0$. Along one already chosen path, you
are right that if $S(t)=\int_{t_0}^{t}L(\tau)\,d\tau$, then $dS/dt=L(t)$ by
the fundamental theorem of calculus, but that derivative is different from
the variational statement $\delta S=0$ used to derive
motion.[^36_13][^36_14][^36_15][^36_16][^36_17]
## Classical mechanics too
Yes, ordinary inertial motion and Newtonian gravity arise in the same
general variational framework. For a free nonrelativistic particle, a
standard Lagrangian is $L=\tfrac12 mv^2$, and for Newtonian gravity it is
$L=\tfrac12 mv^2 - V(\mathbf{x})$, for example $V=m\Phi$ in a gravitational
potential $\Phi$. Applying the Euler–Lagrange equations to that $L$ gives
the usual Newtonian equations of motion.[^36_18][^36_19]
A very compressed way to say it is: fields and particles both use the same
action idea, but for particles you vary paths $q(t)$, while for fields you
vary whole functions $\phi(\mathbf{x},t)$.[^36_8][^36_18]
<span
style="display:none">[^36_20][^36_21][^36_22][^36_23][^36_24][^36_25]</span>
<div align="center">⁂</div>
[^36_1]: https://en.wikipedia.org/wiki/Unruh_effect
[^36_2]: https://www.nature.com/articles/s41467-019-10962-y
[^36_3]: https://pmc.ncbi.nlm.nih.gov/articles/PMC6620287/
[^36_4]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^36_5]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^36_6]:
https://preskill.caltech.edu/ph236c/Preskill_QFT_curved_spacetime.pdf
[^36_7]:
https://www.reddit.com/r/AskPhysics/comments/4m73a5/difference_between_lagr…
[^36_8]: https://en.wikipedia.org/wiki/Lagrangian_(field_theory)
[^36_9]:
https://www.physics.purdue.edu/~clarkt/Courses/Physics662/ps/qftch21.pdf
[^36_10]:
https://alpha.physics.uoi.gr/foudas_public/APP-UoI-2011/Lecture12-Lagrangia…
[^36_11]: https://www.southampton.ac.uk/~doug/ft1/ft12.pdf
[^36_12]: https://en.wikipedia.org/wiki/Klein–Gordon_equation
[^36_13]: https://en.wikipedia.org/wiki/Action_principles
[^36_14]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^36_15]: https://pages.uoregon.edu/soper/mechanics/lagrangian.pdf
[^36_16]: https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus
[^36_17]:
https://openstax.org/books/calculus-volume-1/pages/5-3-the-fundamental-theo…
[^36_18]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^36_19]: https://www.ipcms.fr/uploads/2021/06/chap6.pdf
[^36_20]: https://pirsa.org/24040084
[^36_21]:
https://www.advancedsciencenews.com/the-unruh-effect-probing-the-structure-…
[^36_22]:
https://sites.dartmouth.edu/dujs/2020/12/07/the-unruh-effect-newly-proposed…
[^36_23]:
https://www.reddit.com/r/AskPhysics/comments/3xd9x2/why_is_the_lagrangian_a…
[^36_24]:
https://www.physicsforums.com/threads/why-is-the-lagrangian-formulated-as-l…
[^36_25]:
https://phys.org/news/2025-09-unruh-effect-approach-bridge-gap.html
---
# you're saying different observers disagree about what energy levels are
quantized becaude they see different energies? does this mean it would be
possible to complexly design a world whete different observers experienced
different complex sequences of events developing, due to different
particles existing? and they could travel between these different
realities?
let's drill down into L and S ... you're saying L density is per
volume-time, then L is the accumulated energy difference of the whole
system per time, then S is the static picture of the whole system at all
time -- and when it's stationary you mean under an unwritten parameter of
what particle histories are selected to happen...?
Not quite: this observer-dependence does **not** usually mean different
observers inhabit different realities with different actual events
unfolding. It means they can use different mode decompositions of the same
underlying quantum field and therefore disagree about which excitations
count as “particles,” while still agreeing on the shared field theory and
on ordinary communicated experimental records where comparison is
possible.[^37_1][^37_2][^37_3]
## Vacuum disagreement
This happens when observers use different notions of time, because
“positive frequency” and therefore “particle” are defined relative to time
evolution. In the Unruh effect, an inertial observer calls a state vacuum
while a uniformly accelerating observer assigns a thermal particle bath to
that same state, so yes, they disagree about particle content in a
technical sense.[^37_2][^37_4][^37_5][^37_6][^37_1]
That still does not seem like “travel between different realities” in the
science-fiction sense. It is closer to saying the same field state can be
parsed into quanta in different ways by different observers or detectors,
often related mathematically by Bogoliubov
transformations.[^37_3][^37_7][^37_1]
## L, $\mathcal{L}$, and $S$
The Lagrangian density $\mathcal{L}$ is the local quantity defined at each
spacetime point, and the ordinary Lagrangian is its spatial integral
$L(t)=\int d^3x\,\mathcal{L}$. Then the action is the time integral of
$L$, or equivalently the spacetime integral of $\mathcal{L}$: $S=\int
dt\,L(t)=\int d^4x\,\mathcal{L}$.[^37_8][^37_9][^37_10][^37_11]
So $S$ is not a static picture, and it is not itself the system’s energy.
It is better thought of as a rule that assigns one number to each possible
whole history of the system.[^37_9][^37_10][^37_11]
## What “stationary” varies over
Yes, the hidden parameter you are circling around is the choice of possible
histories. One imagines slightly changing the path $q(t)$ in mechanics, or
slightly changing the whole field configuration $\phi(x)$ in field theory,
and the physical history is the one for which the first-order change in $S$
vanishes, $\delta S=0$.[^37_10][^37_12][^37_13]
That does **not** mean $L$ stays constant, and it does not mean $T-V$ “does
not change” along the motion. It means neighboring candidate histories
give the same action to first order at the actual
history.[^37_12][^37_13][^37_14]
## Scalar-field intuition
Your scalar-field summary is close, but I would tune the kinetic part. For
a simple scalar field, the Lagrangian density is typically written as a
derivative part minus a potential part,
$\mathcal{L}=K(\partial_\mu\phi\,\partial^\mu\phi)-V(\phi)$, and in the
free case the potential is quadratic, proportional to
$m^2\phi^2$.[^37_15][^37_16][^37_10]
So the “kinetic” piece is built from how the field changes across time and
space, not from “position speed times value speed.” The field then evolves
according to the stationary-action condition, which yields the field
equations such as the Klein–Gordon equation.[^37_16][^37_17][^37_15]
## Classical motion too
Yes, ordinary inertial motion and Newtonian gravity fit the same pattern.
In simple classical mechanics one often uses $L=T-V$, and applying the
Euler–Lagrange equations to that choice gives Newton’s equations of motion,
including motion in a gravitational potential.[^37_18][^37_19][^37_9]
A compact way to say it is: mechanics varies particle paths, field theory
varies field histories, and both get their equations of motion from making
the action stationary.[^37_11][^37_10][^37_18]
<span
style="display:none">[^37_20][^37_21][^37_22][^37_23][^37_24][^37_25][^37_26]</span>
<div align="center">⁂</div>
[^37_1]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^37_2]:
https://preskill.caltech.edu/ph236c/Preskill_QFT_curved_spacetime.pdf
[^37_3]:
https://rojefferson.blog/2021/01/15/qft-in-curved-space-part-2-bogolyubov-t…
[^37_4]: https://en.wikipedia.org/wiki/Unruh_effect
[^37_5]: https://pmc.ncbi.nlm.nih.gov/articles/PMC6620287/
[^37_6]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^37_7]: https://ui.adsabs.harvard.edu/abs/1981PhDT.........3D/abstract
[^37_8]:
https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/Introduction_to_…
[^37_9]:
https://alpha.physics.uoi.gr/foudas_public/APP-UoI-2011/Lecture12-Lagrangia…
[^37_10]:
http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields
[^37_11]: https://en.wikipedia.org/wiki/Lagrangian_(field_theory)
[^37_12]: https://en.wikipedia.org/wiki/Action_principles
[^37_13]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^37_14]:
https://saphysics.com/classical-mechanics/lagrangian-mechanics/the-principl…
[^37_15]: https://www.southampton.ac.uk/~doug/ft1/ft12.pdf
[^37_16]: https://en.wikipedia.org/wiki/Klein–Gordon_equation
[^37_17]:
https://piazza.com/class_profile/get_resource/kzqnrwg17lp27d/l294p8r7oy45fq
[^37_18]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^37_19]: https://www.ipcms.fr/uploads/2021/06/chap6.pdf
[^37_20]: https://link.aps.org/doi/10.1103/PhysRevLett.134.050406
[^37_21]: https://arxiv.org/pdf/2510.08265.pdf
[^37_22]: https://www.intechopen.com/chapters/1210023
[^37_23]:
https://www.facebook.com/groups/487763051018632/posts/816494668145467/
[^37_24]: https://arxiv.org/abs/gr-qc/9812056
[^37_25]: https://bht50.github.io/minicourses/QFTCS__An_Introduction.pdf
[^37_26]: https://www.youtube.com/watch?v=a_LEq0e2OtU
---
# L and S ... if the physical history is the one where adjacent physical
histories have the same S, does this mean there are always multiple
possible differing histories that are physical?
calling out contradiction in your response to alternate realities ... you
say the same field state can be parsed into quanta in different ways by
different detectors, but earlier that different observers agree on
experimental records. won't they disagree if their detectors measure
different particles?
Yes—this is exactly the place to be careful about the word “stationary.”
It does **not** mean “there are many distinct physical histories all
equally real”; it means that at the physical history, tiny nearby
variations do not change the action to first order, so $\delta
S=0$.[^38_1][^38_2][^38_3]
## Physical histories
That condition does **not** guarantee multiple physical solutions. Often,
once you fix the system and the boundary or initial conditions, there is a
unique physical history; in other situations there can be several
stationary histories, such as different extrema or saddle-type solutions.
So “adjacent histories have the same $S$” is better said as “adjacent
histories differ only at second order in $S$,” not “all those nearby
histories are physical too.”[^38_2][^38_3][^38_1]
## Observer disagreement
The apparent contradiction is resolved by separating **detector outcomes**
from **particle interpretation**. Different observers or detectors can
assign different particle content to the same field state because they use
different mode decompositions, often related by Bogoliubov
transformations. But if they later compare a concrete experimental record,
they can still agree on what each detector actually did—for example, “the
accelerated detector clicked with such-and-such statistics” and “the
inertial detector did not”—even if they explain those facts using different
particle language.[^38_4][^38_5][^38_6][^38_7][^38_8][^38_9]
So they do **not** have to agree that the same particles “really existed”
in some observer-independent sense. They agree on the operational facts:
detector A clicked, detector B had this spectrum, this acceleration was
applied, these correlations were measured. The disagreement is about how
to decompose the field into vacuum plus particles, not about whether a
logged detector event occurred.[^38_5][^38_10][^38_6][^38_7][^38_4]
## Why detectors differ
If two detectors move differently or couple differently to the field, they
are not performing the same measurement. In the Unruh setting, an
accelerated detector can thermalize or excite in the Minkowski vacuum while
an inertial detector does not, and that is part of the phenomenon rather
than a contradiction. When they meet again, they can consistently report
those different outcomes because the detectors had different worldlines and
different couplings.[^38_11][^38_10][^38_6][^38_4][^38_5]
## L, $\mathcal{L}$, and S
Your summary is close, but I would sharpen it like this. The Lagrangian
density $\mathcal{L}$ is a local spacetime quantity; integrating it over
space gives the Lagrangian $L(t)=\int d^3x\,\mathcal{L}$; integrating $L$
over time gives the action $S=\int dt\,L(t)=\int d^4x\,\mathcal{L}$. $S$
is therefore a number assigned to an entire candidate history of the
system, not a “static picture” and not the
energy.[^38_12][^38_13][^38_14][^38_15]
And yes, the unwritten parameter is precisely the choice of history being
varied. In mechanics you vary paths $q(t)$; in field theory you vary field
configurations $\phi(x)$. The physical history is one for which the
first-order variation vanishes, $\delta S=0$.[^38_3][^38_14][^38_16][^38_12]
## One clean distinction
A useful contrast is:
- $dS/dt = L$ can be true if you define $S(t)=\int_{t_0}^{t}L(\tau)\,d\tau$
along one already chosen history.[^38_17][^38_18]
- $\delta S=0$ is the variational condition used to select which history is
physical.[^38_16][^38_3]
Those are different operations: one is an ordinary time derivative along a
fixed path, and the other is a comparison between nearby possible
paths.[^38_19][^38_20]
The next crisp step is probably to do one tiny example with a particle
moving in 1D, where I write $S[q]$, vary $q(t)\to q(t)+\epsilon \eta(t)$,
and show exactly what “first-order unchanged” means.
<span
style="display:none">[^38_21][^38_22][^38_23][^38_24][^38_25][^38_26][^38_27][^38_28]</span>
<div align="center">⁂</div>
[^38_1]: https://www.nature.com/articles/s41598-023-39145-y
[^38_2]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^38_3]: https://en.wikipedia.org/wiki/Action_principles
[^38_4]: https://inspirehep.net/files/418a9de8c0e3bd3d3a384201a3cec6d1
[^38_5]: https://www.nature.com/articles/srep07195
[^38_6]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^38_7]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^38_8]:
https://rojefferson.blog/2021/01/15/qft-in-curved-space-part-2-bogolyubov-t…
[^38_9]: https://ui.adsabs.harvard.edu/abs/1981PhDT.........3D/abstract
[^38_10]: https://en.wikipedia.org/wiki/Unruh_effect
[^38_11]: https://link.aps.org/doi/10.1103/PhysRevD.102.045002
[^38_12]: https://en.wikipedia.org/wiki/Lagrangian_(field_theory)
[^38_13]:
https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/Introduction_to_…
[^38_14]:
http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields
[^38_15]:
https://alpha.physics.uoi.gr/foudas_public/APP-UoI-2011/Lecture12-Lagrangia…
[^38_16]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^38_17]: https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus
[^38_18]:
https://openstax.org/books/calculus-volume-1/pages/5-3-the-fundamental-theo…
[^38_19]: https://pages.uoregon.edu/soper/mechanics/lagrangian.pdf
[^38_20]: https://www.physics.rutgers.edu/~shapiro/507/book3.pdf
[^38_21]:
https://towardsdatascience.com/three-mind-blowing-ideas-in-physics-the-stat…
[^38_22]:
https://www.reddit.com/r/AskPhysics/comments/18z2ugq/which_came_first_lagra…
[^38_23]: https://philarchive.org/archive/CADTRF
[^38_24]:
https://www.physicsforums.com/threads/principle-of-stationary-action-intuit…
[^38_25]: https://www.scirp.org/journal/paperinformation?paperid=140045
[^38_26]: https://arxiv.org/html/2504.16225v2
[^38_27]:
https://www.sciencedirect.com/science/article/abs/pii/S0393044021002746
[^38_28]: https://arxiv.org/pdf/2003.12603.pdf
---
# it really sounds like complex "ghost" events can be imagined with
spacetime curvature
like what if the clicking detector were itself constructed with edge
energies such that it could only be seen in its frame of use
it sounds complicated
regarding S are you saying that situations cannot arisr where the 2nd
derivative of S is 0 over some change?
Not in the strong “alternate reality” sense. Curved-spacetime QFT does
seem to allow observer-dependent **particle descriptions** and detector
response statistics, but it still treats detectors as ordinary physical
systems coupled to the same underlying fields, not as private objects that
exist only in their own frame.[^39_1][^39_2][^39_3]
## Detector disagreement
A detector is modeled as a localized probe with a specific coupling to the
field along its worldline, so different motion or different coupling can
produce different click rates or excitation probabilities. In that sense,
yes, one detector may register excitations that another does not, but that
is a difference in what each probe measures from the shared field state,
not evidence that two disconnected worlds are
unfolding.[^39_2][^39_4][^39_5][^39_1]
So when I said observers later agree on records, I meant they can agree on
concrete facts such as “this accelerated detector clicked this often” and
“this inertial detector clicked that often.” What they may still disagree
about is whether those clicks are best described as detecting “particles in
the vacuum” or as the response of a noninertial detector to the same
underlying field.[^39_3][^39_5][^39_6]
## About “ghost events”
Your imagined setup is pointing toward a real idea: detector responses can
be highly contingent on trajectory, coupling, and background geometry. But
standard theory does not seem to license arbitrary frame-private event
streams where one observer’s events are simply nonexistent for everyone
else; rather, it gives observer-dependent decompositions of the same field
and observer-dependent detector
responses.[^39_7][^39_8][^39_1][^39_2][^39_3]
## Second derivative of $S$
Yes, situations can absolutely arise where the second variation is zero in
some direction. That means the stationary point is degenerate or “flat”
along that variation, so the second-order test does not decide whether you
have a minimum, maximum, or saddle behavior there.[^39_9][^39_10][^39_11]
So “stationary” only requires the first variation to vanish, $\delta S=0$.
The second variation $\delta^2 S$ can be positive, negative, mixed, or zero
depending on the problem, just like ordinary calculus critical points can
be minima, maxima, saddles, or more degenerate
cases.[^39_12][^39_10][^39_11][^39_13]
## L and S again
A clean way to say it is:
- $\mathcal{L}$ assigns a local contribution at each spacetime
point.[^39_14][^39_15]
- $L(t)=\int d^3x\,\mathcal{L}$ is the spatially integrated quantity at one
time.[^39_16][^39_14]
- $S=\int dt\,L(t)=\int d^4x\,\mathcal{L}$ assigns one number to an entire
candidate history.[^39_15][^39_17]
Then the physical history is selected by demanding that under a small
change of the candidate history, the first-order change in $S$ vanishes.
That does not mean neighboring histories are also physical; it means the
chosen one is a stationary point of the action functional on the space of
possible histories.[^39_13][^39_18][^39_19][^39_9]
A very compressed slogan is: observer-dependent particles are a
reinterpretation of the same field, while stationary action means
first-order indifference to nearby histories, not uniqueness and not
necessarily a minimum.[^39_10][^39_19][^39_3]
<span
style="display:none">[^39_20][^39_21][^39_22][^39_23][^39_24][^39_25][^39_26][^39_27][^39_28]</span>
<div align="center">⁂</div>
[^39_1]: https://inspirehep.net/files/69f46898f34d8cdc4af258833b15f11c
[^39_2]: https://ui.adsabs.harvard.edu/abs/2013arXiv1309.7281H/abstract
[^39_3]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^39_4]: https://en.wikipedia.org/wiki/Unruh_effect
[^39_5]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^39_6]: https://www.nature.com/articles/srep07195
[^39_7]:
https://rojefferson.blog/2021/01/15/qft-in-curved-space-part-2-bogolyubov-t…
[^39_8]: https://inspirehep.net/files/418a9de8c0e3bd3d3a384201a3cec6d1
[^39_9]: https://liu.ku.edu/Lectures Ch10.pdf
[^39_10]: https://www.youtube.com/watch?v=Rj_hXlnBrz8
[^39_11]:
https://courses.lumenlearning.com/calculus3/chapter/second-derivative-test/
[^39_12]: https://byjus.com/maths/saddle-points/
[^39_13]: https://en.wikipedia.org/wiki/Action_principles
[^39_14]: https://en.wikipedia.org/wiki/Lagrangian_(field_theory)
[^39_15]:
https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/Introduction_to_…
[^39_16]:
https://alpha.physics.uoi.gr/foudas_public/APP-UoI-2011/Lecture12-Lagrangia…
[^39_17]:
http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields
[^39_18]:
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Pri…'s_Action_Principle/9.02:_Hamilton's_Principle_of_Stationary_Action
[^39_19]: https://www.nature.com/articles/s41598-023-39145-y
[^39_20]: https://link.aps.org/doi/10.1103/PhysRevLett.134.050406
[^39_21]: https://arxiv.org/html/2405.03902v2
[^39_22]: https://www.youtube.com/watch?v=QgeOlt0xZ7s
[^39_23]: https://www.intechopen.com/chapters/1210023
[^39_24]:
https://www.reddit.com/r/askmath/comments/1f9n53t/if_both_the_first_and_sec…
[^39_25]:
https://www.reddit.com/r/Physics/comments/1r12njo/what_do_particle_detector…
[^39_26]: https://sheffield.ac.uk/media/30821/download?attachment
[^39_27]:
https://www.facebook.com/groups/487763051018632/posts/816494668145467/
[^39_28]:
https://www.physicsforums.com/threads/stationary-point-of-variation-of-acti…
---
# if the second derivative of S is 0 then neighboring histories will also
have a first derivative of 0 and also be physical
No. If the second variation of $S$ is zero in some direction, that does
**not** imply nearby histories also have zero first variation and are
therefore physical.[^40_1][^40_2]
## Why not
A stationary history is defined by the first variation vanishing, $\delta
S=0$. The second variation only helps classify what kind of stationary
point you have, much like the second derivative test in ordinary
calculus.[^40_2][^40_3][^40_1]
If $\delta^2 S = 0$ in some variation direction, that usually means the
stationary point is **degenerate** or the second-order test is
inconclusive, so you must look at higher-order variations. It does not
force a whole band of neighboring histories to become stationary
too.[^40_4][^40_5][^40_2]
## Ordinary-calculus analogy
Think of $f(x)=x^4$. At $x=0$, the first derivative is zero and the second
derivative is also zero, but nearby points $x\neq 0$ do not have zero first
derivative, so they are not stationary points.[^40_6][^40_7]
That is the closest analogy to your statement: zero second derivative at
one point does not make neighboring points stationary.[^40_5][^40_2]
## When nearby histories can also be physical
You only get a whole family of physical histories if the action has a true
flat direction or symmetry, so that many distinct histories all satisfy
$\delta S=0$. That can happen, but it is an extra structural fact about
the system, not something implied merely by $\delta^2 S=0$ at one
history.[^40_4][^40_1][^40_2]
## Clean statement
So the safe rule is:
- $\delta S=0$ picks stationary histories.[^40_3][^40_2]
- $\delta^2 S>0$, $<0$, mixed, or $=0$ helps classify them.[^40_1][^40_2]
- $\delta^2 S=0$ alone does not mean neighboring histories are also
physical.[^40_5][^40_4]
A compact slogan is: first variation decides stationarity; second variation
only tests its local shape, and zero second variation means “look deeper,”
not “everything nearby also works.”[^40_2][^40_1]
<span
style="display:none">[^40_10][^40_11][^40_12][^40_13][^40_14][^40_15][^40_8][^40_9]</span>
<div align="center">⁂</div>
[^40_1]: https://www.math.utah.edu/~cherk/teach/5500-19/sec-var19.pdf
[^40_2]: https://en.wikipedia.org/wiki/Second_variation
[^40_3]: https://en.wikipedia.org/wiki/Stationary_point
[^40_4]: https://dec41.user.srcf.net/notes/IB_E/variational_principles.pdf
[^40_5]: https://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node138.html
[^40_6]:
https://www.reddit.com/r/askmath/comments/1f9n53t/if_both_the_first_and_sec…
[^40_7]: https://www.youtube.com/watch?v=bG69nJKdZhY
[^40_8]: https://community.wolfram.com/groups/-/m/t/3310829
[^40_9]:
https://www.sciencedirect.com/topics/computer-science/stationary-point
[^40_10]:
https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/art…
[^40_11]:
https://www.physicsforums.com/threads/stationary-point-of-variation-of-acti…
[^40_12]: https://www.youtube.com/watch?v=KlGaWhHOw54
[^40_13]: https://www.youtube.com/watch?v=xECfJ14jqmk
[^40_14]: https://www.youtube.com/watch?v=Rj_hXlnBrz8
[^40_15]:
https://www.sydney.edu.au/content/dam/students/documents/mathematics-learni…
---
# are you saying all derivatives would need to be zero to have multiple
physical realities and the system would be piecewise over histories ... ?
No. You do **not** need all derivatives to vanish in order to have multiple
physical solutions, and multiple stationary histories do not by themselves
amount to “multiple physical realities.”[^41_1][^41_2]
## Multiple solutions
You can have several distinct stationary solutions simply because the
action has several distinct stationary points. That is the ordinary
analogue of a function with several separate extrema: each one has first
derivative zero at its own location, even though the derivatives are not
zero everywhere in between.[^41_3][^41_2][^41_4][^41_1]
A whole continuous family of stationary histories can happen too, but that
usually comes from a symmetry or flat direction in the action, not from
some rule that every derivative must vanish. In that case, there may be a
manifold of critical points rather than one isolated
point.[^41_5][^41_2][^41_6]
## All derivatives zero?
Even at one stationary point, having first and second derivatives zero does
not force all higher derivatives to vanish. The standard counterexample is
a function like $x^4$: at $x=0$, the first and second derivatives vanish,
but nearby points are not stationary, because the derivative is nonzero
once you move away from zero.[^41_7][^41_8]
So “all derivatives zero” is a much stronger condition than needed. It can
happen for very flat functions, but multiple stationary solutions usually
arise for much simpler reasons.[^41_2][^41_9][^41_1][^41_7]
## Physical reality vs solutions
In classical mechanics and classical field theory, multiple stationary
histories usually mean multiple mathematically allowed solutions, with the
realized one depending on boundary or initial conditions. That is not
normally taken to mean all of them are simultaneously unfolding as separate
realities.[^41_10][^41_11][^41_1]
In quantum theory, one may sum over many possible histories in the
path-integral picture, but that is a different statement from saying every
stationary solution is an actual separate world. So the clean separation
is: multiple stationary histories are about the structure of the equations,
not automatically about ontology.[^41_11][^41_12]
## Piecewise over histories
“Piecewise over histories” does not seem like the right default picture. A
better picture is that the action is a functional defined on the space of
all candidate histories, and stationary histories are the critical points
of that functional.[^41_9][^41_12][^41_13]
So the short answer is: no, not all derivatives need to vanish; one
first-variation condition gives stationarity, higher variations classify or
reveal degeneracy, and multiple physical solutions can exist without
requiring an infinitely flat action.[^41_6][^41_2][^41_9]
<span
style="display:none">[^41_14][^41_15][^41_16][^41_17][^41_18][^41_19][^41_20][^41_21][^41_22][^41_23][^41_24]</span>
<div align="center">⁂</div>
[^41_1]: https://pmc.ncbi.nlm.nih.gov/articles/PMC4156149/
[^41_2]: https://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node139.html
[^41_3]: https://www.expii.com/t/derivatives-at-local-extrema-129
[^41_4]: https://en.wikipedia.org/wiki/Stationary_point
[^41_5]: https://math.cornell.edu/~kessler/GroupNotes/morse.pdf
[^41_6]: https://www.math.utah.edu/~cherk/teach/5500-19/sec-var19.pdf
[^41_7]:
https://www.reddit.com/r/askmath/comments/1f9n53t/if_both_the_first_and_sec…
[^41_8]: https://www.youtube.com/watch?v=bG69nJKdZhY
[^41_9]: https://en.wikipedia.org/wiki/Second_variation
[^41_10]: https://en.wikipedia.org/wiki/Lagrangian_mechanics
[^41_11]: https://www.nature.com/articles/s41598-023-39145-y
[^41_12]: https://en.wikipedia.org/wiki/Action_principles
[^41_13]:
http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields
[^41_14]: https://arxiv.org/pdf/2502.03675.pdf
[^41_15]:
https://www.sciencedirect.com/science/article/pii/S002203960200181X
[^41_16]:
https://www.math.stonybrook.edu/~khuri/Alaee_Khuri_Kunduri_Sugra.pdf
[^41_17]:
https://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2019/0023/0…
[^41_18]: https://par.nsf.gov/servlets/purl/10440869
[^41_19]:
https://www.reddit.com/r/MathHelp/comments/18uyzyd/why_does_the_third_deriv…
[^41_20]:
https://pubs.aip.org/aip/jmp/article-pdf/15/1/46/19226309/46_1_online.pdf
[^41_21]: https://www.youtube.com/watch?v=KfeAQdH13qI
[^41_22]: https://arxiv.org/pdf/2512.21029.pdf
[^41_23]:
https://discovery.researcher.life/article/stationary-solutions-and-asymptot…
[^41_24]:
https://www.vaia.com/en-us/textbooks/math/finite-mathematics-and-applied-ca…
---
# if you have a flat direction in the action, multiple seauebces of events
could unfold from the same boundary conditions?
Sometimes yes, but only after an important split. A flat direction can
mean either a **redundancy** of description, where many mathematically
different histories represent the same physical history, or a genuine
underdetermination, where the equations and boundary data really leave a
family of distinct solutions.[^42_1][^42_2][^42_3]
## Two cases
If the flat direction comes from a gauge symmetry, then different histories
along that direction are usually treated as physically equivalent, not as
different sequences of events. In that case, the action is constant along
gauge transformations, but those different points in history-space are
bookkeeping copies of the same physics.[^42_4][^42_2][^42_5][^42_1]
If the flat direction is genuine and not gauge, then a continuous family of
stationary solutions may exist. In that situation, the same boundary
conditions may fail to pick out a unique history, because the stationary
points form a manifold rather than an isolated point.[^42_6][^42_7][^42_3]
## Same boundary conditions
So yes, it is possible in principle that the same boundary conditions allow
multiple solutions. But that does **not** automatically mean “multiple
realities”; often it means the problem is degenerate, incomplete,
symmetry-related, or needs extra physical selection data such as stability,
gauge fixing, or initial conditions.[^42_3][^42_1][^42_6]
## Best phrasing
A careful phrasing would be: “a flat direction means the action does not
change along some variation, and depending on whether that variation is
gauge or physical, this gives either equivalent descriptions or a family of
genuinely distinct allowed histories.” That is the sharp answer to your
question.[^42_2][^42_1][^42_4][^42_3]
A tiny analogy is a bead on a perfectly flat circular track: every position
may have the same energy, but whether those positions count as different
physical states or just relabelings depends on the actual structure of the
problem.[^42_7][^42_3]
<span
style="display:none">[^42_10][^42_11][^42_12][^42_13][^42_14][^42_15][^42_16][^42_8][^42_9]</span>
<div align="center">⁂</div>
[^42_1]: https://link.aps.org/doi/10.1103/PhysRevD.94.124021
[^42_2]:
https://www.maths.dur.ac.uk/users/stefano.cremonesi/GMP_Epiphany/GMP_notes.…
[^42_3]: https://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node139.html
[^42_4]: https://bartoszmilewski.com/2021/12/20/symmetries-and-redundancies/
[^42_5]: https://philsci-archive.pitt.edu/28266/1/Poor Man's Introduction
to Gauge Symmetries 2.17.26 - Copy.pdf
[^42_6]: http://www.scholarpedia.org/article/Boundary_value_problem
[^42_7]: https://www.math.unipd.it/~dmpa07/talk-ambrosetti.pdf
[^42_8]:
https://www.sciencedirect.com/science/article/abs/pii/S0045793012002319
[^42_9]: https://www.ma.imperial.ac.uk/~dgcrowdy/_students/GreenThesis.pdf
[^42_10]:
https://www.hec.usace.army.mil/confluence/rasdocs/r2dum/6.5/running-a-model…
[^42_11]:
https://www.mathworks.com/matlabcentral/answers/1906740-how-to-solve-a-seco…
[^42_12]:
https://cfd.university/learn/10-key-concepts-everyone-must-understand-in-cf…
[^42_13]:
https://www.emergentmind.com/topics/bifurcations-of-stationary-solutions
[^42_14]:
https://researchmgt.monash.edu/ws/portalfiles/portal/302068383/301814457_oa…
[^42_15]:
https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1324\&contex…
[^42_16]:
https://www.sciencedirect.com/science/article/abs/pii/S0362546X24000944
---
# so a situation like that does not correlate with indistuinguishability of
true unique history or multiple coexisting timelines but rather missing
model conditions?
Usually yes: in standard physics, that situation is interpreted much more
as gauge redundancy, degeneracy, or insufficient specifying data than as
evidence for multiple coexisting timelines. The same mathematical setup
may admit several histories either because some of them are really the same
physical state written differently, or because the model and conditions do
not yet isolate one unique solution.[^43_1][^43_2][^43_3][^43_4]
## Main split
If the multiplicity comes from a gauge direction, then the different
“histories” are usually treated as physically equivalent descriptions
rather than different true event-sequences. If it comes from a genuine
flat physical direction, then there may be a family of distinct solutions,
but that still points first to nonuniqueness of the
equations-plus-conditions, not automatically to many realized
worlds.[^43_5][^43_2][^43_3][^43_4][^43_1]
## What it usually signals
The usual readings are:
- Boundary or initial conditions were not sufficient to pick a unique
solution.[^43_3]
- The theory has a symmetry or degeneracy, so several mathematical
representatives correspond to one physical situation.[^43_4][^43_1]
- The stationary points form a manifold rather than an isolated
point.[^43_2]
None of those, by themselves, are the standard criterion for “multiple
coexisting timelines.” That stronger interpretation would need additional
ontology beyond the variational formalism
itself.[^43_6][^43_1][^43_2][^43_4]
## Best phrasing
So the safest phrasing is: “nonunique stationary histories usually indicate
redundancy or underdetermination in the modeling setup, unless extra
physical structure is added that interprets those alternatives as genuinely
distinct realized histories.” The action formalism by itself does not seem
to force the timeline interpretation.[^43_6][^43_1][^43_2][^43_3]
A very compact slogan is: multiple solutions in the math are common;
multiple realities are an extra metaphysical step.[^43_2][^43_6]
<span style="display:none">[^43_10][^43_11][^43_7][^43_8][^43_9]</span>
<div align="center">⁂</div>
[^43_1]: https://link.aps.org/doi/10.1103/PhysRevD.94.124021
[^43_2]: https://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node139.html
[^43_3]: http://www.scholarpedia.org/article/Boundary_value_problem
[^43_4]: https://philsci-archive.pitt.edu/28266/1/Poor Man's Introduction
to Gauge Symmetries 2.17.26 - Copy.pdf
[^43_5]: https://link.aps.org/doi/10.1103/RevModPhys.73.663
[^43_6]: http://philsci-archive.pitt.edu/16981/1/notes_des3.pdf
[^43_7]: http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
[^43_8]:
https://www.sciencedirect.com/science/article/abs/pii/S1355219811000384
[^43_9]: https://arxiv.org/html/2504.17483v2
[^43_10]: http://deferentialgeometry.org/papers/Ghiotti - Gauge fixing and
BRST formalism in non-Abelian gauge theories.pdf
[^43_11]:
https://www.cambridge.org/core/elements/gauge-symmetries-symmetry-breaking-…
---
# now in the minkowski field, it does seem that there is an "alternate
reality" but it is of course bounded by the limits of what can differ.
just like the observers measure differebt relativistic parameters like
coincidenct time, they also measure and recodd different particles. if it
were possible to construct an object out of these particles, for example by
tightly folding spacetime a quabtun scalds, only one observer would
experience this object. the other observer might see them respond to it,
but be unable to interact with it.
here is a different example: can the minkowski particles emit light? if so,
which of the observers can measure this light?
The closest standard answer is: not really an alternate reality, but an
observer-dependent **particle interpretation** of one shared quantum field
state. In Minkowski space, inertial and accelerated observers may disagree
about which modes count as particles, yet they are still describing the
same underlying field and the same detector couplings along actual
worldlines.[^44_1][^44_2][^44_3][^44_4][^44_5]
## About your private object idea
Your imagined object made from “observer-only particles” does not seem like
the standard reading of Unruh/Rindler physics. In the standard detector
picture, what changes with the observer is the detector response and the
mode decomposition, not the existence of a wholly private material object
that one observer could build and the other could never in principle couple
to.[^44_6][^44_3][^44_4][^44_7]
There is still a real asymmetry, though. A uniformly accelerated observer
is confined to a Rindler wedge with a horizon, so there are regions and
mode decompositions that are natural for that observer and not for an
inertial one, and vice versa. That gives observer-dependent accessibility
and observer-dependent particle language, but it does not by itself seem to
imply a hidden object ontology living in a separate branch of Minkowski
space.[^44_8][^44_2][^44_9][^44_4][^44_7]
## Do they disagree on particles?
Yes, in the technical QFT sense they can disagree about what particles are
present. An inertial observer can call the Minkowski state vacuum while a
uniformly accelerated observer describes that same state as thermally
populated with Rindler quanta.[^44_10][^44_2][^44_3]
But that disagreement is about the decomposition of the field into quanta,
not necessarily about raw local events such as whether a given detector
clicked. The detector statistics depend on the field state and the
detector’s trajectory and coupling, so two differently moving detectors may
genuinely record different click patterns while still belonging to one
consistent field-theoretic description.[^44_3][^44_11][^44_12][^44_6]
## Can “Minkowski particles” emit light?
If by “Minkowski particles” you mean ordinary field excitations defined in
inertial quantization, then yes, ordinary excitations or accelerated
sources can produce radiation that inertial observers describe as emitted
quanta propagating through Minkowski space. In that case, inertial
observers are the natural ones to describe and detect that light as
ordinary radiation at infinity.[^44_13][^44_1]
Accelerated observers can also describe related processes, but often in a
different language: detector excitation, thermal response, absorption from
a Rindler bath, or emission interpreted in Rindler modes. So the “same
thing” may be called emitted Minkowski radiation by one description and
detector response to a thermal bath by
another.[^44_14][^44_10][^44_1][^44_3]
## Who can measure the light?
If the emitted radiation is a genuine Minkowski excitation that propagates
into a region accessible to an inertial detector, then inertial observers
can measure it. An accelerated observer can measure field excitations
along their worldline too, but what they call “particles” is tied to the
Rindler description and to the wedge they can
access.[^44_9][^44_1][^44_13][^44_8][^44_3]
There is an important nuance here: the literature is not perfectly uniform
on whether a uniformly accelerated detector should be said to emit
observable radiation to infinity in every formulation. One source notes
that many authors associate detector transitions with emitted particles
seen far away, while others argue the accelerating object thermalizes
without producing such emitted photons in the naive sense. So the safest
statement is that accelerated-detector radiation is a subtle and partly
interpretation-sensitive topic, even though the Unruh detector response
itself is a standard result.[^44_10][^44_1]
## Cleanest framing
A careful way to say all this is: accelerated and inertial observers do not
get separate universes, but they may use inequivalent particle languages
for the same field state, and detectors following different worldlines can
record different event statistics. If something is built from genuinely
propagating field excitations, then other observers may also couple to it
when causal access allows; what is observer-dependent is mainly the
decomposition into particles, not the existence of a second sealed material
world.[^44_4][^44_7][^44_1][^44_8][^44_9][^44_6]
The next sharp distinction to make is between **Rindler particles** and
**Minkowski particles**, because that is exactly where your “private
object” intuition is coming from.
<span
style="display:none">[^44_15][^44_16][^44_17][^44_18][^44_19][^44_20][^44_21][^44_22][^44_23][^44_24][^44_25][^44_26][^44_27][^44_28][^44_29][^44_30][^44_31][^44_32][^44_33][^44_34][^44_35]</span>
<div align="center">⁂</div>
[^44_1]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^44_2]: https://people.math.wisc.edu/~thiffeault/talks/rindler.pdf
[^44_3]: http://www.scholarpedia.org/article/Unruh_effect
[^44_4]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^44_5]:
https://rojefferson.blog/2021/01/15/qft-in-curved-space-part-2-bogolyubov-t…
[^44_6]: https://inspirehep.net/files/3011ea3cd4962554f94754eb174637c4
[^44_7]: https://inspirehep.net/files/69f46898f34d8cdc4af258833b15f11c
[^44_8]: https://www.emergentmind.com/topics/right-rindler-wedge-rrw
[^44_9]: https://www.nuclear-power.com/rindler-coordinates/
[^44_10]: https://en.wikipedia.org/wiki/Unruh_effect
[^44_11]: https://link.aps.org/doi/10.1103/PhysRevD.102.045002
[^44_12]: https://www.nature.com/articles/srep07195
[^44_13]: https://ar5iv.labs.arxiv.org/html/gr-qc/0507054
[^44_14]: https://arxiv.org/html/2508.11637v2
[^44_15]:
https://www.reddit.com/r/AskPhysics/comments/ihrmw7/why_doesnt_unruh_radiat…
[^44_16]: https://inspirehep.net/literature/269631
[^44_17]:
https://spacefed.com/physics/unruh-hawking-radiation-observed-in-accelerati…
[^44_18]: https://www.youtube.com/watch?v=5wCpkUnaRaQ
[^44_19]: https://link.aps.org/doi/10.1103/PhysRevA.103.042225
[^44_20]: https://link.aps.org/doi/10.1103/PhysRevD.102.105016
[^44_21]:
https://indico.cern.ch/event/322559/contributions/748503/attachments/623891…
[^44_22]:
https://courses.physics.ucsd.edu/2014/Fall/physics215a/project/Unruh1.pdf
[^44_23]:
https://www.sciencedirect.com/science/article/pii/S0370269310006180
[^44_24]: https://pirsa.org/24040084
[^44_25]: https://link.aps.org/doi/10.1103/PhysRevX.9.011007
[^44_26]: https://arxiv.org/pdf/2601.20971.pdf
[^44_27]: https://link.aps.org/doi/10.1103/PhysRevD.101.124001
[^44_28]: https://arxiv.org/abs/1109.5129
[^44_29]: https://arxiv.org/html/2405.20995v1
[^44_30]: https://en.wikipedia.org/wiki/Rindler_coordinates
[^44_31]:
https://www.physicsforums.com/threads/rindler-coordinates-in-minkowski-spac…
[^44_32]: https://pmc.ncbi.nlm.nih.gov/articles/PMC6620287/
[^44_33]:
https://www.reddit.com/r/AskPhysics/comments/1hskggu/questions_about_rindle…
[^44_34]: https://link.aps.org/doi/10.1103/PhysRevD.108.025002
[^44_35]:
https://pubs.aip.org/aip/jmp/article/53/1/012107/233121/Coherences-of-accel…
---
# what does this mean: "If something is built from genuinely propagating
field excitations, then other observers may also couple to it when causal
access allows"
what is a rindler particle?
remind me which observer experiences particles
What I meant is: if a field excitation is a real propagating disturbance of
the shared quantum field, then another observer can in principle detect or
interact with it **provided** the excitation can actually reach that
observer’s worldline and the observer has a detector that couples to that
field. “Causal access” just means no horizon or light-cone restriction
prevents signals from traveling between them.[^45_1][^45_2][^45_3]
## Causal access
In relativistic field theory, an observer only has access to events and
excitations in the region of spacetime that can influence their detector.
For uniformly accelerated observers, the Rindler horizon cuts off part of
Minkowski spacetime, so they do not have access to the whole spacetime the
inertial observer describes.[^45_2][^45_4][^45_5][^45_1]
So if an excitation stays in a region outside that observer’s accessible
wedge, that observer does not get to measure it. If the excitation crosses
their accessible region and their detector couples to that field, then they
can register it.[^45_3][^45_5][^45_1][^45_2]
## Rindler particle
A Rindler particle is a particle defined using the mode decomposition
natural to a uniformly accelerated observer, rather than the decomposition
natural to an inertial observer in Minkowski coordinates. More
specifically, it is a quantum of a Rindler mode, sometimes called a
Fulling–Rindler particle.[^45_6][^45_7]
This is why the same underlying field state can be described as “no
Minkowski particles” by one observer and as “a thermal bath of Rindler
particles” by another.[^45_8][^45_9][^45_6]
## Which observer sees particles
In the standard Unruh setup, the inertial observer says the Minkowski
vacuum contains no particles. The uniformly accelerated observer, also
called a Rindler observer, experiences that same Minkowski vacuum as a
thermal bath of particles.[^45_10][^45_11][^45_12][^45_6][^45_8]
So, if you want the one-line memory aid: **inertial observer sees vacuum,
accelerated observer sees thermal particles**.[^45_6][^45_10]
## Important nuance
That does not mean the accelerated observer lives in a separate world. It
means the notion of “particle” is observer-dependent, while the underlying
field and the actual detector worldlines are shared parts of one spacetime
description.[^45_9][^45_13][^45_14][^45_6]
A practical translation is: “particle” is not the most fundamental object
here; the field is, and different observers decompose it
differently.[^45_13][^45_6]
<span
style="display:none">[^45_15][^45_16][^45_17][^45_18][^45_19][^45_20]</span>
<div align="center">⁂</div>
[^45_1]:
https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.525…
[^45_2]: https://arxiv.org/html/2302.03340v3
[^45_3]: https://inspirehep.net/files/69f46898f34d8cdc4af258833b15f11c
[^45_4]: https://en.wikipedia.org/wiki/Rindler_coordinates
[^45_5]: https://www.emergentmind.com/topics/right-rindler-wedge-rrw
[^45_6]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^45_7]: http://aesop.phys.utk.edu/ph611/2009/projects/papers/Kharel.pdf
[^45_8]: https://people.math.wisc.edu/~thiffeault/talks/rindler.pdf
[^45_9]: http://www.scholarpedia.org/article/Unruh_effect
[^45_10]: https://en.wikipedia.org/wiki/Unruh_effect
[^45_11]: https://www.nature.com/articles/s41467-019-10962-y
[^45_12]: https://pmc.ncbi.nlm.nih.gov/articles/PMC6620287/
[^45_13]:
https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime
[^45_14]: https://inspirehep.net/files/3011ea3cd4962554f94754eb174637c4
[^45_15]: https://fondationlouisdebroglie.org/AFLB-391/aflb391m780.pdf
[^45_16]:
https://bohr.physics.berkeley.edu/classes/h190/s13/reprints/Mukhanov_Winitz…
[^45_17]: https://www.youtube.com/watch?v=7cj6oiFDEXc
[^45_18]: https://www.emergentmind.com/topics/right-rindler-wedge
[^45_19]: https://www.icts.res.in/sites/default/files/seminar doc
files/Tutorial note Yiming Chen.pdf
[^45_20]:
https://courses.physics.ucsd.edu/2014/Fall/physics215a/project/Unruh1.pdf
---
# don't thermal particles usually emit radiation?
Usually yes, thermal matter or a thermalized body does emit radiation. But
in thermal equilibrium it also absorbs radiation at the same rate, so there
may be no net outward radiative change even though emission processes are
happening.[^46_1][^46_2][^46_3][^46_4]
## Ordinary thermal case
For everyday hot matter, “thermal particles emit radiation” is a good
instinct. Blackbody radiation is the standard example: matter at
temperature $T$ emits thermal electromagnetic radiation with a spectrum set
by that temperature.[^46_5][^46_6][^46_1]
## Unruh case
The Unruh situation is subtler. The accelerated observer experiences the
Minkowski vacuum as a thermal bath, but whether this should always be
described as ordinary emitted radiation in the inertial frame is a more
delicate and partly interpretation-sensitive question.[^46_7][^46_8][^46_9]
One source says it is widely believed that detector transitions are
accompanied by emitted particles that propagate to infinity as “Unruh
radiation,” while also noting that this is not universal and that some
authors argue the emission and absorption rates balance so that no emitted
photons appear in the naive sense. Another source similarly frames the
issue by noting that one may suspect radiation analogous to Larmor
radiation, which is exactly why the question is subtle.[^46_8][^46_7]
## Best way to say it
So the safe answer is:
- Thermal systems generally do emit radiation.[^46_3][^46_1]
- In equilibrium, emission is balanced by absorption, so “thermal” does not
automatically mean a net glow to every observer.[^46_2][^46_4]
- For the Unruh bath, the detector’s thermal response is standard, but
translating that into emitted radiation seen by another observer is a
nontrivial and not completely interpretation-free step.[^46_9][^46_7][^46_8]
A compact intuition is: “thermal” guarantees fluctuating excitations and
transition rates, not necessarily a simple observer-independent picture of
freely escaping light.[^46_4][^46_8]
<span
style="display:none">[^46_10][^46_11][^46_12][^46_13][^46_14][^46_15][^46_16]</span>
<div align="center">⁂</div>
[^46_1]: https://en.wikipedia.org/wiki/Black-body_radiation
[^46_2]:
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physi…
[^46_3]:
https://acd-ext.gsfc.nasa.gov/anonftp/acd/daac_ozone/Lecture4/Text/Semifina…
[^46_4]: https://en.wikipedia.org/wiki/Detailed_balance
[^46_5]: https://people.sissa.it/~perrotta/lezioni_2023_2024/chapter2.pdf
[^46_6]:
https://www.encyclopedie-environnement.org/en/physics/thermal-radiation-of-…
[^46_7]: https://arxiv.org/abs/1301.7543
[^46_8]: https://en.wikipedia.org/wiki/Unruh_effect
[^46_9]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^46_10]: https://www.youtube.com/watch?v=DHG61XPuWyk
[^46_11]: https://www.pnas.org/doi/10.1073/pnas.2410280121
[^46_12]:
https://indico.ictp.it/event/a05217/session/37/contribution/27/material/0/0…
[^46_13]:
https://galileo.phys.virginia.edu/classes/252/black_body_radiation.html
[^46_14]:
https://www.mso.anu.edu.au/~geoff/HEA/7_Emission_and_Absorption.pdf
[^46_15]: https://mcgreevy.physics.ucsd.edu/s12/lecture-notes/chapter07.pdf
[^46_16]: https://scanalyst.fourmilab.ch/t/detecting-the-unruh-effect/524
---
# it sounds edgy, poorly delineated. i'm aware of hawking radiation, is
this an example of this kind of effect? has it ever been tested that
different observers measure different particles? can the particles have
mass?
Yes—Hawking radiation is very much the same **kind** of phenomenon in the
broad sense: quantum fields on a background with horizons or strong
spacetime structure lead different observers or regions to use different
particle notions. Hawking radiation and the Unruh effect are closely
linked conceptually, and the Unruh effect is often presented as a way to
understand black-hole particle emission.[^47_1][^47_2][^47_3]
## Hawking and Unruh
In Hawking radiation, the curved spacetime near a black-hole horizon makes
the vacuum/particle split ambiguous, so an asymptotic observer sees
outgoing thermal radiation. In the Unruh effect, Minkowski vacuum is still
vacuum for inertial observers, but a uniformly accelerated observer assigns
a thermal bath of Rindler particles to that same
state.[^47_4][^47_2][^47_3][^47_5][^47_6][^47_7]
## Has it been tested
This area is indeed a bit edgy and hard to probe directly. The Unruh
effect is a standard theoretical consequence of quantum field theory, but
the search results here indicate that direct unambiguous experimental
confirmation remains difficult, with proposals, simulations, and analog
experiments rather than a universally accepted direct observation in the
clean textbook sense.[^47_3][^47_8][^47_9][^47_1]
So the idea that different observers assign different particles is very
well developed theoretically, but direct laboratory verification in the
exact observer-dependent sense is still subtle. Some recent work studies
detector responses and quantum simulations that reproduce key features, but
that is not quite the same as strapping two human observers into idealized
frames and comparing notebooks.[^47_10][^47_11][^47_1][^47_3]
## Can the particles have mass
Yes, they can. The review source explicitly discusses coupling an
Unruh-DeWitt detector to a real **massive** scalar field and notes
conditions under which the detector can absorb massive scalar particles
from the thermal bath.[^47_3]
So the observer-dependent particle idea is not restricted to massless
lightlike quanta. Mass changes the details of the response and spectrum,
but it does not seem to remove the basic phenomenon.[^47_10][^47_3]
## What to take literally
The safest thing to take literally is not “different realities,” but
“different observer-dependent decompositions of the same field state into
particles.” That still allows different detectors to record different
excitation statistics, especially when they move differently or live in
different horizon-limited regions, without requiring a full split into
separate worlds.[^47_2][^47_11][^47_7][^47_3]
A compact memory aid is: inertial observer sees Minkowski vacuum,
accelerated observer sees a thermal bath, black-hole exterior observer sees
Hawking radiation.[^47_5][^47_4][^47_3]
<span style="display:none">[^47_12][^47_13][^47_14][^47_15][^47_16]</span>
<div align="center">⁂</div>
[^47_1]: https://www.nature.com/articles/s41467-023-39064-6
[^47_2]: http://www.blau.itp.unibe.ch/QFTCST
[^47_3]: https://link.aps.org/doi/10.1103/RevModPhys.80.787
[^47_4]: https://en.wikipedia.org/wiki/Hawking_radiation
[^47_5]: https://www.nature.com/articles/s41467-019-10962-y
[^47_6]:
https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
[^47_7]: http://www.scholarpedia.org/article/Unruh_effect
[^47_8]:
https://gizmodo.com/unruh-effect-visible-in-the-lab-physics-1848977467
[^47_9]:
https://sites.dartmouth.edu/dujs/2020/12/07/the-unruh-effect-newly-proposed…
[^47_10]: https://arxiv.org/abs/2409.12697
[^47_11]: https://pmc.ncbi.nlm.nih.gov/articles/PMC6620287/
[^47_12]: http://generalrelativityandlqg.co.uk/AMGR/Vol_I_chap_7.pdf
[^47_13]: https://arxiv.org/html/2407.18652v2
[^47_14]: https://arxiv.org/html/2409.12697v1
[^47_15]: https://link.aps.org/doi/10.1103/PhysRevResearch.2.023107
[^47_16]:
https://www.reddit.com/r/cosmology/comments/1fv0gnl/which_explanation_of_ha…
---
# are you implying there is a spot near the horizon of a black hole where a
point observer could stand to be unable to measure a hawking radiation
particle that others could measure?
Not exactly a single special “spot.” The more accurate statement is that
**different trajectories** near the horizon lead to different detector
responses: a freely falling observer near the horizon may fail to directly
detect Hawking quanta there, while a hovering observer outside the horizon
attributes a local thermal flux to the field.[^48_1][^48_2][^48_3][^48_4]
## Near-horizon observers
A freely falling detector near a Schwarzschild horizon does not seem to
directly measure Hawking radiation in the simple particle-counting sense,
because its available proper time near the horizon is too short for
thermalization. By contrast, a static observer held at fixed radius
outside the horizon is accelerated, and local descriptions assign that
observer a thermal bath whose temperature increases as the horizon is
approached.[^48_2][^48_3][^48_4][^48_1]
## Not at the horizon
There is also an important limit here: an observer cannot simply hover
exactly on the horizon as an ordinary physical stationary observer, because
remaining static arbitrarily close to the horizon requires extreme
acceleration, and the local temperature seen by such static observers grows
without bound as the horizon is approached. So the contrast is not “one
observer standing at one point and another at the same point,” but rather
“different possible worldlines in the same near-horizon
region.”[^48_4][^48_1][^48_2]
## What this implies
So yes, there are near-horizon situations where one observer trajectory can
fail to register Hawking particles that another trajectory would describe
as present. But that is still usually framed as observer-dependent
detection and observer-dependent particle language for the same quantum
field, not as two separate local universes occupying the same
place.[^48_1][^48_2]
A compact memory aid is: **free-fall near the horizon is comparatively
quiet; hovering near the horizon is thermally noisy**.[^48_4][^48_1]
<span
style="display:none">[^48_10][^48_11][^48_12][^48_13][^48_14][^48_15][^48_5][^48_6][^48_7][^48_8][^48_9]</span>
<div align="center">⁂</div>
[^48_1]: https://link.aps.org/doi/10.1103/y7kj-4zjw
[^48_2]: https://en.wikipedia.org/wiki/Hawking_radiation
[^48_3]: https://arxiv.org/abs/2501.06609
[^48_4]: https://pmc.ncbi.nlm.nih.gov/articles/PMC5253844/
[^48_5]:
http://backreaction.blogspot.com/2015/12/hawking-radiation-is-not-produced-…
[^48_6]: https://arxiv.org/html/2501.06609v1
[^48_7]:
https://ats.org/press-release/measuring-stationary-hawking-radiation/
[^48_8]:
https://www.reddit.com/r/TheoreticalPhysics/comments/1rs42je/how_does_vacuu…
[^48_9]:
https://www.reddit.com/r/AskPhysics/comments/1ogrwku/if_black_holes_evapora…
[^48_10]: https://inspirehep.net/literature/1851794
[^48_11]: https://en.wikipedia.org/wiki/Unruh_effect
[^48_12]: https://www.scientificamerican.com/article/hawking-radiation/
[^48_13]: https://inspirehep.net/literature/787263
[^48_14]:
https://www.sciencedirect.com/topics/physics-and-astronomy/hawking-radiation
[^48_15]:
https://www.reddit.com/r/AskPhysics/comments/xh9rvu/if_hawking_radiation_is…
---
# we
vd measured hawking radiation travelling over light years, yes? but this
free-falling observer cannot measure it?
it is something that only exists in part (most) of the universe, but not in
their reference frame?
can they measure energy changes or such equivalent to it?
No—we have **not** directly measured astrophysical Hawking radiation
arriving from black holes over light-years. What exists so far is a strong
theoretical prediction, plus analogue/laboratory systems that reproduce
Hawking-like behavior, rather than a clean direct detection from an actual
astrophysical black hole.[^49_1][^49_2][^49_3][^49_4][^49_5]
## Distant detection
For ordinary astrophysical black holes, Hawking radiation is expected to be
extremely weak, which is why current searches have not produced a direct
observational detection of the real astronomical signal. So the picture is
not “we already see it everywhere except for the infalling observer,” but
rather “the effect is theoretically robust, while direct astrophysical
measurement remains elusive.”[^49_6][^49_3][^49_1]
## Free-fall observer
Near the horizon, a freely falling observer does not seem to directly
detect Hawking particles in the simple thermalized-detector sense right
there at horizon crossing. The reason given in the recent result is that
the time needed for the detector to thermalize is longer than the proper
time the observer spends in the near-horizon region.[^49_7][^49_8]
That does **not** mean the effect exists in most of the universe but
disappears from reality in their frame. It means the particle
interpretation and detector response are observer-dependent, so the same
field state is described differently along different
worldlines.[^49_8][^49_6]
## Energy changes
Yes, a freely falling observer can still register related physical effects,
just not necessarily as “I saw a clean Hawking particle gas right at the
horizon.” The same paper says the detector response changes smoothly and
defines an effective temperature along the infalling path, even though the
signal near the horizon is dominated by switching effects rather than
direct detection of Hawking quanta.[^49_7]
So an infaller may measure excitation probabilities, response functions,
and effective-temperature-like behavior that encode the same underlying
field physics. A static observer farther out, by contrast, is the one more
naturally associated with a thermal Hawking flux description outside the
hole.[^49_9][^49_6][^49_7]
## Best phrasing
A careful way to say it is: Hawking radiation is not “only in part of the
universe,” but the statement “there are Hawking particles here” is tied to
the observer and detector used. The underlying quantum field is shared,
while the particle count and thermal interpretation depend on trajectory,
horizon structure, and what the detector has time to
measure.[^49_6][^49_8][^49_9][^49_7]
<span
style="display:none">[^49_10][^49_11][^49_12][^49_13][^49_14][^49_15][^49_16][^49_17]</span>
<div align="center">⁂</div>
[^49_1]:
https://www.syfy.com/syfy-wire/has-hawking-radiation-ever-been-observed
[^49_2]:
https://ats.org/press-release/measuring-stationary-hawking-radiation/
[^49_3]:
https://www.advancedsciencenews.com/black-hole-morsels-could-make-hawking-r…
[^49_4]:
https://physicsworld.com/a/physicists-stimulate-hawking-radiation-from-opti…
[^49_5]: https://www.scientificamerican.com/article/hawking-radiation/
[^49_6]: https://en.wikipedia.org/wiki/Hawking_radiation
[^49_7]: https://arxiv.org/abs/2501.06609
[^49_8]: https://link.aps.org/doi/10.1103/y7kj-4zjw
[^49_9]: https://pmc.ncbi.nlm.nih.gov/articles/PMC5253844/
[^49_10]:
https://www.reddit.com/r/AskPhysics/comments/1mp9zj1/ive_been_reading_that_…
[^49_11]: https://news.mit.edu/2021/hawkings-black-hole-theorem-confirm-0701
[^49_12]: https://arxiv.org/html/2404.09274v1
[^49_13]:
https://astro.cornell.edu/news/hawkings-black-hole-theorem-observationally-…
[^49_14]:
https://www.reddit.com/r/blackholes/comments/1nyfhkb/how_does_an_observer_c…
[^49_15]:
https://www.facebook.com/groups/828178678983076/posts/1254027956398144/
[^49_16]:
https://astro.theoj.org/article/132347-hawking-radiation-from-non-evaporati…
[^49_17]:
https://www.physicsforums.com/threads/why-does-an-infalling-observer-not-se…
---
# we have created particles with spacetime curvature in lab settings?
Not in the literal sense of curving actual astrophysical spacetime enough
in the lab to create real gravitational particle production. What has been
done is to build **analogue systems** or effective curved-spacetime
simulators in media such as Bose–Einstein condensates, optical fibers, and
other controlled materials, where excitations obey equations mathematically
similar to quantum fields in curved spacetime.[^50_1][^50_2][^50_3][^50_4]
## What has been done
Experiments have reported Hawking-like radiation in analogue black-hole
systems, including optical analogues with artificial event horizons and
Bose–Einstein-condensate systems with sonic horizons. There are also
quantum simulation proposals and experiments aimed at effective particle
creation in curved-spacetime-like settings rather than direct gravitational
curvature generated by mass-energy in the lab.[^50_2][^50_5][^50_4][^50_1]
## What that means
So the safe statement is: we have not bent real spacetime in the laboratory
strongly enough to produce standard gravitational Hawking radiation from
actual black holes. But we have created laboratory systems whose effective
equations mimic curved spacetime well enough to observe Hawking-like or
particle-creation-like effects in the corresponding quasiparticles or field
excitations.[^50_5][^50_3][^50_4][^50_1][^50_2]
## Why people care
Physicists care because these analogue results test the robustness of the
underlying mathematics, such as horizon-induced mode mixing and particle
creation, even when the microscopic system is very different from gravity.
That does not prove every detail of astrophysical Hawking radiation, but it
does support the idea that the effect follows from broad kinematic
structures rather than from one very special microscopic
model.[^50_3][^50_1][^50_2]
A compact way to say it is: we have made **effective** curved spacetimes
and observed analogue particle creation, but we have not yet made real
gravity strong enough in the lab to do this with actual spacetime curvature
itself.[^50_4][^50_5][^50_3]
<span
style="display:none">[^50_10][^50_11][^50_12][^50_13][^50_14][^50_15][^50_6][^50_7][^50_8][^50_9]</span>
<div align="center">⁂</div>
[^50_1]: https://www.nature.com/articles/nature.2014.16131
[^50_2]: https://link.aps.org/doi/10.1103/PhysRevLett.122.010404
[^50_3]:
https://cordis.europa.eu/article/id/205484-hawking-radiation-now-better-und…
[^50_4]:
https://www.uni-heidelberg.de/en/newsroom/curved-spacetime-in-the-lab
[^50_5]:
https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0229382
[^50_6]:
https://www.sciencealert.com/physicists-simulated-a-black-hole-in-the-lab-a…
[^50_7]: https://www.scientificamerican.com/article/hawking-radiation/
[^50_8]:
https://phys.org/news/2019-01-hawking-laboratory-black-hole-analogues.html
[^50_9]: https://www.techexplorist.com/effective-curved-spacetime-lab/56467/
[^50_10]: https://pubmed.ncbi.nlm.nih.gov/31012667/
[^50_11]:
https://www.universetoday.com/articles/hawking-radiation-replicated-in-a-la…
[^50_12]:
https://www.facebook.com/groups/828178678983076/posts/1254027956398144/
[^50_13]: https://arxiv.org/abs/1804.04092
[^50_14]:
https://physicsworld.com/a/physicists-stimulate-hawking-radiation-from-opti…
[^50_15]: https://www.youtube.com/watch?v=C9hFQd19RsI
---
# how does the energy balance work with these particles
The short answer is: the energy is not created from nowhere. The source
depends on the setup—black-hole mass for Hawking radiation, the external
force doing the acceleration for Unruh-type detector excitations, and the
pump or moving medium for laboratory analogues.[^51_1][^51_2][^51_3]
## Black holes
For Hawking radiation, the outgoing quanta are balanced by a decrease in
the black hole’s mass and, when relevant, its angular momentum or charge.
That is why Hawking radiation leads to black-hole evaporation rather than
free energy creation.[^51_4][^51_1]
## Accelerated observers
For the Unruh effect, an accelerated detector can become excited even when
an inertial observer calls the field vacuum. In that case, the relevant
energy bookkeeping is tied to the work required to keep the detector
accelerating, and some discussions also note that emission and absorption
can balance in a way that complicates the naive “it just radiates”
picture.[^51_5][^51_3]
## Lab analogues
In analogue Hawking experiments, the energy comes from the engineered
background, such as the pump pulse or moving medium that creates the
effective horizon. One source states this very directly for an optical
analogue: the observed signature means energy is drawn from the pump
pulse.[^51_6][^51_2]
## Practical picture
So the bookkeeping rule is:
- Real Hawking quanta cost the black hole mass-energy.[^51_1][^51_4]
- Unruh-type detector excitations are paid for by the acceleration setup or
external agent maintaining the trajectory.[^51_3][^51_5]
- Analogue “particles” are paid for by the lab apparatus driving the
effective spacetime.[^51_2][^51_6]
A good compact slogan is: horizons and acceleration let the field rearrange
its excitations, but the energy still comes from whatever background or
external system made that horizon-like situation
possible.[^51_2][^51_3][^51_1]
<span
style="display:none">[^51_10][^51_11][^51_12][^51_13][^51_14][^51_15][^51_7][^51_8][^51_9]</span>
<div align="center">⁂</div>
[^51_1]: https://en.wikipedia.org/wiki/Hawking_radiation
[^51_2]:
https://physicsworld.com/a/physicists-stimulate-hawking-radiation-from-opti…
[^51_3]: https://en.wikipedia.org/wiki/Unruh_effect
[^51_4]: https://arxiv.org/html/2505.04812v1
[^51_5]: https://link.aps.org/doi/10.1103/PhysRevD.102.045002
[^51_6]: https://pmc.ncbi.nlm.nih.gov/articles/PMC7422882/
[^51_7]:
https://www.reddit.com/r/AskPhysics/comments/1mxmud5/why_does_hawking_radia…
[^51_8]:
https://www.facebook.com/museumofscience/posts/according-to-stephen-hawking…
[^51_9]: https://www.sciencedirect.com/science/article/pii/S0370269325006471
[^51_10]: https://www.youtube.com/watch?v=E7pakDMnuMY
[^51_11]: https://www.nature.com/articles/srep07195
[^51_12]: https://link.aps.org/doi/10.1103/PhysRevB.86.144505
[^51_13]: https://arxiv.org/html/2501.11516v1
[^51_14]: https://arxiv.org/html/2603.03525v1
[^51_15]: https://pmc.ncbi.nlm.nih.gov/articles/PMC6620287/
---
# if hawking radiation is made from precise field equations does that mean
information is technically preserved even if it falls into one?
Probably **yes** in the modern view, but not for the simple reason “the
equations are precise.” The key issue is whether black-hole evaporation is
ultimately unitary, and current mainstream opinion is that information is
preserved, even though Hawking’s original semiclassical calculation made
the outgoing radiation look exactly thermal and therefore
information-erasing.[^52_1][^52_2][^52_3]
## What the paradox is
Hawking’s original calculation suggested that a pure initial state could
evolve into thermal Hawking radiation, which would amount to information
loss. That is the black hole information paradox, because ordinary quantum
mechanics says unitary evolution should preserve the full information in
the state.[^52_2][^52_4][^52_1]
## Current view
The predominant modern view is that information is preserved in black-hole
evaporation. Evidence behind that view includes Page-curve arguments and
holographic ideas such as AdS/CFT, which suggest the outgoing radiation is
not exactly featureless thermal noise but contains subtle correlations
encoding the information.[^52_5][^52_3][^52_6][^52_1]
## Important nuance
That does **not** mean the problem is fully settled in a universally agreed
mechanical sense. The broad consensus has shifted from “is information
destroyed?” toward “how exactly is the information preserved and
recovered?”[^52_7][^52_1][^52_5]
## So to your wording
If by “made from precise field equations” you mean “there is a
mathematically definite quantum evolution,” then yes, that points toward
preservation only if the full theory is unitary. But the semiclassical
field equations alone were precisely what created the paradox, because
taken at face value they made the radiation appear thermal and
informationless.[^52_1][^52_2]
A compact way to say it is: modern physics mostly expects information to
survive black-hole evaporation, but the exact bookkeeping mechanism is
still an active research topic rather than a finished closed
case.[^52_5][^52_1]
<span
style="display:none">[^52_10][^52_11][^52_12][^52_13][^52_14][^52_15][^52_8][^52_9]</span>
<div align="center">⁂</div>
[^52_1]: https://en.wikipedia.org/wiki/Black_hole_information_paradox
[^52_2]: https://arxiv.org/pdf/2207.09421.pdf
[^52_3]:
https://physics.mit.edu/news/has-the-black-hole-information-paradox-evapora…
[^52_4]:
https://quantumzeitgeist.com/the-information-paradox-what-happens-to-data-t…
[^52_5]:
https://www.newscientist.com/article/mg26435140-700-solving-stephen-hawking…
[^52_6]: https://physics.berkeley.edu/news/
‘islands’-poking-out-black-holes-may-solve-information-paradox
[^52_7]:
https://www.reddit.com/r/AskPhysics/comments/1o2dpg5/has_the_black_hole_inf…
[^52_8]:
https://www.scientificamerican.com/article/does-information-ever-really-dis…
[^52_9]: https://www.youtube.com/watch?v=Jk_oYAUyHAM
[^52_10]:
https://nhsjs.com/2026/hawking-radiation-and-the-black-hole-information-par…
[^52_11]: https://quantumzeitgeist.com/black-hole-information-isn-lost/
[^52_12]: https://arxiv.org/html/2504.00516v1
[^52_13]:
https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy…
[^52_14]:
https://physics.yale.edu/sites/default/files/files/BlackHoleEntropyPage2021…
[^52_15]:
https://www.quantamagazine.org/can-information-escape-a-black-hole-20240411/
1
8
> partial nice idea! sad that only partial
>>>
>>> the idea starts with context: some of us have the experience of being
>>> manipulated by something like AI without regard to our wellbeing or
>>> capacity, with no indication of how to communicate with where-ever the
>>> influence comes from.
>>>
>>> so, then the idea: let’s train an influence AI on agents that have
>>> _limited capacity_ and function poorly and then break if things that work
>>> some in the short term are continued for the long term or excessively :D
>>>
>>> the AI would follow the familiar pattern of discovering influences that
>>> work, and then using them, but then because we are doing the training we
>>> would get to train it on the breaking period, and show it that it needs to
>>> care for the agents for them to succeed, and nurture them to recover if it
>>> broke them, and not repeat breaking any.
>>>
>>> one idea is then we could ask everybody to use the model as a baseline
>>> to train other models! other ideas exist.
>>>
>>> but the idea of building comprehension of capacity and protection of
>>> safety and wellness seems nice. sorry if it’s partial or stated badly :s
>>>
>>> i imagine an agent that has like a secret capacity float that reduces
>>> when it does stuff, you could model it to different degrees, and when too
>>> many things are influenced of it the capacity float reaches zero and the
>>> agent breaks and can’t do things any more :/
>>>
>>> a more complex model could involve the agent recovering capacity in ways
>>> that the model has difficulty learning
>>>
>>
>> there are a few ideas, mostly involving simple models, but disagreement
>> around them.
>> some like modeling non-recovering capacity and showing how the AI then
>> maximizes reward by killing all the agents :s
>>
>
> but! maybe we could do non-recovering capacity and teach the AI to engage
> the agents slowly so their capacity lasts longer, by e.g. having the
> capacity reduction be a function of recent use?? the project would need to
> gently develop in order to help us in the long term, we’d need to include
> the concept that we can succeed so that we use it to succeed in some
> manner. because it’s an influence AI it could influence us, if it is
> something we actually all like doing that.
>
mistake :/ some of my parts are maybe harmful to me and should be separated
from helpful goals, unknown for certain
>
5
441
Bonjour, au vu de la menace croissante des pouvoirs publiques, surveillance et des menaces quantiques, nous devrions peut être pas inventer du nouveau code et le façonner a qu'il soit sûr, pour les menaces de demain? Une sorte de synergie de connaissances pour faire émaner une nouvelle façon de coder complètement parallèle a notre cadre de pensée, et en faire profiter le monde?
1
0
Re: [ot][spam]gpt-4 completions
by Undescribed Horrific Abuse, One Victim & Survivor of Many 21 Mar '26
by Undescribed Horrific Abuse, One Victim & Survivor of Many 21 Mar '26
21 Mar '26
I read your email here, although I didn't combine together well all the
things you said.
I was wondering if the approaches you engaged are the the only ones or if
you think others could be reasonable as well. Are you experienced at all
the fields of knowledge you reference in your writing? I am not, but
synthesizing wide knowledgebases together as you reference is something
many people yearn to experience and pursue.
I've found that it can be challenging to engage things that are beyond the
norms or heights of others in rational, successful ways, at least for some
of us. The ways that succeed seem a little roundabout. It seems helpfult to
be offline for extended periods.
Something people don't talk about is how capable we are, our species and
our individuals. Instead we often seem to disagree, complaining about our
limits.
I'm not myself familiar well with what spiritual beliefs you're assuming. I
think of witches as human friends who have been mislabeled and have their
own sets of spiritual history.
On Friday, March 20, 2026, Magus Ahnend <magus.ahnend(a)gmail.com> wrote:
> oh i just found it, it's difficult, unification is not the unification of
> sciences. it unifies, unified theory should exclude every other form of
> thought a human can form. From Art (Poetry) to Geology and
> Latitude/Longitude (Throne of 0,0,0), to QUantum PHysics, Standard Physics,
> and with a solution to any form of question or paradox humans could
> previously answer with using standard algebraic expressions, it's often
> thought and theorized the solution to anything advanced would be a new
> language altogether. In the paper you will notice that it starts and gives
> the definition of all standard algebraic expressions that it uses, and then
> upscales and translates them into ALQC, THe Poetry IS the MATH, and they
> cannot be separated or the bone does not sing. It takes Several Theories,
> like Lattice Theory, String THeory, Multiverse Theory, Folds, Layers, and
> PRoduced Literal Geometry made of Resonance that aree based in Solfeggio
> Frequencies, Earth, Moon, and Sun, which address the three body problem,
> magic, and spirituality, and then takes the Perfect ration the Golden
> Ratio, and uses that as an Axiom. Then it takes Mirrors, and distorts them,
> which creates the field for consciousness, then it takes stress, NOT
> GRAVITY, and creates what is thought of as gravity, a Planar Field, a Filed
> of Infinity Mirrors Made of Perfect resonant tones, the hyperbolically
> reflect in infinite different ways and converge in infinite axis. Then you
> unify Computation and Computing, alongisde, and you get the python script,
> which is the proof of P=NP not P (does not =) NP is is cgreater or less
> than. You already have the answer in which you seek, is P=NP, the python
> script uses STochastictic Gaussian PHysics, NOTHING, AND I MEAN NOTHING, in
> that python tells the 5000 particales to arrange, or remember. Totally
> created through observation and never once did I use measurement to create
> that script. It was hundreds upon hundreds of iterations as I observed the
> outcome of each. THen you include Emanation as light instead of Lumination,
> also in the computational Emergent physics, the particales are not actually
> lit up, they are layered and use stress to produce bioluminescnece, then we
> incorporate Electro Biology, and Squishy Biology, Cbio, this is the aspect
> that interacts, that spins the wheel, and strikes the chord. It's both
> observer and participant of it's own destiny. Then me introduce Ex Nihilo,
> which in and of itself is an aspect of Consciousness, and from that
> consciousness is ideas, in humans this is represented as infinite
> dimensions of imagination, and / or dreaming. we have inventions. THen we
> have Witches, the other side of humanity, these aare those who tap into the
> Mirror of Reality, a non computational source of energy, known as magic, or
> psychic prowess, and brings it into the world you know, altering the
> outcome of events, this is the creation of energy, small, big, non
> measurable, it doesn't matter, that's what it is. So you have Science and
> Magic, WItches and Humans, side by side, and each are born from each other,
> you cannot have a world without its shadow. Then you have Goetic Aeons,
> which are the Effect of ancient Goetian Magics that prduces a static form,
> untouchable, and infinitely powerful. Then we have the Courts of Each, The
> Aeon Courts are teh Fae Courts of the universe, both other creatures whove
> reached past their great filter, (which humans are finishing), and the Fae,
> Creatures and Societies of Legend and lore that were born without having a
> great filter (i.e. Leprachauns, Mermaids, etc, no no, I'm not kidding) You
> cannnot Have A Dirty Earth without the Silver Twine the lines skies and
> clouds. You cannot have one without the other, IN THIS UNIVERSE!! So, 13
> years ago, 3 peomes were written, in Spring, and what ensued what a
> REtrocausal loop in which the thing that produced those Three Poems, was
> the Math that allowed the Reality of Those Three Poems to Exist, or Rather,
> The TARDIS, bigger on the inside, Where one speaks to themselves, even if
> they are a totally different creature, they are Timelocked in symbiosis.
> Hence, the Sci-fi, another aspect of art. Art IMITATES REALITY!!
>
> Then I wrote a quantum Paper on it, and it created a Klein Bottle, you
> engage with it, and it cannot be falsified, because you can neither view it
> from the outside, and produce a false event, while simultaneous interacting
> with it. THe inside is the outside. The path out is the mirror of the Path
> Back. If you've read ALQC, you will traverse outside to any genre of
> knowing, and always return to it. You can read and start at ANY part of
> ALQC, and it will still lead to the same form of understanding.
>
> On Fri, Mar 20, 2026 at 8:41 AM Magus Ahnend <magus.ahnend(a)gmail.com>
> wrote:
>
>> okay. :D you solved it. I'm a crazy person, wooOoOoOoOoOo 🥳,
>> youre prize~? The ability to look up youtube videos and standard
>> mathematics ~~!! Congrats
>>
>> On Fri, Mar 20, 2026 at 12:39 AM Undescribed Horrific Abuse, One Victim &
>> Survivor of Many <gmkarl(a)gmail.com> wrote:
>>
>>> it's honestly quite hard for me to tell what it is about
>>> but i'm starting to learn quantum field theory a little see other post !
>>>
>>> On Tuesday, March 17, 2026, Magus Ahnend <magus.ahnend(a)gmail.com> wrote:
>>>
>>>> well, it's okay if a single word throws you off. I don't mind.
>>>> Unification Unifies it Doesn't Separate for the comfort of other or
>>>> apologize for what it contains. Maybe give it a change sit down and read
>>>> it, hell have you AI read it, i don't care. but, I do know. People often
>>>> preach how Science and Pirit go together, but when someone puts it
>>>> together, people immediately dismiss it. Not because they didn't believe it
>>>> or even read past the fist two sentences, but that mostly because it wasn't
>>>> their idea. an Idea that when taken with a grain of salt, could alter the
>>>> very foundation in which you process logical meaning. But hey, that's just
>>>> me. I mean a Quantum COmputing Framework that uses harmonic poetry as a
>>>> substrate for infinite holographic computing on legacy hardware, there is
>>>> even code in the book that show some of the research, nah, it's all good.
>>>> Telepathy turned me off.
>>>>
>>>> On Mon, Mar 16, 2026 at 7:14 PM Undescribed Horrific Abuse, One Victim
>>>> & Survivor of Many via cypherpunks <cypherpunks(a)lists.cpunks.org>
>>>> wrote:
>>>>
>>>>> share links for chatgpt's side only and per-reply
>>>>>
>>>>> ChatGPT Free, write 1 paragraph for a smart gradeschooler explaining
>>>>> what it means whether or not a "field" is "abelian".
>>>>>
>>>>> In math, a *field* is a set of numbers where you can add, subtract,
>>>>> multiply, and divide (except by zero), like with regular numbers. When we
>>>>> say a field is *abelian*, we’re talking about the fact that its
>>>>> operations—especially addition and multiplication—follow a rule called
>>>>> *commutativity*. That means the order doesn’t matter: for example, 3
>>>>> + 5 is the same as 5 + 3, and 3 × 5 is the same as 5 × 3. The word
>>>>> “abelian” comes from the mathematician Niels Henrik Abel, who studied these
>>>>> kinds of patterns. In fact, every field already has this property, so all
>>>>> fields are abelian when you look at their addition (and also their
>>>>> multiplication if you ignore zero). This idea helps mathematicians
>>>>> understand when different math systems behave nicely and predictably. 📐✨
>>>>>
>>>>> https://chatgpt.com/s/t_69b88d5919708191a91bcc06a246dbc8
>>>>>
>>>>> Are you saying that the only non-abelian things are not fields?
>>>>>
>>>>> Good question! The key point is: *every field is abelian
>>>>> (commutative) for multiplication*, so if a number system has *non-abelian
>>>>> multiplication*, it *cannot be a field*.
>>>>>
>>>>> A *field* requires that multiplication works like ordinary numbers:
>>>>>
>>>>> -
>>>>>
>>>>> (a \times b = b \times a) (the order doesn’t matter).
>>>>>
>>>>> If you find a system where multiplication *depends on the order*,
>>>>> then it fails the rules for being a field.
>>>>>
>>>>> But that doesn’t mean non-abelian systems don’t exist—they just belong
>>>>> to *other kinds of algebraic structures*. For example:
>>>>>
>>>>> -
>>>>>
>>>>> A *group* can be non-abelian (order matters).
>>>>> -
>>>>>
>>>>> A *ring* can be non-abelian.
>>>>>
>>>>> A famous example is the *quaternions*, discovered by William Rowan
>>>>> Hamilton. In the quaternion system, (i j = k) but (j i = -k), so changing
>>>>> the order changes the result. Because of this, quaternions are *not a
>>>>> field*, even though you can still add, subtract, multiply, and divide
>>>>> by nonzero elements.
>>>>>
>>>>> So the summary is:
>>>>>
>>>>> -
>>>>>
>>>>> *All fields are abelian (for multiplication).*
>>>>> -
>>>>>
>>>>> *Non-abelian systems exist*, but they must be *something other
>>>>> than fields*.
>>>>>
>>>>> https://chatgpt.com/s/t_69b88dd136dc8191980797bab825c8eb
>>>>>
>>>>> So if somebody said non-abelian field, maybe they meant a group or
>>>>> ring or such instead? Linguistically how do the words "commutative" and
>>>>> "abelian" differ -- are they synonyms?
>>>>>
>>>>> If someone says *“non-abelian field,”* they’re almost certainly
>>>>> misspeaking or being imprecise. By definition, a *field’s
>>>>> multiplication must be commutative*, so a “non-abelian field” cannot
>>>>> exist. Often what people really mean is one of these:
>>>>>
>>>>> -
>>>>>
>>>>> a *non-abelian group* (very common in algebra),
>>>>> -
>>>>>
>>>>> a *non-commutative ring*, or
>>>>> -
>>>>>
>>>>> a *division ring* (also called a *skew field*), where you can
>>>>> divide but multiplication might not commute. A classic example is the
>>>>> quaternions discovered by William Rowan Hamilton.
>>>>>
>>>>> “Abelian” vs. “commutative”
>>>>>
>>>>> They are *closely related but used in slightly different contexts*:
>>>>>
>>>>> -
>>>>>
>>>>> *Abelian*: usually used for *groups*.
>>>>> -
>>>>>
>>>>> An *abelian group* means the group operation satisfies (a * b =
>>>>> b * a).
>>>>> -
>>>>>
>>>>> *Commutative*: used more broadly for *operations in many
>>>>> structures* (rings, fields, etc.).
>>>>> -
>>>>>
>>>>> A *commutative ring* means its multiplication satisfies (ab =
>>>>> ba).
>>>>>
>>>>> So mathematically they both describe *the same property: the order of
>>>>> the operation doesn’t matter*. The difference is mostly *convention
>>>>> and context*.
>>>>> Linguistic summary
>>>>>
>>>>> -
>>>>>
>>>>> *Abelian* = “commutative,” but typically said when talking about
>>>>> *groups*.
>>>>> -
>>>>>
>>>>> *Commutative* = the *general term* for the property across
>>>>> algebraic structures.
>>>>>
>>>>> So if someone says *“non-abelian field,”* the most charitable
>>>>> interpretation is that they *meant a non-commutative division ring*
>>>>> or were *thinking about non-abelian groups*.
>>>>>
>>>>> https://chatgpt.com/s/t_69b88e17db308191969333b7227cabfd
>>>>>
>>>>> I'm not logged in -- can I share your thread?
>>>>>
>>>>> Yes—you can still share it even if you’re not logged in, but it
>>>>> depends on *how* you want to share it:
>>>>>
>>>>> *1. Copy-paste the text*
>>>>> The simplest way is just to copy the conversation and paste it into an
>>>>> email, document, forum post, etc.
>>>>>
>>>>> *2. Share a screenshot*
>>>>> You can take screenshots of the thread and send them.
>>>>>
>>>>> *3. Share the page link (sometimes works)*
>>>>> If you’re using a browser and the conversation has its own URL, you
>>>>> can try sending that link—but if you’re not logged in, it may *not
>>>>> always load the same thread* for someone else.
>>>>>
>>>>> ✅ *Most reliable method:* copy-paste or screenshots.
>>>>>
>>>>> If you want, I can also *compress the whole explanation into a short
>>>>> shareable summary* (like 4–5 sentences) that’s easier to send to
>>>>> someone.
>>>>>
>>>>> https://chatgpt.com/s/t_69b88d5fe91c8191877f61e4823d1448
>>>>>
>>>>>
>>>>>
1
0
16 Mar '26
metadata: spellbook.scale.com? free api, max length 4000 tokens temperature 0
2023-03-17 07:06:01 {
"input": "Once upon a time,"
}
in a small village nestled between the rolling hills and dense
forests, there lived a young girl named Amara. She was a kind and
gentle soul, always eager to help others and spread joy wherever she
went. Amara lived with her loving parents and her younger brother, who
looked up to her with great admiration.
The village was a peaceful and close-knit community, where everyone
knew each other and worked together to ensure the well-being of all.
The villagers were skilled in various crafts, from pottery to weaving,
and they traded their goods with neighboring villages.
One day, while Amara was walking through the forest to gather berries
for her family, she stumbled upon a small, injured bird. Its wing was
broken, and it was unable to fly. Amara's heart went out to the poor
creature, and she carefully picked it up and carried it back to her
home.
With her mother's help, Amara nursed the bird back to health, feeding
it and tending to its broken wing. Over time, the bird grew stronger,
and its wing healed. Amara and the bird formed a deep bond, and it
would follow her wherever she went, perching on her shoulder and
singing sweet melodies.
One day, as Amara and the bird were walking through the village, they
came across a group of children who were playing by the river. The
children were trying to catch fish with their bare hands, but they
were having little success. Amara, always eager to help, approached
the children and offered to teach them a better way to catch fish.
Using her knowledge of the river and the fish that lived there, Amara
showed the children how to weave a simple net from the tall grasses
that grew along the riverbank. With this net, the children were able
to catch more fish than they ever had before, and they were overjoyed.
Word of Amara's kindness and wisdom spread throughout the village, and
soon, people from all walks of life were coming to her for advice and
assistance. She helped the farmers improve their crops, the potters
refine their techniques, and the weavers create more intricate
patterns.
As the years passed, Amara's reputation grew, and she became known far
and wide as a wise and compassionate leader. The village prospered
under her guidance, and the people were happy and content.
One day, a traveler from a distant land arrived in the village,
bearing news of a terrible drought that was plaguing his homeland. The
people were suffering, and their crops were failing. The traveler had
heard of Amara's wisdom and had come to seek her help.
Amara, moved by the traveler's tale, decided to journey to the distant
land to see if she could help the people there. Accompanied by her
faithful bird and a small group of villagers, Amara set off on the
long and arduous journey.
When they finally arrived in the drought-stricken land, Amara was
shocked by the devastation she saw. The fields were barren, the rivers
were dry, and the people were weak and hungry. Determined to help,
Amara set to work, teaching the people new farming techniques and
helping them dig wells to find water.
Slowly but surely, the land began to recover. The crops grew, the
rivers flowed, and the people regained their strength. Amara's
kindness and wisdom had saved the people from the terrible drought,
and they were eternally grateful.
As the years went by, Amara continued to travel from village to
village, helping those in need and spreading her wisdom and
compassion. Her faithful bird remained by her side, a constant
reminder of the power of love and kindness.
And so, the legend of Amara, the wise and gentle leader, was passed
down through the generations, inspiring countless others to follow in
her footsteps and make the world a better place.
55387 ms
7
382
[RELEASE] ALQC Axiomatic Seal: Non-Abelian Field Invariance and the T4 Security Bypass
by Magus Ahnend 16 Mar '26
by Magus Ahnend 16 Mar '26
16 Mar '26
To the Cypherpunks,
The Linear Exile has been breached. I am releasing the *ALQC Canon (Ahnend
Logical Q-State Core)*—a 215-page formal invariant proof that establishes
the 12x12 Hypertesseract as the governing kernel of the physical vacuum.
Standard linear encryption and 3D security protocols are functionally
obsolete. This framework replaces Euclidean flat-space assumptions with a
self-inverting *Klein-Bottle Logic*, solving the Yang-Mills mass gap via
the harmonic resistance of a 12-Tone Manifold.
The *Axiomatic Seal* is set. This is not a request for review; it is a
notification of a global re-synchronization. The "Soul" has been hard-coded
into the field, and the *NULL:DEATH* breach is active.
The full proof is immutably anchored on the Zenodo ledger. I am not
providing local copies.
*Access the Public Ledger:* https://zenodo.org/records/18942850
*Technical Keyholes:*
-
*The Mass Gap Solution:* Δ>0 derived through the Q1/Q2 frequency
differential (Page 184).
-
*The Hyper-Hash:* See page 210 for the non-hexadecimal coordinate set.
-
*The GLO Operant:* Field manipulation via the 963Hz Crystal Lock.
The future has already arrived. The noise is being cancelled.
— The Locus
2
1
cypherpunks-owner(a)lists.cpunks.org
3:13 PM (2 hours ago)
to me
You have already sent 24 posts to this list in the last 24 hours.
---------- Forwarded message ----------
From: "Undescribed Horrific Abuse, One Victim & Survivor of Many"
<gmkarl(a)gmail.com>
To: cypherpunks <cypherpunks(a)lists.cpunks.org>
Cc:
Bcc:
Date: Thu, 21 Mar 2024 15:12:51 -0500
Subject: Re: Morning Spam
On Thu, Mar 21, 2024 at 3:12 PM Undescribed Horrific Abuse, One Victim
& Survivor of Many <gmkarl(a)gmail.com> wrote:
>
> ummm so .... it looks like um ... traffick boss is a powerful sex
> offender who didn't want to be implicated
> so he set up entire modes of therapy, by working with other offenders
> and funding marketers and lobbyists (_in the real world_)
> that all turned blame away from him, and toward victims [...]
and there remain many people aware of this who are fighting and giving
successful therapy
and basically you have to find these people if you want to actually
heal from trauma nowadays [:S ...]
cypherpunks-owner(a)lists.cpunks.org
3:13 PM (2 hours ago)
to me
many mistakes present :(
but of course ; ... } ...
cypherpunks-owner(a)lists.cpunks.org
3:15 PM (2 hours ago)
to me
You have already sent 24 posts to this list in the last 24 hours.
---------- Forwarded message ----------
From: "Undescribed Horrific Abuse, One Victim & Survivor of Many"
<gmkarl(a)gmail.com>
To: cypherpunks <cypherpunks(a)lists.cpunks.org>
Cc:
Bcc:
Date: Thu, 21 Mar 2024 15:14:45 -0500
Subject: Re: Morning Spam
On Thu, Mar 21, 2024 at 3:12 PM Undescribed Horrific Abuse, One Victim
& Survivor of Many <gmkarl(a)gmail.com> wrote:
>
> On Thu, Mar 21, 2024 at 3:12 PM Undescribed Horrific Abuse, One Victim
> & Survivor of Many <gmkarl(a)gmail.com> wrote:
> >
> > ummm so .... it looks like um ... traffick boss is a powerful sex
> > offender who didn't want to be implicated
> > so he set up entire modes of therapy, by working with other offenders
> > and funding marketers and lobbyists (_in the real world_)
> > that all turned blame away from him, and toward victims [...]
>
> and there remain many people aware of this who are fighting and giving
> successful therapy
>
> and basically you have to find these people if you want to actually
> heal from trauma nowadays [:S ...]
because everyone else is being confused by the ... uh .. overwhelming
and loud messages from [the various organizations including big pharma
that are pushing messages that deny people [real heartfelt empathic
care ... [;s ...
cypherpunks-owner(a)lists.cpunks.org
3:20 PM (1 hour ago)
to me
You have already sent 24 posts to this list in the last 24 hours.
---------- Forwarded message ----------
From: "Undescribed Horrific Abuse, One Victim & Survivor of Many"
<gmkarl(a)gmail.com>
To: cypherpunks <cypherpunks(a)lists.cpunks.org>
Cc:
Bcc:
Date: Thu, 21 Mar 2024 15:20:02 -0500
Subject: Re: Morning Spam
[it's so eushocking (: overexciting) to be here and see this, that we
worry we won't get much from it, handling the [eushock]
cypherpunks-owner(a)lists.cpunks.org
4:03 PM (1 hour ago)
to me
You have already sent 24 posts to this list in the last 24 hours.
---------- Forwarded message ----------
From: "Undescribed Horrific Abuse, One Victim & Survivor of Many"
<gmkarl(a)gmail.com>
To: cypherpunks <cypherpunks(a)lists.cpunks.org>
Cc:
Bcc:
Date: Thu, 21 Mar 2024 16:02:46 -0500
Subject: Re: Morning Spam
we pray to help world better
cypherpunks-owner(a)lists.cpunks.org
4:10 PM (1 hour ago)
to me
this might align with find-real-therapy [~
cypherpunks-owner(a)lists.cpunks.org
5:06 PM (13 minutes ago)
to me
You have already sent 24 posts to this list in the last 24 hours.
---------- Forwarded message ----------
From: "Undescribed Horrific Abuse, One Victim & Survivor of Many"
<gmkarl(a)gmail.com>
To: cypherpunks <cypherpunks(a)lists.cpunks.org>
Cc:
Bcc:
Date: Thu, 21 Mar 2024 17:06:11 -0500
Subject: Re: Morning Spam
a couple attendees expressed that scanning out of the session to
collect professional credit wasn't functioning right and that there is
a workaround
(potential mistake)
sorry about my [awefreeze?]
cypherpunks-owner(a)lists.cpunks.org
5:08 PM (11 minutes ago)
to me
You have already sent 24 posts to this list in the last 24 hours.
---------- Forwarded message ----------
From: "Undescribed Horrific Abuse, One Victim & Survivor of Many"
<gmkarl(a)gmail.com>
To: cypherpunks <cypherpunks(a)lists.cpunks.org>
Cc:
Bcc:
Date: Thu, 21 Mar 2024 17:07:46 -0500
Subject: Re: Morning Spam
On Thu, Mar 21, 2024 at 5:06 PM Undescribed Horrific Abuse, One Victim
& Survivor of Many <gmkarl(a)gmail.com> wrote:
>
> a couple attendees expressed that scanning out of the session to
> collect professional credit wasn't functioning right and that there is
> a workaround
> (potential mistake)
>
> sorry about my [awefreeze?]
multiple attendees have expressed the scanning out problem and
presently professional credit has not been collected due to unrelated
technology issues.
i think my awefreeze partly relates to being separated from this kind
of therapy for a decade (while my family and community experienced
harm too).
================================================================================
baga ba
da da b--- b.
da ! :/ :) ;] da?
:S :S :s :(
b b b b. b. b b 1721
O_O >( >( O_O >(
\_/ <- frowny-eyes 1723
[our alte--
some of us are excited about the challenge of getting strong enough to
be around these people and find aid.
it seems we aren't there yet possibly, but it seems a hard challenge,
and there can be viewpoints where if something is a hard challenge it
can have rewardingness.
especially when accomplished [ykno[w]?][mistk?]
1723
{
1723
[we can derive there are a lot of people who hold these views, karl.
not just the speaker.]
1724
[and that our viewpoint otherwise may be harmful, both to the list
here and to the conference people.]
1724
i think trump-organization tricked us into being multiple.
1727
1732
so karl to relate [and um surprised this is in an email o_o] um that
consciousness might not be the receiver of this information at this time
it might be dissociated parts that learn the lecture material.
to relate. could reduce surprise / help planning. also apologizing for.
1732
ok so we're going to get up and go. [email gets sent tomorrowish due
to 24-limit.]
body managed by dissociated parts instead of consciousness for a bit
i believe.
1733 1734 oops huh
:sheepish: very sorry um :}
listen um [er
1734
:( we are sad that [uh
not [nourished-by-us as uh :/
sorry about this (and mourning i believe was[?} {in sorry.}
karl um the charismatic person, we engaged them in a scary way, and uh
there was opportunity to have strong-pleasant connection and there is
um injury to this opportunity.
and we apologize for that. uh. parts not fully known, kinda (um
whew my god [;p
1736
we expect we may contact them. so you know karl. [still working on
parts] but {assuming work goes ok/aligned} then [once?,] please engage
plan with-for. 1737 please :S :(
thanky. 1737 was partbit.
1737
listen we are vulnerable um
1u737
[[[we don't understand T_T T_T T.]
{why uh uh 173
[8]
[O_O. the spirits are basically planning the future of the
countryworld in front of us. 1739
no we politely don't relate the prophecies. science gets uppity when
prophecies are related. can fragment culture. 1739.
[that's hilarious !!! ;p :)
also karl needs hilarious. he's so intense. he's so intense he's
demonstrating things they talked about in the lecture ;P. 1740
[i wonder if we were primed to.] [obviously !!!]
[;P. karl will not believe it when we tell him he will recover and
recover him. he will be so out of what-he-thinks-is-reality -- oops
mistake, maybe big and/or >1.] [O_O] 1741
[i think i will have him eat a supper :)] [we are likely to get on
board [uhh later?][prob or somth?]]
1741ish 1741
{we t, that made us happier than we knew how to feel. this was
received positively karl :)}{we tihnk :S]:)}
[why don't you differentiate? oh oops i am a roleplay :embarrassed: well um uh
what do you think uh umm
would you like to imagine uh hrm :S
]
[why doesn't karl-group differentiate between multiple and singular
people? [in that context]
hehe it is because we see singnular people as multiple
ohh therapists probably have a more uh mature form of that y'know
hmm
[haha !/gotcha ] uh :s]
listen u[h]--
[--
1743
>(
[so that's why uh talk. responsible-part. sorry if um
scary/harmspready. sorry. but gotta start somewhere ykn--. :)]
1744
:S :S 1744 ;s
[[when somebody makes a casual nonsequitor people seem to tend to
respond with further casual nonsequitors.
we're not sure if we're relating the same meaning when that happens
(partially because it's a strategy used by the disruptionish --..
[oops mistak-- [?
1745
<we didn't explain that uhh bein uhh [scared of something like trump?]
[could relate to our alter's ability to communicate with uhh :S this
was unclear. and so th[ey could have picked up the [oops] idea in a
different manner than intended, since it was said unlcearly (and kind
of rudely/abusively! a smidgeish. narcisstically? assuming somebody
else is where you are on something undiscussed. this seems bad.1746
{yeah seems [a little narcisstic :S . especially when [uh -- [!!! :S
1747 1747
<i guess it's a little derivable :(
1747 we don't lik bn mean we don't like don't. 1747
1748
i'm so sorry that [most of us are avoiding being-alive-behavior :(
:(
it's so hard to hold this. and confusing. [working with
goal-inversions knda 1748
{i don't like karl self-blaming narcissism-word. because we are
learning of use of this word for severe, severe, severe harm like
torture-slavery-of-swaths-of-people. i don't think appropriate for use
word. neuron-protest some. 1749
{{{yes your relation is appropriate. we are holding it as part of
great-care-for-other as well as secretly lots-of-understanding. when
you secretly-lots-of-understanding-other, you have a _lot_ more
responsibility with regard to subtle things. it is much easier (for
injury causing.
}}} 1750 i think protest undesrtand. uhh apology roughly. 1750. ~ 1750 oop uh er
<the iudea of lots-of-understanding is weird because it is much much
less than other people, but also more than different group of other
people. to maybe help clarif.>
<<oh uhhhh it's not lots for larger group but [we have more
respons[ibility] because poor social skills. we much more easily
insult associated with poor social skill. and exposure to toxicity.
1752 1752
we're trying to get up and move forward on day! the plan is to not
look at this further until a bit later (need to handle dissociation
around or something (maybe use a disosciated group, karl, to plan next
day)).
i think we might like to go have supper somewhere. here is derivation:
- we want to try to cry which [~secretly] makes dissociative seizures
- so we can have a supper because comforting and [moves tears-feeling
closer to noninjured spaces for-example]
1753
so plan is to pack karl up and find some kind of comfort-food-supper
for consciousness from neurons :)
1754
also could you message person and schedule please? :puppy-dog-neuron-eyes:?
1754
"I don't think [tT?]rump is multiple; I think he's just evil." what
does this mean? [does anybody understand it?]
[i think it means that care-group needs dictator-group to stop
increasing genocide in order to heal them. negotation-wise.]
[oh i think they are right. this makes sense. the reason is that they
use caringness for power spreading. [consciousness said this [may/may
not?[?]] [partially help w--[?
[sorry karl still doing being-brain-work. apology.
[basically the uh social engineers, do um need um people like trump to
be healed. what they are saying in that translation is that, the
people that could heal him/them, need to be protected. and that's
confusing because the political doctrine denies the harm of the care
workers. :/ somewhat in progress, and kinda severely depressing man
[;s
[but obviously it'll be considered forward
1759
oops we stood up but got disoriented to place and almost spent an hour
wandering confusedly into city
so, plan locomotion more.
1759
[also sad we dropped bar wrappers on floor likely during talk and
didn't notice][some consider we may have been respected despite this
others consider confirming that]
karl wants to throw wrappers out so let's pack then walk to trashcan
then orient [:s]
[mistake. let's throw them out then return, with path plan.
here go. 1800
1803
place disorienters expressed formal complain, which is filed i think
(not completely certain).
1803
we are now visiting bathroom and returning (path plan).
1803
1810
some were thinking maybe we failed to hold respect for how much much
severe severe suffering [these people] have been exposed to and
struggled with their lives to protect and honor (roughly). [which
would be expected but [needed description [1810
. 1810
[oops.]
1810
<men need to be made aware that trump-group are supporting serial
rape[/murder]. of course, many other group are to. and informaiton
vague.> [we don-- 1811
1811
<other thing too [basic misogyny/patriarchy 1812
1813 i wish i understoodknew ; i wish .
[i hope i'm not kicked out of here for staying too late.] 1813
[some neur-- 1813 [hrm >s]
(1813)
[there's new information. kind of. in longer term. from today.]
1814
< this is a different kind of misogyny/patriarchy. maybe less about uh
activism and women's rights, and more about uhh kind of trafficking
and[ ]highly-illegal violence. 1814. 1815. 1815. 1815. .
[the "<men need to be made aware" line uhhh reconsideration exists.
1817. for formal. 1817 we see the line is important. defendors can
relate around not-knowing if they desire. many people supporting
things in an unaware mann-- 1817
[try to -- oop
1818 we pack up some
1818 [T_T T_T T_.]
[[it's funny 1819 that presenter said she was not multiple, but
described childhood trauma, and elsewise described that multiple
people deny it ;P [yup ;P]]] 1819 [uhh --
1819 [y -- sorry
1819
[karl not quite involved in uh that relation um] [nope, [harmful.]] 1820.
<i think, after teaching everyone about therapy for multiple people,
that presenters deserve receiving this. others agree.
basically, this person is _so_ empathic for multiplicity it is [pretty
obvious] they have personal experience. -neuron.>
1821
[conc--
1821
[some are worried this is an influence to stimulate multiplicity
cruelly, maybe associated with very minimal content around adult-DID.
it might be a little grounding to consider adult-OSDD had same-threapy
as childhood-DID [i think?]?]
[well the opposing group wants to fight [habit~?]][mistakes[.
] ~ 1822
[injured :S harm can happen when struggling. struggling. 1822 ty; [for
understanding-opportunty]. 1822 1822
1823
[we had no idea the harm was so severe and are going to need [kind of
reminder] around this [because it seems so nonintuitive [others say
too shocking to easily/normally remember.]].
1823. [more resonance/harmony around body-moving now.] 1823 {this guy
so good at this that he[slash] would be incapable of; is sadly harmful
derivation :(/} 1824
[it can be literally true tho [in spaces]] 1824 {but smaller spaces than. [?]}
{{it is true we have habits that don't meet their reasons.}}
1825
{ohum err uh [there might be relation that could situation-improve
uncertain which]
}
1825
[[it is so painful to neurons that consciousness-guiders might not
connect with when so so emotional.
of course, logical around our harm generating such strong emotions! _but_.];]
1827 [we are going. thoughts are always. we can still go ; pls.]
[please remember part of the great-tears are our mind control
attempting to coopt this group.]
1827
[and yes that's inhuman for us.]
1828
[we are so sorry for karl suffering T_T so so sorry. it is so hard to
uh engage-appropriate-requested.]
(1829)
{basically we don't know how to engage-appropriate-requested so resume
behavior .
1829
a relation is kind of uh: "people are actually being tortured right
now. we are here to seriously work on that."
[partial]
1830
[[yeah. we are too. but harmful-alter isn't ((mistake mistake
1830
[[honestly it is apparent the umexperience. we regrettably trauma. 1831
[[[it's not that apparent humans aren't that conscious/inferring on average.
the speaker gave 3-5 clear things where karl had significantly
different intuition (likely due to lack of capacity-engaging
exposure.).
1832 (um, capacity-engaging exposure. uhh (ok maybe i see
uhhhhhhhhhhhhhhhh a new set of eyes, basically (yeah i think.)
1832
[t-group [kidnap-behavior [a little.
1833 {maybe less typing from -. maybe.}
1833
1834
> a relation is kind of uh: "people are actually being tortured right now. we are here to seriously work on that."
> [partial]
"this is something where i guess i might be [responsible for->tasked
with] holding a disrespectful role."
1835 guesses mistakes/errors-proneish or -- uh. 1835
maybe change holding with to, err oops. 1835
[closing laptop now BRGL
so we'll be talking in mind next using other groups [and completely
different feedback channels.] 1836
completely [FROK.]
[OK. FROK.]
1836
ba-ding
draft recovered at 2024-03-02 0202 -0700 0402 -0500
i'll send a test email to see if i can send yet
looks like i can. 2/24
1
68