It is understood that waves are produced when there's an oscillation in some medium, for sound that would be air, for light that would be the electromagnetic field, but when we describe matter as waves then what is the medium that is waving? In other words, what medium is the wave function describing the oscillations of? what is actually waving when we describe an electron as a wave?

Also, when we perform the double slit experiment with light, is it the electromagnetic wave or the wave function that is causing the interference pattern? Is the wave function of the photon actually the same as its electromagnetic wave or are they two unrelated concepts?

>>16699836 (OP)
A wave function is a section of a C-line bundle.

>>16699836 (OP)
It's an information encoding about very small things that happens to develop in a wave-like pattern.

It's a function shaped like a wave.

>>16699883
>>16699891
>>16699993
Can someone please write a non-AI generated answer?

>>16699836 (OP)
a function that represents a wave.

It's a subcategory of wave equation used to represent certain quantum waveforms. Obviously.

>>16699836 (OP)
The term wave is used just because the PDE that characterizes the solution seems like the original vibrating string PDE. I've never heard any other justification for it.

>>16700340
I wrote the answer (>>16699883) that's the definition in geometric quantization. Git gud, casul.

>>16700657
Get some reading comprehension and read the OP, that's not what I was asking.

>>16699836 (OP)
>for light that would be the electromagnetic field
le exaggerated sigh
no
the electromagnetic field is a field, i.e. a mathematical construct. points in spacetime do NOT have little arrows hanging off them with labels saying how much electrical oomph there is in them

>>16699883
I fucking hate you mathematicians and your made-up language
what the fuck is a C-line

>>16700689
>points in spacetime do NOT have little arrows
Of course, not in a literal sense, but we assign such arrows to points in space anyway when solving problems.
I understand that it is an abstract field and that there is really no electric or magnetic field extending through all the universe. But it's a useful abstract way to model light as an electromagnetic wave.
Could the same idea be used to describe matter waves? For example that electrons are manifestations of an "electron field"?

>>16700690
A C-line bundle is a vector bundle who fiber is C, the set of complex numbers. I should have been a bit more precise and said wave functions are sections of the said bundle.

>>16700794
>>16699883
Fuck off, no serious person thinks of wavefunctions like this. You are a clown

>>16700799
Any person who's ever done QFT in curved spacetime knows all these things. It's called geometric quantization. As I said, git gud.

>>16700794
>C
oh you meant C
and what does this "sections through bundle" approach buy you?

>>16700756
>Could the same idea be used to describe matter waves?
yes, this is commonly done

>>16699836 (OP)
>In other words, what medium is the wave function describing the oscillations of? what is actually waving when we describe an electron as a wave?
This is mostly philosophy. What is "space" even? For a quantum field, we just use [math]\mathbb{R}^4[/math] as indices for operators that all act on a single universal wave function. The interpretation of the indices as being "close" or "far" from each other comes from how we define the algebraic relations of the operators.

>Also, when we perform the double slit experiment with light, is it the electromagnetic wave or the wave function that is causing the interference pattern? Is the wave function of the photon actually the same as its electromagnetic wave or are they two unrelated concepts?
First of all, I recommend Lamb's article on the term "photon" and why he thinks it's retarded (https://link.springer.com/article/10.1007/BF01135846). I tend to agree with him, usually it is better to think in terms of the fields instead.
The way I think of it is like this: In a double slit experiment, you excite an electromagnetic field mode with a (close to) definite wave number. But this mode is short-lived because of interactions with the atoms in the slits; very quickly, you end up in a superposition of states where the occupation of the modes can be described very similarly to the classical solution of the problem. You then have another transition where one of the atoms in the photo plate ends up in its excited state, and the probability of this transition to happen at each point also ends up proportional to the classical amplitude.
But at every moment, you only have [math]\textit{one}[/math] wave function, which simultaneously describes all of the electromagnetic field modes and all the atoms in the experiment.

>>16701012
It buys me a coordinate-free way to talk about wavefunctions. Try doing quantum mechanics in non-Cartesian coordinates. You will quickly see how undergraduate heuristics like “a wavefuncfion is a function from R^3 to C” falls apart. Then realize that curved manifolds (such as our spacetime) don’t admit a global Cartesian coordinate system, so that heuristic doesn’t even make sense.

Meanwhile, I can freely talk about quantizing particles on any space with this approach. For example a particle on a sphere. A C-line bundle immediately tells me what spin is.

>>16701068
>I recommend Lamb's article on the term "photon" and why he thinks it's retarded
Kek, this was entertaining to read. It's kind of funny how he dunks on photons as particles, but is fine with calling other particles, you know, particles. The presentation is also very comfy. It's like your grandpa telling you stories from his youth. But the message is clear to anyone who's done quantum mechanics in any serious capacity. And I think the last page of Lamb's article really nails it.
>The "Complementarity Principle" and the notion of wave-particle duality were introduced by N.Bohr in 1927. They reflect the fact that he mostly dealt with theoretical and philosophical concepts, and left the detailed work to postdoctoral assistants. It is very likely that Bohr never, by himself, made a significant quantum mechanical calculation after the formulation of quantum mechanics in 1925-1926.
People (even physics professors, surprisingly enough) always love making these hand-wavy heuristic arguments about muh wave-particle duality or muh uncertainty principle, even though they were ad hoc "intuition" of the Old quantum theory.

And when you start doing QFT, all this vague lingo disappears completely. You're dealing with operator-valued fields. No uncertainty principle or wave-particle duality is used to actually derive any results or compute any cross-sections. There is simply none of that lingo in the math.

>>16701142
>It's kind of funny how he dunks on photons as particles, but is fine with calling other particles, you know, particles.
To be fair, "particles" are much less misleading for massive fields. You really do have a (semi-) classical limit where the dynamics are described by corpuscles, whereas the classical limit of the electrodynamic quantum field is still a classical field.
It gets interesting for a solid's displacement ("phonon") field, which can have all kinds of excitation spectra. Depending on the context, I suppose the classical limit could be best described by a field or a by a corpuscular theory.

>>16700856
yeah, you're not a physicist at all. you're just a mathematician who is trying to ape physics

>>16701106
our spacetime is not curved on the scale of quantum interactions
wtf are you on about

>>16701415
>dude if you don't handwave instead of being precise you're not a physicist
I have given you the exact physical motivation behind what I said. Wavefunctions have to be described using the bundle language of differential geometry, because we live on a curved manifold called spacetime. Without such a language, your description might as well be gobbledygook. Not only I have given you the physical motivation, I have also given you the theoretical motivation. Geometric quantization provides a precise algorithm for quantizing a classical system. There's ambiguities arising in certain cases (particularly on some curved manifolds) where there's no canonical choice of the Hilbert space. These things show up in e.g. the Unruh effect. That two observers, one in inertial and one Rindler frame, observe either empty space or a thermal bath of particles, reflect this non-unique choice of the Hilbert space.
>>16701640
Didn't know particles didn't have mass and/or energy. Quantum fields suddenly have a vanishing stress-energy tensor? News to me.

Theres likely a model of physics where you can treat substrate reality as informational interactions between entangled photons. Theyre massless, travel at c and dont experience time. Thats how holographic theory is derived. Planck scale resolves zenos paradox.

>>16702034
blah blah. Stop coping, you're not a physicist.

>>16702034
oh, you've quantized gravity? can you post a pic of your nobel prize diploma?
fucking faggot

>>16702135
You’re the one who’s not a physicist it seems. Are you even interested in understanding natural phenomena or do you just want to play in a lab like a child?

>>16702135
You’re the one who’s not a physicist it seems. Are you even interested in understanding natural phenomena or do you just want to play in a lab like a child?
>>16702154
Atomic physics and even nuclear physics is well within the scale of classical gravity aka general relativity. Quantum gravity effects only begin to manifest at Planck scales or around 10^-35 m. Atomic physics happens at angstrom scales, so 10^-10 m. This is a 25 order of magnitude difference. For comparison, this is the same order of magnitude difference as between the observable universe and kilometer scales (so like a small town).

Retards like you who make these magical assumptions that “gravity doesn’t matter at atomic scales because we can’t observe it” are genuine solipsists. It’s like stumbling upon a fallen tree in a forest and saying “well I can’t be sure that tree fell at any point because nobody saw it fall”. We have empirical confirmation of GR, so by extrapolation it should hold at atomic as well. And quantum gravity would have a negligible effect at such scales as I have explained. Retard.

>>16702212
you're basically claiming that quantum field potential bends spacetime
fine, show your work then

>>16702212
there's nothing in natural phenomena which indicates that wavefunctions are 'sections of line bundles'. That's just made up bullshit

>>16702244
nothing he said is mathematically incorrect
he just failed to show how it's relevant to physics

>>16702234
It's called semiclassical gravity.
[eqn]G_{\mu\nu} = \langle T_{\mu\nu}\rangle[/eqn]
where [math]\langle T_{\mu\nu} \rangle[/math] is the expectation value of the stress energy operator. It's an operator because it's composed of quantum fields, which are operators. This is a standard framework in which Unruh derived the Unruh effect and Hawking derived the Hawking radiation. Both of these are semiclassical approximations and don't require quantizing the gravitational field.

If your retarded ass would have taken quantum beyond undergraduate level, you would have easily drawn parallels to semiclassical electrodynamics. There, we do
[eqn]\partial_\mu F^{\mu\nu} = \langle J^\nu \rangle[/eqn]
where [math]\langle J^\nu \rangle[/math] is the expectation value of the fermionic current. It lets you, for example, compute absorption and stimulated emission in atoms without invoking QED aka quantizing the electromagnetic field. Section 5.8 of Sakurai 2nd edition. We don't need to quantize the electromagnetic field in this case, because the distance scales are large enough that classical electrodynamics, with its linear electric and magnetic fields, works just fine and QED would be overkill (the corrections would be way too small to matter).

I repeat. Git gud.

>>16702268
>>16702034
>Didn't know particles didn't have mass and/or energy. Quantum fields suddenly have a vanishing stress-energy tensor? News to me.

>>16702273
where in Hawking or Unruh's work do they talk about wavefunctions being sections of line bundles? note how you'll deflect now and start coping.

>>16702273
>the expectation value of the stress energy operator
is a purely mathematical construct
Unruh radiation doesn't exist, Hawking radiation doesn't exist either
you are being very cagey calling them "approximations" - you have to renormalize AND hide the imaginary terms under the rug and only then can you come out with observables that nobody has ever observed because "a single particle in a vacuum" is not something that exists out there

>>16702268
he's incorrect because nothing he said is relevant

>>16702297
>where do Hawking and Unruh use differential geometry to talk about QFT in curved spacetime?
Geez, I don't know. Maybe when they talk about expectation values, which require wavefunctions? Because I have already stated in this very thread that the only way you can talk about wavefunctions on curved manifolds is as sections of a [math]\mathbb{C}[/math]-line bundle. I recommend you consult these
https://www.youtube.com/watch?v=C93KzJ7-Es4
https://ncatlab.org/nlab/show/geometric+quantization

Hawking's paper:

https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-43/issue-3/Particle-creation-by-black-holes/cmp/1103899181.full

ctrl+f: bundle
0 results

>>16702311
>starts deflecting and lying as expected
of course they talk about wavefunctions you retard. show me where they talk about line bundles

>>16702301
Yeah, bro, they don't exist. Because... they just don't ok. Even though we don't have actual empirical null results regarding those. People like you have actual brain damage and fail to make basic deductions.
>>16702304
Cope and seethe.

>>16702316
>DUDE DEFLECTION
>DUDE LIES
You're retarded. Stay in your lane.
>>16702315
Now do the same for Bohr's paper on the hydrogen atom and ctrl-f "Hilbert space". Hint: the language of principal and associated bundles was developed at about the same time as Hawking radiation. We have since improved our understanding of both significantly. By "we" I don't mean you. You are completely underqualified to talk about this. So pipe down.

>>16702317
kindly go fill up Russel's teapot, I feel like a cuppa
I like how you avoid the rest of the argument but, just to rub it in further
- you cannot "simply" go from Minkowsky space to Einstein space basis, rewrite your field equation and call it a day; string theorists tried it and got stuck in there for 40 years
- gravitons would have to be absolutely everywhere if they exist, since if as you say some elementary particles have rest mass, they must interact gravitationally with other massive particles (of course it doesn't really happen like that, if you fix the momentum of a particle to, for example, zero, it will smear its position out to the edge of the universe so to talk of "rest mass of the electron" is just stupid)

>>16702323
fuck off fascistic retard, i am free to call out cranks and crackpots like you
>b-but it wasn't developed then
then you should be able to quote some significant physics result which does use line bundle language instead of quoting papers which don't talk about line bundles at all and then claiming that they validate your pseudointellectual wankery, fucking moron

>>16702331
>>16702323
>inb4
by line bundle language, i mean one where wavefunctions are treated as sections of line bundles. don't start posting links to gauge theory like an illiterate dumbfuck

>>16702328
>muh Russell’s teapot
Both Hawking radiation and the Unruh effect give you the precise conditions under which they occur. This is absolutely nothing like muh Russell’s teapot. Your thinking is that of a flat earther, quite literally.
>the Earth is curved
>b-b-but it looks flat!
>yeah, but you can see ships disappear beyond the horizon
>t-t-this is bullshit. The earth must be flat!
>so explain why they disappear
>I have never seen them disappear myself, so you’re lying
>You can even measure the earth’s diameter by comparing shadows in Alexandria and Syene at equinox
>dude, I’ve never been there! Stop deflecting.

>>16702331
I have kindly given you a link to a lecture which explains why doing quantum mechanics in non-Cartesian coordinates leads to the language of bundles. The motivation is very basic. Watch it. If I’m a crackpot, then so is the professor who presented this stuff. Just give the fuck up, Mr Antifa. Go pray to Kamala instead of arguing over things you don’t understand.

>>16702340
notice how you can't actually give a significant physics result which uses line bundle language for wavefunctions, so you're forced to deflect when your lies are called out.
>you a link to a lecture
that's from a series called "Lectures on the Geometric Anatomy of Theoretical Physics". from the title, you can obviously tell that these lectures are mathematics and not physics
https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

>>16702356
>>16702340
>Lecture 2: axioms of set theory
bruhh. no physicist gives a shit about set theory

>>16702311
>https://ncatlab.org/nlab/show/geometric+quantization
>Unfortunately, we can’t quantize all such observables while still sending Poisson brackets to commutators, as we did at the prequantum level. So at this point things get trickier and my brief outline will stop. Ultimately, the reason for this problem is that quantization is not a functor from the category of symplectic manifolds to the category of Hilbert spaces
kek
yeah, newsflash, faggot, we don't live in Hilbert space

>>16702356
I gave you the physical justification, which should be obvious to you if you have an inkling of intellect
>particles travel in spacetime
>particles have mass
>so they must curve spacetime according to GR, at least in regimes way below Planck scale, where we know GR breaks down. This includes atomic and nuclear scales.
>there is absolutely nothing indicating some magical “cutoff” where GR suddenly stops working
>so quantum phenomena on your usual atomic and nuclear scales happen on curved spacetime as per GR. Why? Because there’s mass and energy involved. You know, the QM Hamiltonian.
>however the usual prescription of a wavefunction as some kind of a function from R^3 to the complex numbers only works in Cartesian coordinates. It fails in any other coordinates.
>but the foundational principle of GR is the principle of covariance, which states that Nature doesn’t have a preferred coordinate system. It doesn’t even know what coordinates are.
>so this naive prescription is downright nonsensical and we need a coordinate-free way to talk about wavefunctions if we don’t want to live in a looney world where laws are only laws sometimes, but conviently go away when I want to.
>so we need the language of bundles to truly understand what a wavefunction is
>you can obviously tell that these lectures are mathematics and not physics
Even though the lecture explicitly talks about the wavefunction of quantum physics and the immediate applications to physics. Right… I expected this non-retort. We all know physicists never use mathematics.
>>16702359
I gave you a specific fucking lecture titled “quantum mechanics in curved spacetime”. Now this is a proper deflection.
>>16702360
Oh, so quantum mechanics is wrong? Come up with a better model that explains the hydrogen atom spectrum then.

>>16702373
*yawn* more deflection. i don't really care about your made up justifications. you can justify any bullshit if you try hard enough. come back when you actually have a physical result using line bundle language for wavefunctions.

> talks about the wavefunction of quantum physics
so? that doesn't make it physics and i don't think the professor claims that either. any grifter can talk about 'quantum energy' and how it relates to 'spirituality'. that doesn't make him a physicist. do you really need these elementary things explained to you?

>>16702396
Ok, I'm genuinely tired of this non-conversation. It's like throwing pearls before swine.
>a physical result using line bundle language for wavefunctions
Was already stated. Geometric quantization may result in a non-unique choice of Hilbert space. In particular, two different observers in the Unruh effect observe two different, unitarily inequivalent QFT vacua.

>>16702414
i asked you for a physical result and you start blabbing about your irrelevant mathematical formalism which has produced no physics. boring.

>>16702429
So the Unruh effect is not a physical result? Ok...

>>16702437
you should stop appropriating mr. unruh's results

>>16702443
Really? We have copyright laws for physical derivations? How many lawsuits has Newton filed already?

>open Newton’s Principia
>ctrl-f “Lagrangian”
>0 results
>this Lagrangian mechanics business is all lies and deflection. The guy should have not appropriate Sir Newton’s results.

>>16702443
no bro, you don't understand
they managed to derive something that looks almost like the unruh effect bro
the theory is super-useful even though it makes no verifiable predictions bro
hilbert spaces, bro
bro, pls

>>16702445
are you stupid? just post what i asked for in >>16702429 and i'll shut up. of course you can't so you keep deflecting and coping.

>>16702455
next he'll start saying some retarded set theory transfinite axiom of choice bullshit is totally important to physics because some mathematician gave a lecture on set theory or something

>>16702457
The Unruh effect.
>>16702455
Rent free.

>>16702475
>starts appropriating others' work again

>>16702356
>https://youtu.be/C93KzJ7-Es4?t=1629
>a solution to the problem is to forget about this
so what if we obtained an imaginary term... it may still be locally true using this ONE COOL TRICK!
this is high comedy

>>16702478
refer to >>16702449. I didn’t derive any of this btw. This is a standard result in geometric quantization. It tells us why the Unruh effect takes place and connects to the more fundamental problem: there is no notion of THE global vacuum in semiclassical gravity. So the quirky “dude Sonic sees particles when he accelerates fast” immediately raises basic questions about the Standard Model. Like what even is the Higgs vacuum expectation value if there’s no global vacuum? What did we actually measure at the LHC? Can we maybe probe these gravitational effects by observing the Higgs field interacting with particles? Can we explain the g-2 anomaly this way? You know, actual research.

This is the kind of stuff people do if they live in a sensible world where GR and QFT aren’t schizophrenically separated into two separate realms. But retards like you look at le math and immediately discard it because math hurts me brain uwu.

>>16702480
>he couldn’t follow
>he couldn’t argue back
>so he starts picking at random phrases instead
Now this is comedy.

>>16702504
>random phrases
no, my nigger
no
I suffered through whole MINUTES of this bs to see when he introduces fiber bundles... and I'm not sorry I did, this is hilarious, and it just goes on like that
>oh if we just fix these two parameters by hand, it all works out
lmao

>>16702503
>It tells us why the Unruh effect takes place
wrong. the unruh effect, if real, is already explained and predicted by unruh. 'muh line bundles' is just noise which adds nothing of value. you're just trying to steal credit for others' work and it's pathetic
>Higgs vacuum expectation value if there’s no global vacuum?
it's obviously an approximation. in the real world there is no lorentz invariance because of the big bang but that doesn't mean the big bang is relevant to experiments probing local quantities for which lorentz invariance is a valid approximation. and 'muh line bundles' doesn't address any of this anyway because it's provided no real physical results (as your coping and deflecting has shown), just more tedious and dubious formalisms, which is why it's also not used by actual physicists.

>>16702551
>https://youtu.be/Way8FfcMpf0?t=1051
lmao
just fucking lol

>>16702551
>in the real world there is no lorentz invariance because of the big bang