/sci/ - Science & Math

Of course there's a deeper understanding. There are two more mathematical approaches to quantization that you can consider and both reduce to the naive canonical quantization procedure you described when you are dealing with topologically trivial phase spaces.

One approach is called deformation quantization and it focuses on how the algebra of observables is deformed to be non-commutative in quantum mechanics. I must confess I know little about this one, but it one of the mathematicians that is associated with it, Maxim Kontsevich, won the Field's medal.

Another approach I know a little bit more about is called geometric quantization and it focuses on constructing the quantum mechanical Hilbert space from the classical phase space considered as a symplectic manifold.

>>15968632
>Hamiltonians
is that a fun club for the singing dark fellow from the broadway show or something

>>15968648
When do you typically learn that? While doing QFT as a graduate?

>>15968669
You don't typically learn it at all unless you want to or it's relevant for your research. I'm a postdoc fwiw.

You don't need to know any QFT to learn this (although physicists don't typically learn about fiber bundles unless they get heavily into QFT). As long as you understand differential geometry geometric quantization should be comprehensible (with some effort).

Here are a couple of reviews:
https://arxiv.org/abs/1801.02307
https://arxiv.org/abs/1606.06407

>>15968684
Thanks, I'm saving them for later. I'm currently an undergrad, so that seems beyond my abilities atm.

>>15968632
>Is there some deeper understanding I don't have or should I just swallow this pill?
>Because this introduction to this mathematical formalism is fishy af

Yes, it is really weird. That's why it's the first chapter of the book. Quantum mechanics isn't normal. The pill you actually have to accept is that this is the math that describes the measurements, and when you use it, it works.
That "deeper understanding" is the bit Feynman's famous for saying nobody has.
"Shut up and calculate."

>>15969392
so happens like math predicts, even if weird without making intuitive sense?

>>15969400
you probably don't have a big enough data set for quantum mechanics to make intuitive sense yet.

Yes, it happens like the math predicts. It happens exactly like the math predicts. The math completely describes it.

Have you studied spherical harmonics yet? Plot the spherical harmonics on a graph for different values of the quantum numbers. What's that look like?

That's the math. The math works.

>>15969406
>Yes, it happens like the math predicts. It happens exactly like the math predicts. The math completely describes it.
what does QM math say happens when you clone the observer? from observer's perspective?

>>15969409
i think that really depends on how you clone them
i don't really know what you mean though.
are you asking something about distinguishable vs indistinguishable particles, or fermi exclusion?

>>15969412
no I mean what does the math for duplicating the observer looks like? what does it predict happens next for observer? treat the observer like a mathematical object or something, assume 1:1 copy. pretend you didn't have breakfast

>>15969415
i don't think that's the sort of question that quantum mechanics describes. i mean, theoretically, you could write down the wave functions and say "now they're here", which is what I think you're getting at

but how many particles are in your body? you're not finishing that equation before you die. that's probably more a question for statistical mechanics, and statistical mechanics isn't really impressed by it.

the only QM particle I can think of is that particles with the same quantum numbers cannot occupy the same space. but the meaning of "the same space" is a little broad depending on your knowledge of momentum and anyways your clone probably isn't literally occupying exactly the same space as you.

i don't think anything special happens next to the observer. maybe they start making out.

QM deals with stuff like systems of up to 5 particles, but you're talking about a fully-self-interacting system of like 10^100 particles. someone might have a good guess, but no one knows or has ever known for sure

>>15969428
*"the only QM problem i can think of" not particle

anyways nothing special happens when you say "now they're here"
you're basically asking "what happens when you have two boxes?" nothing interesting. you have two boxes. the end

>>15969428
that's a lot of words for "I don't know". so are you saying QM math cannot describe what happens in the hypothetical scenario that an observer is copied 1:1, from the observer's point of view? or are you saying that it might be able to describe but you in particular have no fucking clue on how to even think about it?

>>15969429
>you have two boxes. the end
I was not asking from your point of view copying the box, rather from the box's point of view, after copying it.

>>15969430
go fuck yourself idiot, if you can't figure out the difference in perspective between two inanimate objects you don't deserve to be here lmao

>>15969434
your chimpout clearly indicates your brain bsod the fuck out

>>15969435
you're literally asking me about a box's subjective experience of reality. that's retarded. at first i thought you were that other physicist but now i think you're just trolling

either you prove you're not trolling or you say something entertaining, or else i'm gonna stop talking to you

>>15969436
well you clearly can't wrap your head around it, that's for sure. that revolt you are feeling, that is your neural networks shitting themselves.

>>15968632
>fishy af
yes

QM is not basedon deep knowledge. Its just replacing the classical solution with wavic solution

>>15969409
answer this or else!

>>15969409
You cannot clone the observer.

https://en.m.wikipedia.org/wiki/No-cloning_theorem

>>15970425
is the observer quantum?

>>15970425