/sci/ - Science & Math

all of qm is nonsense

Mathematicians can define them rigorously but physics plebs are too low IQ to understand anything other than hand waving.

>>15372364
explain how then

>>15372366
No, I don't cast pearls before the swine.

>>15372357
That's the name of the game anon. Concepts such as differentiation, Fourier series, delta functions etc., were used prevalently throughout physics before rigorous definitions.

>>15372357
>Quantum field theorists
>mathimatically rigorous way
its not their job though is it

>>15372357
What does not mathematically rigorous even mean in this context? Every step in the path integral formalism is defined.

>all possible paths are taken because muh free will!!!!
feynman was just another wootroon.

Path integrals aren't rigorous. There's no way around that, ever. It's over. The issue is that there's no rigorous way to compute amplitudes. We would like one, but we use path integrals because those are the best option, presently.

>>15372366
Yes, for classical QM the path integral is rigorously defined, but for QFTs it's more tricky due to problems with the continuum limit: https://physics.stackexchange.com/q/446774

>>15372498
>for classical QM the path integral is rigorously defined
No, it isn't. If you post what you think is a rigorous definition (in the thread, not a link), I will point out the mathematical flaw.

>>15372501
Can't be bothered, it's in the stack exchange question.

>>15372498
>>15372501
Because I enjoy discussion, I will point out that the quantity on the left in (4) is always real but the quantity on the right is only real for some N. This follows from the factor of i^N on the preceding line. This is not rigorous.

>>15372512
>a sequence of complex values can't converge to a real number
Seriously?

>>15372516
Who are you paraphrasing with your green text?
I don't doubt that it could. The issue is that no one has shown that it does. If you can prove that [math]\left[\lim_\limits{N\to\infty}i^{N/2}\right][/math] is real, that will be a big deal.

>>15372512
>I will point out that the quantity on the left in (4) is always real
??? what are you on, that's a complex amplitude.
>This is not rigorous.
indeed it isn't, the rigorous definition is in imaginary time, the details are in the stackexchange. Tbh this stuff is too advanced for me, and I doubt you'll understand it.

>>15372516
>>15372523
For instance, I think it is standard in the undergrad math curriculum, which you may not be familiar with, to show that [math]\left[\lim_\limits{N\to\infty}\left(-1\right)^N\right][/math] does not converge, and this is pretty much the same problem.

>>15372524
>??? what are you on, that's a complex amplitude.
I think I have made an embarrassing error.

This is the issue that I meant to say: If the modulus squared of the term on the left is real, and the term on the right is proportional to i^{N/2}, then the square of the term on the right will be proportional to i^N, and, thus, real for only some N.

Thank you for pointing out my error. I will not make that one again.

Also, since this error showed up in my book, let me ask someone to post an example of someone who wrote a 300+ page textbook that didn't have 100+ errata corrected in the second edition.

>>15372537
You're actually retarded, if the coefficient on the right is imaginary then its modulus squared is also real.

Wow, actually, if we take the square modulus of the term on the right, it will get multiplied by -i and be real. I am going to have to go think about what I meant by this.

>>15372543
Yes, I was just realizing this before I saw your comment. I will have to think about what I mean here.

>>15372547
I'm surprised at how you even got a phys masters.

>>15372554
If you look at Carroll's Spacetime and Geometry book, he has a sign error in the book's very first equation saying that gravity is repulsive rather than attractive. Are you surprised he finished high school? Everyone makes errors. The more you write, the more errors you will have.

>>15372364
You don't understand it either do you

>>15372496
>no rigorous way to compute amplitudes
This thing could be good, it's fairly new though and because it's not in [insert favorite textbook circa 1978] most people here seem to hate it
https://en.wikipedia.org/wiki/Amplituhedron

COME ON MATHS GREMLINS, PAY MORE ATTENTION.

YOU RETARDS!!!!!!!!!!!

>>15372501
A mathematically rigorous and satisfactory definition of the path integral is related mostly to solving two problems:

1. To give a proper definition of measure on the space of paths (there is no Lebesgue measure - i.e. a σ-finite, translation invariant measure - and therefore another measure shall be used);

2. To give a proper definition of oscillatory integrals (an integral of an oscillating phase on a set of infinite measure is ambiguously defined).

In non-relativistic quantum mechanics, it is possible to define the path integral in imaginary time completely rigorously, making use essentially of stochastic Brownian integration (Wiener measure on paths). In fact, in imaginary time the oscillating phase becomes a damping exponential factor, thus simplifying a lot the definition of the integral, and part of the exponential is used to define the Wiener measure. This is very helpful to study semigroups of the type e−τ(−Δ+V), for suitable potentials V, whenever τ≥0.Under suitable conditions this may also give some information on the unitary group e−it(−Δ+V) (for example, it may be used to prove self-adjointness of (−Δ+V), thus guaranteeing the existence of the unitary group of evolution). The rigorous path integral formula for Schrödinger operators takes the name of Feynman-Kac formula. It can also be extended to some simple quantum field theories of particles interacting with a radiation field (either through minimal coupling or linearly).

quantum field theories of particles interacting with a radiation field (either through minimal coupling or linearly).

>>15372623
...In real time, there have been attempts to define the path integral as an oscillatory integral on the space of paths, using ideas from Hörmander. This is due to Albeverio, Høegh-Krohn, Mazzucchi, and others. However, there are serious complications in this case, and it is possible to give a coherent and consistent definition only in very few special simple cases (such as the harmonic oscillator, and some perturbations of it).

>>15372623
Meds now.

Let me also say that it pokes me in a spot which is very sore when people criticize me for being twelve years out of practice after my rapists had me wrongfully expelled from college twelve years ago. Obviously, the error in question about the amplitude being real is not related to practice, that was simply an error or carelessness, but I feel like there are people watching me try to sort out my error on my computer now saying, "This fucking retard looks like he's twelve years out of practice." Check my physics GRE score while you're at it.

>>15372623
Very humbly, I point out that doing the integral in imaginary time uses t --> (-it) when we know for a fact that t is not equal to (-it). Thus, I dispute the "rigor" of the procedure. That procedure is what I would call a workaround, or a hack.

>>15372635
>>15372650
it's called a change of variables you dumbfuck.

>>15372706
I know what it's called. I will concede that changing one real variable for another is rigorous but I am reluctant to concede that exchanging a real variable for a complex one is rigorous.

You fuckwits pretending to be clever when your mother still wipes your gen-z mouths with your bib still. It's cringey.

>>15378886
Did you get 100% on every test you took in college? No absurdly simple mistakes anywhere? I bet you did have such mistakes, many of them, and if you're not still making them now, I bet it's because you're not being forced to put yourself out there intellectually and you're not doing it on your own. Case in point, look at the errata page for every textbook that was ever written. Everyone has errors. Plenty of them are very stupid and not mere typos, such as mine was not merely a typo.

The issue was that I knew that I had found some problem with the path integral. When I wrote section 60, years later, I was too hasty in reviewing and I just assumed I understood without really thinking about it. Now that I have thought about it, I think the problem was that we cannot guarantee the convergence of the oscillating complex exponential integral. You're wrong if you think my hastiness is evidence of my lack of physical maturity. I wrote a whole long section about exactly this functioning of the amplitude vs the probability in my previous book, Section IV.3: https://vixra.org/abs/1712.0598

It's like saying that someone who takes a wrong turn when they're driving doesn't know the layout of the city they live in. I think the fact is, I am the best physicist in the world. Obviously, I am not the most meticulous physicist in the world or the one with the most physics memorized, but I am the one who overcame the hard conceptual bottleneck that everyone else was stuck on. If my rapists hadn't expelled me from college (wrongfully), I wouldn't be 12 years out of practice and I'd probably be less prone to such obvious, careless errors, but they did and I am 12 years out of practice now. So what? I am not making myself into a great physicist by doing what everyone else can do. I am doing it by doing what others cannot do.

>>15379140

>>15379140
>Jealous
Why were you in jail if I may ask?
>1712.0598v3_compressed.pdf
Did you write this? I can't understand anything as I've never done any physics. Looks impressive though.
>ctrl+f Ricci flow
>2 results
I always wondered... do physicists take classes like Riemannian Geometry or are such (hard) concepts introduced solely in the context of relevant theorems/theories/etc in physics classes?
>If my rapists hadn't expelled me from college (wrongfully), I wouldn't be 12 years out of practice and I'd probably be less prone to such obvious, careless errors, but they did and I am 12 years out of practice now.
What are you talking about anon, what rapists?

>>15379240
I've been to jail many times for assorted demeanors, and I am sill in jail now for a reason that is not clear me. I did write that, and I wrote pic related too which is better, I think. Both are about my research program which I have named the Modified Cosmological Model. I took and undergraduate course in differential geometry but it was an elective. I do not think such things are standard in the physics curriculum. Rather, physicists learn by doing. You get Riemannian geometry from doing GR, abstract algebra/group theory from doing QFT, etc. I think you should be able to decipher the meaning of "my rapists" by consulting the dictionary.

>>15379363
>demeanors
misdemeanors

>>15379140
>Now that I have thought about it, I think the problem was that we cannot guarantee the convergence of the oscillating complex exponential integral.
Ha, I love it. You're fun. I need to read more of your work. In any case the mere fact "stuff exists" pragmatically guarantees such convergence, but in any event local field path integrals make such possible. If and only if the dimensions exceeded such "self-capture", and so entropy were far higher, would convergence not be guaranteed or not possible. Don't have time to read all that but it seems pretty evident you're compounding infinities such that any ergodicity would not emerge by construction of a dissipative system e.g. non-hilbert space without finite locality or locally finite paths.

Honestly reminds me a lot of some formulations of a Zeno-style paradox applied to stochastic systems, but in much the same way by ignoring finite localities is a paradox only of misleading definitions. Very roundabout way to troll, or I guess troll yourself, but I dig it.

>>15379363
>I've been to jail many times for assorted demeanors, and I am sill in jail now for a reason that is not clear me.
You have internet in jail?
>I do not think such things are standard in the physics curriculum. Rather, physicists learn by doing. You get Riemannian geometry from doing GR, abstract algebra/group theory from doing QFT, etc.
I'm impressed by people who have a rigorous grasp of numerous subjects like that.
>I think you should be able to decipher the meaning of "my rapists" by consulting the dictionary.
You're quite correct though my comment was a way to inquire about the matter in more detail. It's not everyday people volunteer such disquieting information in passing the way you did.

>>15379417
You are being deceitful. You know as well as I do that we are in the black-site torture prison in Antarctica, and this isn't the real internet we're on.

>>15379426
>Jealous
Jealous of what?

>>15379417
>a way to inquire about the matter in more detail.
They had some agents accuse of me rape, basically, and then they had another agent impersonate the student justice administrator to expel me from college despite the minimal standard of evidence not being me, at all.

>>15379429
Many things.

>>15379430
>not being *MET*, at all.

>>15379430
Ahhh... you wrote "my rapists" above. This would imply you were raped and that scared me. So why do you think they framed you?

>>15379462
Nm I'm reading the pic. So just the standard female false accusations, got it.

>>15379462
You should kill yourself to avoid what will happen if I can get my hands on you.

>>15379529
But you can't fight so...

>>15379433
Still waiting to hear why convergence is not necessitated via locality as indicated. Wroks just fine as a cauchy sequence and see also bessel's inequality https://en.wikipedia.org/wiki/Bessel%27s_inequality
Or this explanation https://math.stackexchange.com/questions/4648740/proof-of-convergence-of-the-sum-of-components-in-a-hilbert-space

Convergence of sum simply follows and many people have known this for a very long time. In fact, checking on this, your referenced book says as much where the wavefunction can't be normalized given infinity. So you're either not the author (obviously) or don't want to explain all on a sudden why you think this does not guarantee convergence now.

>>15379556
if you provide a rigorous proof of convergence, in the thread, not a link, I will closely examine it.

>>15379595
>Hey anon keep escalating your level of effort I promise eventually I'll reciprocate
Nah. If you knew jack shit you'd know what I'm on about from the plain words used to reference the relevant details. So you're either not the author (as I said no shit) or you somehow don't understand the basics and how they apply. I mean come on basic fucking entropy here. Disappointing.

>>15372357
Who gives a fuck? It's literally just using the Markov property to get you to an analogue of the Chapman-Kolmogorov equations but for field configurations.
>boo hoo hoo I don't understand what's going on unless you start by defining some sets and functors and blah blah blah
Grow the fuck up, who the fuck cares about any of this "rigour" shit when it only gets in the way of you actually making progress?
By the way, what undergrads and low quality mathematicians (but never the good ones) fail to understand is that rigour should never be used to block you from making an argument. Rigour is what you bring in at the end to add any conditions to make sure your argument is rock solid, but you never do research or make first attempts at arguments by sitting around with a thumb up your ass while you ramble on about convoluted and ultimately irrelevant technical details before you've even got any idea about how your argument is going to go. How you actually do good research is making an argument first, trying something out, and then going back and figuring out what conditions you need to make that argument work, and that's when rigour comes in and does its job. Not before.
Following that, there is actually nothing wrong with what physicists are doing even by mathematical standards. It's just a bit of banter some people say for fun but retards take seriously. You try something out that sounds like the right argument, but in physicists' case, experiments can do the job for them and tell them whether they're right or wrong, so the job of rigour (to correct bad intuition) is no longer so important.
This rant isnt directed at you, but rather the actual autistic faggots who unironically think masturbating over rigour is actually what smart mathematicians do.

>>15372623
This was written by ChatGPT, but I still appreciate this quality post. It was eminently interesting.

>>15380354
https://physics.stackexchange.com/q/446824
Kek, it was from stackexchange.

>>15372357
if you don't understand the mathematics of kaubiwachi manifolds there's no much hope in explaining nulecule integralisation. It's a deep dive you're going to have to do by yourself. Good luck!

>>15380437
some people would rather live in delusion than admit they were wrong

>>15372512
Physicists normally use Euclidean path integrals where everything is explicitly real and the exponential of the action has a minus sign to ensure convergence. It is well-defined and rigorous in 1D.

>>15380437
Nice attempt at making up plausible sounding jargon