The h Bar

1:00 PM

oh well then my solution would still be fine

although I still don't understand how to go from such inner product to that being the component up to a sign

@GPhys because you select the component of e_1 by orthogonality, but with a factor +-1 because of the inner product involved

I'm sure @ACuriousMind can explain, I'm in class

Secret

-1

Q: What would happen if the delayed choice quantum eraser experiment was both observed and unobserved?

What I was wondering is if this experiment was conducted, but two people chose the results. The two people would be completely isolated with no knowledge of eachother, and would each choose to observe or not observe the data. Would the results instantly be those of a particle for both if one pe...

It really depends on whether the entangled state is projected away

also c.f. Wigner's friend

Semiclassical

1:22 PM

so, this question is over on MSE:

1

Q: Why Fokker–Planck equation and path integral are equivalent and when?

Why is Path integral equivalent to Fokker–Planck equation, the notion here is unclear to me. Under what assumptions does it hold and why they are similar? In here it says that it's equivalent to Schrodinger equation which makes me even more confused.

mathematical-physics stochastic-pde

i'm trying to decide whether to vote to close, or whether it should be transferred to Physics.SE. as written, it's quite thin and not motivated.

(I haven't done any votes period yet.)

GPhys

He talks about the norm of the g(V,e_(1)) in a way that must mean the parts in the -1 part of the metric pick up a negative sign - is it correct notation to write the magnitude of the |g(V,e_(1))|^2? How should I write it

Semiclassical

@JohnRennie "...for tomorrow we go back to grading" is the TA version of that.

GPhys

I was going to write something like $g_{11}V^1V^1$ and then write below it that it was in the e basis

ACuriousMind

@Semiclassical Since it gives no physical context whatsoever, we would probably debate whether to send it to math.SE if it was posted here. If you'd vote to close it for any reason other than "it's physics", then just vote to close - remember the golden rule of migrations.

0ßelö7

@ACuriousMind Someone commented on my wave equation question with exactly what I had in mind. Guess I don't suck at GR after all.

Secret

1:27 PM

The Fokker-Planck equation looks like stochastic process stuff. In addition, the path integrals don't look like those in QFT

user307388

The torus is $\mathbb R^2/ \mathbb Z^2$ ?

Secret

so the path integrals are likely stochastic path integrals instead of the QFT ones

0ßelö7

@MathAminPhysics yes

user307388

Why?

0ßelö7

@GPhys what you're doing sounds right, I think, but trying to figure it out on a phone isn't working. I'll take a look when I get home

Feel free to just send me the LaTeX solutions, I'm always happy to read GR

ACuriousMind

1:29 PM

@Secret The QFT ones are stochastic ones (where they are rigorously defined).

GPhys

I'm almost completely certain the proof concept is right, but I'm just trying to figure out my notation

Semiclassical

@ACuriousMind Well, I actually like the question (despite the poor framing of it).

0ßelö7

@MathAminPhysics That's literally the definition.

Semiclassical

And I do consider it to have physical content...just not well-explained at all

ACuriousMind

@Semiclassical Then you could consider editing it to make it better, then vote to migrate

0ßelö7

1:30 PM

Do you know the polygon construction of 2-surfaces?

Semiclassical

Yeah, that's fair.

I don't care enough to do that, alas.

user307388

No.

Semiclassical

So it's a moot point :P

Secret

@ACuriousMind Ok nvm, I must have mixed them up with this:

chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/…

0ßelö7

ACM is ignoring me so he won't help. Google "torus via gluing" or something @MathAminPhysics

ACuriousMind

1:33 PM

@Secret Huh? That's precisely the kind of path integrals that appear in QM/QFT. The point is that these are the same as the stochastic ones - the standard QM integral integrates over the Wiener measure, which is the stochastic integral of the Wiener process (better known to physicists as Brownian motion).

user307388

I know its definition via gluing. But I do not know why that definition equals to $\mathbb R^2/ \mathbb Z^2$ .

0ßelö7

You're just periodically identifying parts of the plane. @MathAminPhysics do you understand what the implied action of Z^2 is?

And what a quotient group is?

Semiclassical

The Wikipedia link provided by the poster of said question is relevant: en.wikipedia.org/wiki/Langevin_equation#Equivalent_techniques

Secret

I guess I have a poor background on them (and statistics in general), I thought that those that is used in chemistry don't contain field (operators) and thus they are different from those in QFT (which has fields in them)

ACuriousMind

@Secret The path integral formalism is precisely the formalism in which the fields are not operators.

user307388

1:36 PM

identifying the $\mathbb Z^2$ in $\mathbb R^2$ with the identity element

Secret

Aren't the creation and annhilation operators that appeared in QFT integrals part of the field.
.... nvm, I need huge revision

0ßelö7

Not quite, you identify points that differ by an element of Z^2

Semiclassical

I'm forgetting stuff as well, unfortunately. I imagine there's a dictionary to be made

user307388

The set of those points is isomorphic to $ \mathbb Z^2$, I think.

0ßelö7

No.

Semiclassical

1:41 PM

something like QM : statistical physics :: Schrodinger equation : Langevin equation

But I'm not sure about that, and I don't remember what the analogue of Fokker-Planck would be.

user307388

My definition of that quotient group was wrong?

Semiclassical

or maybe FP is what's analogous to the Schrodinger equation? Ugh, it's been a while since I thought about this stuff

0ßelö7

That set is uncountable, it's not going to be isomorphic to a countable group.

Semiclassical

pah, I mutter that nonsense out loud and then I find this remark on the Fokker-Planck page: "A derivation of the path integral is possible in the same way as in quantum mechanics, simply because the Fokker–Planck equation is formally equivalent to the Schrödinger equation"

Secret

well.... I don't even know what Langevin equation is. Are physics graduates supposed to know about stochastic stuffs when they learn statistical mechanics?

If yes, then my old uni does a very poor job at teaching it because they said nothing about stochastics

0ßelö7

1:45 PM

I would think a proper course in stochastics goes well beyond the math that physicists know.

Semiclassical

I think it's usually reserved for grad-level treatments

user307388

Thanks.

0ßelö7

@MathAminPhysics I think you need to draw a picture

Secret

Even though I always ramble about how hard number theory is to me, the maths subject that I have litterally no background on is nearly all of stochastics

0ßelö7

Draw R^2 and Z^2, then pick a point and check which points end up in the same equivalence class when you take the quotient.

Jasper

1:48 PM

@0ßelö7 The book Knowing the Odds by Walsh treats elementary probability, measure-theoretic probability, discrete stochastic processes and continuous stochastic process all in one, if you are interested.

Semiclassical

What one counts as 'knowledge of stochastics' also varies quite a bit

for instance, most physicists will certainly not have seen a rigorous treatment of it

Secret

Sounds a nice thing to add to my reading list

Semiclassical

by contrast, I think a lot more physicists would know there's a relation between statistical field theory with temperature T is related to a quantum field theory over an imaginary time $iT$.

e.g. the answer here: physics.stackexchange.com/a/35136/55641

0ßelö7

@Jasper no time for more books

Anonymous

2:17 PM

@0ßelö7 That's what I tell people nowadays when they suggest me new books :P

0ßelö7

@Blue have you read 5 volumes of spivak and 4 volumes of Reed and Simon yet?

Anonymous

@0ßelö7 Yeah, but in another universe.

Mithrandir24601

@0ßelö7 Always time for more books

Anonymous

I wonder which textbook I fully completed reading...

Anonymous

Probably not in the last 5-6 years...

Mithrandir24601

2:39 PM

@Blue I think the only textbook I ever read cover to cover was the one I got for A level further maths

John Rennie

@Semiclassical :-)

@Blue disk is in the post!

Anonymous

@JohnRennie Wow! :D Did they give any link to track the parcel? :)

John Rennie

@Blue no. I sent it using the el cheapo post. It you want tracking it increases the price a lot. Give it ten days. If it never turns up then well, I tried.

Anonymous

@JohnRennie Oh, that's fine. I hope you weren't troubled much. :)

Anonymous

I informed my parents. They'll collect it in case I'm not at house at the time of delivery

John Rennie

2:45 PM

It's just in an envelope, so if you're not in presumably the postman will just put it through the letterbox. It doesn't need to be signed for.

Phase

What's Mathjax for the font used in the Laplace transform?

Anonymous

@JohnRennie Oh, cool!

Anonymous

@JohnRennie My mom was shocked when she heard someone from Europe is sending me a SSD :P She thought you might be a kidnapper or something who is tricking me into revealing my address. lol :'D

John Rennie

I'm secretly a supervillain!! :-)

Semiclassical

what a tweest!

0ßelö7

2:54 PM

@Blue that's what my family thinks Bernardo is

@Blue there's not a lot of reason to read a book absolutely 100%

Anonymous

@0ßelö7 Oh, I'm pretty sure @BernardoMeurer kidnaps people and asks for booze as ransom.

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