The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...
yst 19:36
If you want to perform measurements we get into the murky realms of interpretations
yst 19:35
As long as you don't want to perform any measurements there's no question there
yst 19:35
Yes.
yst 19:29
the Wigner function $W(q,p)$ cannot be a probability density to find the system with position $x$ and momentum $p$ because that phrase makes no sense in QM to begin with - quantum systems do not have simultaneous sharp values of $x$ and $p$
yst 19:28
@User198 no it doesn't
yst 19:27
The Schrödinger equation is a deterministic evolution equation for all quantum systems
yst 19:27
it makes no sense to just apply this claim of "determinism" to the quantum version when that underlying interpretation no longer holds
yst 19:26
@User198 Well, but that "you don't lose information" interpretation of the evolution equation is tied to the interpretation of the classical phase space density as a genuine probability density
yst 19:09
I understand what the word means, I just don't see its relevance here :P
yst 19:09
@User198 Yeah, I don't know what anything I talked about is supposed to have to do with determinism
yst 19:07
I don't know what this has to do with determinism
yst 18:53
E.g. the WKB approximation also already yields the exact energy levels for the QHO
yst 18:53
In any case, if by "Liouville's theorem holds", you just mean that you can take the evolution equation with the Poisson bracket instead of the Moyal bracket (because all the higher order terms in the Moyal bracket vanish in the case of the HO Hamiltonian), that's one of the many ways in which the harmonic oscillator is "semiclassically exact", i.e. you can often get the correct answers by just taking everything to first order in $\hbar$ or something like that
yst 18:44
Also, "holds for potentials at most quadratic" is the coward's way to say "holds for the free particle and the harmonic oscillator and nothing else" :P
yst 18:41
And again, there is no direct physical interpretation of the Wigner (or any of the other equivalent) functions
yst 18:39
@User198 What does "the Liouville theorem holds" even mean in this context?
yst 15:21
As I said above - e.g. in the case of the LC connection these geodesics will be the "shortest paths" in the sense of distance/length given by the metric
yst 15:19
In general there is not really much more to say - what exactly that means depends on what your connection means, i.e. why you're looking at that particular affine connection in the first place
yst 15:19
They are the paths along which tangent vectors are transported parallel in the sense defined by the connection
yst 15:17
but if you don't have a metric, just an affine connection, you can't say "this isn't the shortest path" because there is no notion of "shortest path" except the one from the connection
yst 15:16
Which is why you usually induce the connection as the LC connection from a metric, since then the notion via the connection agrees with the distance notion from the metric
yst 15:16
@DIRAC1930 The connection defines what "shortest line" means!
yst 15:15
@DIRAC1930 yes (but they could be the same, since there are also different metrics for which the LC geodesics are the same)
yst 15:10
@DIRAC1930 What do you mean by "physically understand"? What mathematical operation are you trying to perform here?
yst 15:02
Yes, that equation just defines a submanifold of $\mathbb{R}^n$
yst 15:00
but none of the metrics can change that the torus is a torus
yst 14:59
You can look at surfaces, e.g. like the torus, and then consider different metrics on them
yst 14:59
Can you express in actual mathematical terms what you're referring to? Because a metric - like a connection - is by definition a structure on a manifold.
yst 14:58
I can only repeat: I don't know what that means.
yst 14:57
I don't know what that means
yst 14:55
I don't understand the setup you're imagining here - what do you mean you "only have access to what affine connection I was using"? By definition, an affine connection is a structure on a manifold, so you have a manifold. You can't have a connection and not know what manifold it's on, that doesn't make any sense
yst 14:52
What does it mean to "know the shape" or not know it?
yst 14:52
I don't understand the question
yst 14:51
The only formal meaning I can guess for "plotting" a manifold is embedding it in an $\mathbb{R}^n$, and such embeddings exist for arbitrary manifolds, you don't need any connections or metrics for that
yst 14:50
I don't know what the affine connection is supposed to have to do with plotting the manifold
yst 14:48
You can embed any manifold into an $\mathbb{R}^n$, there's your "shape", what's the problem?
yst 14:48
@DIRAC1930 What do you mean by "doesn't even know what shape"?
yst 09:48
@TobiasFünke well, it doesn't state who has the cognitive dissonance...
Fri 19:50
@Feynmate Obviously there was an intended play on the double meaning of "smash" but actually that can be read as something much worse than I intended so I'm going to delete it (but my reply to Slereah was just because grammatically the only possible referent for "they" was "the particles" :P)
Fri 18:58
@Slereah ...the particles?
Thu 21:47
I spent a lot of time today trying to nail down what people meant when they said "we need someone to be accountable for X" and in the end they all gave up because they couldn't actually present any notion of it that made sense in context that wasn't trivial
Thu 21:46
@qwerty That's what people say if they realize they don't actually know what they mean :P
Thu 21:40
We had a pretty tiring workshop at work today and someone asked me if I always have to argue about what words mean and I just went "YES"
Thu 21:38
you should know by now that I think etymology is serious business ;P
Thu 21:33
but in the North it's perfectly normal to greet someone with "moin" at midnight
Thu 21:32
It's actually very interesting how regional these German greetings are - I also like to use "moin" (also duplicated to "moin moin" - for greetings/parting words duplication seems to be common in German) where the etymology is unclear but it's a northern greeting - all the southern Germans assume it comes from "morgen" = morning and get confused when you use it when it's not morning
Thu 21:25
@qwerty I mean I didn't invent it, someone else infected me with it, too :P
Thu 21:23
@Feynmate also the letters I use make it seem more weird than it is - if you start to put more sibilance on the "i", adieu essentially turns into ad-tschö (the 'ö' is the same sound as the "eu")
Thu 21:21
@watchme the "seng" just tells us you're Bavarian :P
Thu 21:19
@qwerty yeah, I think it's kinda meant to be cute but that's not a normal mechanism in German - but it's infectious - most people just repeat it back to me :P