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00:00 - 17:0017:00 - 23:00

Obliv
Obliv
17:11
dude what is Callen on about here:
"From the atomic point of view, the macroscopic equilibrium state is associated with incessant and rapid transitions among all the atomic states consistent with the given boundary conditions. If the transition mechanism among the atomic states is sufficiently effective, the system passes rapidly through all representative atomic states in the course of a macroscopic observation; such a system is in equilibrium"
what does "sufficiently effective" mean and what is a transition mechanism..
I don't want to rely on my intuition but i'm guessing he's describing maximal entropy state
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naturallyInconsistent
naturallyInconsistent
@Obliv An isolated system has fixed macrostate labels like total energy, total volume, etc, but it is always transitioning from one microstate to another. A system that is traversing so many microstates when being measured by slow human senses, that it is essentially equally likely to be in all of those microstates that are allowed by the specification of the macrostate, is called to be in equilibrium
At that point, Callen has not yet motivated microstates and macrostates, so this is him trying to build a basic version of that
Obliv
Obliv
@naturallyInconsistent Thank you >_< that makes sense
So the unique conditions he mentions are if the system hasn't evolved to the most likely macrostate yet
ACuriousMind
ACuriousMind
@Obliv Just try to apply this to a concrete example: A gas in a box at a certain temperature has a gazillion atomic states corresponding to positions and momenta of the particles, it "transitions" between these states simply by the passage of time and the particles moving around and colliding with each other and the box. This is "sufficiently effective" if the timescale on which we observe the gas is not so small that the particles only move negligibly
Obliv
Obliv
Oh I see
naturallyInconsistent
naturallyInconsistent
17:33
@Obliv yeah, unique conditions like ortho- and para- states of hydrogen or oxygen or nitrogen or whatnot, where the transition rate is so small that when we do experiments, we find that it takes measurably long to equilibriate. That if we do measurements before the equilibriation, we find a mixture even if we might think that there is only one type of particle inside.
Physics is so full of phenomena, that it is vastly easier to simply state some specific examples of the kind of scenario that we want students to pay attention to, and to generalise from, than to only work in terms of abstract statements.
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2 hours later…
fqq
fqq
19:47
@lucabtz to add to acm's good considerations, think about whether you want to live in Italy. Unfortunately a PhD is not very valuable there compared to more advanced economies (but not completely useless and might still be worth doing if you enjoy it)
user 70432
user 70432
I've always thought of Italy as an advanced economy.
> highly developed social market economy
re: Wikipedia
fqq
fqq
I said more advanced
Italy's economy has been lagging behind comparable countries in the last few decades. Specifically relevant to what I was saying, it has one of the lowest rates of university education in the oecd, and still struggle to employ the few graduates properly
OTOH university education tends to be pretty good. This results in European physics departments (and to a lesser degree tech companies etc) being full of Italians
Sanjana
Sanjana
20:02
There was some PSE answer which showed some fallacy when assuming complex exponential in place of sines and cosines in some ODE ansatz. I cannot find it. Can anybody give me the link to that Q/A?
 
1 hour later…
bolbteppa
bolbteppa
21:05
@Sanjana How would you get hyperbolic solutions, you'd need to assume exponentials with arbitrary coefficients right, maybe that's what they were saying?
@Mr.Feynman None of it is relevant, if Heisenberg etc had used say a different word than "interpretation" this entire industry would likely not have sprung up
Sanjana
Sanjana
@bolbteppa Yes, that's true...But no the fallacy was that only certain class of ODEs (I think linear ODEs) support such ansatz...Otherwise we are not allowed to do so.
bolbteppa
bolbteppa
Once you enter the realm of non-linear anything, all bets are off
Sanjana
Sanjana
Speaking of nonlinearity, I had a question on experimental status of GR. People say that GR is validated because it predicted GWs... But GWs are only linear effects of GR, right? Is there something within the already detected GWs which is a signature of the non-linearity of GR? Because, there might be many non-linear theories which give Fierz-Pauli theory when linearized. How do GWs indicate that GR is the correct theory of gravity?
bolbteppa
bolbteppa
21:23
GR gravitational waves aren't just linear effects of GR right
The analogy to EM is that they are solutions of the free equations and are field equations like EM, physically you can expect that the dominant behavior is linear like EM waves but in reality there would be non-linear effects
Mr. Feynman
Mr. Feynman
@bolbteppa I said later I was not talking about interpretations of QM. I used the word "interpretation" quite loosely but what I meant is that as of now theoretical physics is so far ahead than experimental physics, that we have a plethora of different theories or conjectures (some of them being more influential than others of course) that can't be established yet
Sanjana
Sanjana
@bolbteppa I mean, when deriving the GW equation for example, we literally do $g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu}$ and proceed. Sometimes, even some parameters like ADM mass can be guessed while staying within the linear regime.
Idk...maybe you are right. I am planning to study next, how they make these numerical GR templates
imbAF
imbAF
22:18
One of the things that characterizes the S.E is the fact that it's solution must satisfy norm conservation: $\int\psi(x,t)*\psi(x,t)dx=1$. I have two questions and perhaps someone can tell me what the right approach is:
The norm is the square root of the inner product of a state vector with itself. But here, clearly we are considering the square of it, why?
The above integral is essentially saying that the probability to find the particle somewhere in space is 1 for when the system is at the state $\psi$. But can it not be that the
system changes state as time passes by, which means that while the probability of the system being somewhere in space, when considering all the possible states in which the system can be, is one, when considering only a particular state or less than the total amount of possible states, then it can happen that the probability is less then one, because we are disregarding the rest of states in our initial integration.
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