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Computing heat capacities in Bohmian Mechanics
(06-02-2016, 03:01 AM)Schmelzer Wrote: Sorry, I was unable to interpret this in a meaningful way.  DBB theory does not work in the phase space but in configuration space.

I've been trying to make sense of the original question. Bohmian mechanics attempts to explain the motion of a particle and subsequent measurement as related in the 2 slit experiment. It's a motion related to momentum. Heat mechanics explains energy changes to multiple particles " living" in the same system. That, if anything, is a motion related to an acceleration. I fail to see the "common ground" required for any type of comparison .
Hello poorboy, I wouldn't mind seeing the connection made more explicit myself, but I'm sure it's no mystery.

Bohm's introductory work did in fact talk about the 2-slit experiment, but dBB certainly doesn't only explain that. Realize that many authors use the 2-slit experiment to illustrate their basic idea. Feynman did that, with QED. But in both cases the equations apply to all of QM. Bohm's equivalence principle makes this explicit. It shows that dBB is equivalent to regular QM in all situations; in no way does it rely on 2-slit experiment.

Caveats: I don't know that from my own study, but all dBB experts claim it. Furthermore, although some opponents claim the Equivalence Theorem is flawed in some way, they all agree that it's supposed to apply to all QM not just 2-slit. Yes, some do claim the results don't work for a case like heat capacity. But nobody has shown those flaws, at least not in a peer-reviewed published paper. And if they could demonstrate such a flaw that would be an important publication, immediately accepted; they would definitely go ahead and submit it.

Another caveat, these comments apply only to non-relativistic QM, which is all that's concerned in this heat-capacity issue. Later work has also extended results to relativistic QM, and QFT, although perhaps not completely.

Thus dBB is, at least, supposed to apply not only to position, not only to 2-slit, but also to momentum, spin, multiple particles, and so forth. IF someone thinks there's a problem with that (for all I know, there may be) it's up to them to prove it. Bohm's Equivalence Principle remains unchallenged by any legitimate work.
I continue to debate with Motl on physics.stackexchange. He was aware that I have discussed my non-expertise on physics, I am a layman merely interested in what QM has to say about "reality". I fully admit that. I have to say though, that I don't believe Motl understands the uncertainty principle, which is where much of his naive comments on BM come from. He thinks the uncertainty principle doesn't hold in BM. It most certainly does. The uncertainty principle in BM arises from our ignorance, so it seems to be fully compatible with Motl's commentary linked below. He seems to not understand what the uncertainty principle means in QM and how it differs from what it means in BM.

Such texts as this one remember religious sermons. As quantum theory as it is, in its minimal or Copenhagen interpretation, as relativity, are presented like unquestionable truths.  They cannot be in conflict, out of principle.  If realism or causality, taken together with relativity, lead to Bell inequalities, but quantum theory violates them, one thing is certain: It is not relativity which is false.  So, we have to reject the idea that there is an external reality.  And once there is no possibility to find a causal explanation for the violation of Bell's inequality which does not violate Einstein causality, we have to give up the very idea that observable correlations always have causal explanations, we have to give up even Reichenbach's principle of common cause. 

I'm a realist. In some sense, one can say that this is a belief, also comparable with some religious belief.  One could even make a point: I would not give up realism because of some scientific observation.  Why?  Because i cannot imagine that there could be a reason to believe that these observations could be completely unexplainable, even in principle, by some model of reality.  The "reality" I see around me now may appear to be a hallucination created by some matrix, fine, but then the matrix would be some reality.  I may die and wake up in heaven, or hell.  Then I would probably accept the particular religion which made the claim that this particular place really exists. But all these possibilities would not mean that I give up the belief that there exists some reality. I'm a scientist, because I want to understand this reality.  

The same holds for causality. If there is some correlation, I will believe that it has a causal explanation.  And I will continue to believe this even if I have no idea about what could be this causal explanation. Finding such causal explanations is what scientists do, and like to do.  So, yet unexplained correlations define only scientific problems I have to solve.  What could motivate me to think that there may be correlations which are unexplainable by causal influences?  There is nothing I could imagine.  I'm a scientist because I like to search for causal explanations of observable correlations. 

If I would stop to believe that an external reality exists, and that observable correlations have causes, what would be the point of doing science?  

But if realism and causality are what I accept as the base, the foundation of science, and therefore, unquestionable by scientific evidence, then it follows that another assumption of Bell's inequality has to be rejected.  And the only other assumption is Einstein causality.

So, you reject relativity in the Einsteinian sense? Then, we have to return to the view of Lorentz where there is a "good frame" to do physics in. I have an impossible time understanding what this would mean for the puzzles of relativity. For example, if relativity is just an allusion, and the real physics happens in the special frame, then how are we to understand something like the twin paradox. If my twin flies to outer space and comes back to find the world he once knew is gone, and hundreds of years have passed, how can we explain it as an allusion? His experience is illusory?
First, in the Lorentzian interpretation time dilation is a real effect, moving clocks are slower, moving rulers are shorter.

Why does the moving observer come to a different conclusion? He assumes he is at rest. Then, he uses a synchronization procedure which makes sense only if you are at rest. If you move, you get the synchronization wrong. This becomes important if you change your speed. And, again, behave as if you would think you are in rest, despite the change. Then, the new synchronization is wrong too, but wrong in a different way. So, at the moment when he changes the speed, what he "assumes" to happen "now" changes. The difference becomes bigger with distance. So, if you jump up and down here on Earth when Andromeda is up, the synchronization with Andromeda oscillates with the amplitude of years. Of course, if you ignore this change of synchronization, you get a completely wrong result.

And this wrong result is the consequence of his combining two descriptions which contradict each other: That he is at rest when he flies away, and that he is at rest when he returns. If he errs consistently, so that he assumes he is at rest initially, but moves with double speed when he returns, he will assume that his clock is faster initially, but a lot slower during his return flight, and get the correct result.

It's important to understand that all the same effects happen in Lorentz's view as Einstein's. A preferred frame, where the Universe is at rest, contradicts no actual data at all. And it's supported very well by the Microwave Background Radiation which of course was unknown in 1905 (SR) or 1904 (Lorentz theory). The 1905 paper contains exactly the same math (for all main results) as the 1904 paper and gives the same results. Einstein introduced only a new philosophy, "every frame is equally valid" - with no experimental or observational evidence for it. Lorentz (and Poincare) knew the Principle of Relativity (POR) well - they were the ones who invented it. But they said "it's as though every frame is equally valid". E. said "every frame is equally valid." I think that's a mistake which has caused many decades of confusion and wasted effort.
@Ilja and Secur

No, these comments are totally wrong. In the view of Lorentz, the length contraction was a mechanical affect due to aether wind pushing against a moving body. Yes, the calculation is the same. A moving clock would go slower, but it's an illusion where the "real time" takes place in the aether. According to Lorentz, the twins would never actually age differently since their "real age" would always be defined in the aether. That is 100% documented as the view of Lorentz and it's a simple fact that this is the whole point of a preferred space-time foliation. If you have any sources from Lorentz indicating that's not what he thought, I'd like to see it. I do believe that towards the end of his life, Lorentz was persuaded by general relativity that Einstein was right all along, but the aether theory certainly predicts that the twins won't age differently, since it's not a "real affect" but an "illusion" due to using a "bad frame". You have to use the aether frame to get the correct answer.
As for what Lorentz "really thought", let's not go there; I'm not a psychologist, much less do I talk to the spirits of the dead. His mechanical effect has absolutely nothing to do with "ether wind". Wherever you heard that, recommend you don't read that source again! It's a mechanical effect straight from Maxwell's equations. But none of that's important.

The important point is: In Lorentzian relativity, does that spaceship twin age slower? In other words, is time dilation a real effect? Yes, it is. All effects, in both experiments and any reasonable thought experiment - like the "Twin Paradox" - are identical between Lorentz and Einstein views of special relativity. The only effects we can actually test are time dilation and relativistic mass, so focus on those.

So we have differing opinions on that issue. (As I say, forget any differing opinions re. what anybody might have thought over 100 years ago). Now the question is: how to prove who's right? I'd say the easiest way is to produce a quote from a recognized authority. I can do that ... and will, in a while.

Meanwhile please post a quote, from a recognized authority, claiming that Lorentzian mechanics - as defined in "Electromagnetic Phenomena in a System moving with any Velocity less than that of Light", H.A. Lorentz, 1904 - says that time dilation is NOT a real effect.

BTW if I'm wrong about this, I'll owe you very much for setting me straight!

Thanks in advance.
Ok, here's a pretty good article concerning Lorentz Ether Theory (LET). It's a policy statement at Physics Forums written by a working physicist. If you have any doubts you could post a question there, asking about this article, and as many as a dozen PhD physicists - with jobs at major universities - will tell you it's right. And explain any misunderstandings you may have.

Block Universe (BU) is their name for Einstein's interpretation of Special Relativity.

"For special relativity (SR), the mathematical model is the Minkowski space, a four-dimensional pseudo-Euclidean affine manifold. The symmetry group determining this structure is the proper orthochronous Poincaré (or inhomogeneous Lorentz) group which includes the Lorentz transform.

There are two primary philosophical interpretations: the Block Universe (BU) and Lorentz Aether Theory (LET). The BU considers the universe to exist as a single fixed 4D geometric structure which is not dynamically evolving over time since time is one of the dimensions of the structure. The LET considers the universe to be a 3D world evolving over time and with a single undetectable “true” rest frame.

Both BU and LET use the Lorentz transform, etc., to make all of their experimental predictions, and therefore they are scientifically indistinguishable, making the same experimental predictions in all cases. Because of this experimental equivalence, there is little if any serious ongoing debate between the two in professional physics circles (although the philosophy literature does have ongoing debate)."

Reference https://www.physicsforums.com/insights/p...-universe/

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