Interpretations of QM vs. statistical physics as an "interpretation"?

[Aidyan]

TL;DR Summary

Can we consider interpretations of QM just as classical statistical physics re-interprets classical thermodynamics?

Personally I tend to believe all (or almost all) of the interpretations of QM are unsatisfactory simply because they tell us something that we already know but do not tell us something we don't know. That is, they do not predict new phenomena or principles or properties of matter, etc. that can be tested empirically to confirm or falsify its ontology. Unlike QM itself or relativity and other successful theories in the history of science which did not just describe (re-interpret) classical physics but led to lots of new predictions and explained several phenomena/anomalies which previously couldn't be explained in the frame of classical physics, almost all (perhaps with few exceptions) interpretations of QM tell us something we know already but don't predict anything new and/or explain any anomaly. That's why I tend to dismiss all the interpretations as "anti-historical" since they do not furnish any means to distinguish it, at least in principle, from other interpretations and do not predict some new physics or explain something which could not be explained in orthodox QM.

However, at some point the example of statistical physics came to my mind (you have other examples) and I must admit i got a bit stuck there. Because, the question is how did then the passage from non-statistical thermodynamics to statistical thermodynamics which is, so to speak, a "re-interpretation" of thermodynamics in terms of a classical (i.e. non-quantum) atomistic and probabilistic ontology, lead to new discoveries? And was it able to explain properties of matter that in the conventional thermodynamic theory were previously not explainable? If so which?

I'm not an expert of stat. physics, which might explain how, to my own surprise, I couldn't find a decent and strong example that makes it stand out against non-statistical thermodynamics despite it being celebrated as an extremely successful physical theory. If there are none then my above argument crumbles... ... but can't believe that, that's why I hope to find some. Can someone point out some of these examples?

Note: it is not necessary to agree with my assessment on the interpretations o QM. I would like only to find out for examples which make it clear why we can't consider statistical physics as an interpretation, if any, without having to convince you of my above argument that is not part of the question and that I only added to clarify the context and motivation of the real question.

 

[atyy]

Statistical mechanics allows the microscopic description of matter (ie. the Hamiltonian describing the interactions of the microscopic constituents) to be incorporated into thermodynamics (via a thermodynamic ensemble such as the grand canonical ensemble).

Triumphs of statistical mechanics include the explanation of universal behaviour at criticality by Kenneth Wilson, and the detailed calculation of superconducting behavior by Bardeen, Cooper and Schrieffer.

However, why statistical mechanics works is not totally resolved, as it seems that it should be explained by dynamics, which should be more fundamental. The attempt to do this goes back to Boltzmann's attempt to derive thermodynamic behaviour from dynamics. Boltzmann's kinetic theory should be seen as an attempt to solve the "interpretation problem" of statistical mechanics.
https://arxiv.org/abs/0807.1268
https://cmouhot.files.wordpress.com/2009/04/companion-9.pdf

 

[A. Neumaier]

it should be explained by dynamics, which should be more fundamental. The attempt to do this goes back to Boltzmann's attempt to derive thermodynamic behaviour from dynamics. Boltzmann's kinetic theory should be seen as an attempt to solve the "interpretation problem" of statistical mechanics.

Boltzmann's work is today regarded just as the most elementary approximation to the real dynamics of macroscopic matter. The state of the art in statistical mechanics are the 1PI methods for fluid dynamics and the 2PI methods for kinetic equations. Their interpretation is well established, also the approach to equilibrium.

 

[Demystifier]

And was it able to explain properties of matter that in the conventional thermodynamic theory were previously not explainable? If so which?

It certainly was. E.g. many aspects of phase transitions can be explained by statistical physics but not with thermodynamics.

 

[atyy]

Boltzmann's work is today regarded just as the most elementary approximation to the real dynamics of macroscopic matter. The state of the art in statistical mechanics are the 1PI methods for fluid dynamics and the 2PI methods for kinetic equations. Their interpretation is well established, also the approach to equilibrium.

Any reading that you recommend?

 

[A. Neumaier]

Any reading that you recommend?

There is a quite readable book by Calzetta and Hu:

• E. Calzetta and B.L. Hu, Nonequilibrium quantum field theory, Cambridge Univ. Press, New York 2008.

 

[vanhees71]

Two very good papers for the non-relativistic case are

P. Danielewicz, Quantum Theory of Nonequilibrium Processes
I, Ann. Phys. 152 (1984) 239.
https://dx.doi.org/10.1016/0003-4916(84)90092-7

P. Danielewicz, Quantum Theory of Nonequilibrium Processes
II. Application to Nuclear Collisions, Ann. Phys. 152 (1984)
305.
https://dx.doi.org/10.1016/0003-4916(84)90093-9

 

[atyy]

How about for classical dynamics? Are we able to start from Newton's laws and get an approach to thermodynamic equilibrium?

 

[A. Neumaier]

How about for classical dynamics? Are we able to start from Newton's laws and get an approach to thermodynamic equilibrium?

The functional integral approach used in the 1PI approach should still work, though I haven't seen it applied to classical dynamics.

 

[vanhees71]

One way within classical dynamics is to start from the general Liouville-equation which is an equation for the N-particle phase-space distribution function and derive what's known as the BBGKY-Hierarchie, which has to be truncated somehow. The lowest non-trivial order of the truncation is the Boltzmann transport equation. From there you get to the thermodynamic equilibrium by considering the state of maximum entropy, which is based on the H-theorem which follows from the Boltzmann equation using the principle of detailed balance, which the collision term fulfills within classical dynamics due to spatial and temporal reflection invariance.

Of course, you cannot get a complete argument within classical physics due to the known problems any classical theory of matter has. So you have to envoke QT, and there the H-theorem becomes a very general feature following from the unitarity of the quantum-mechanical time evolution/S-matrix. Also the Gibbs paradox is solved etc.