Wave Function Collapse and Thermodynamic Irreversible Processes

[hyksos]

TL;DR Summary

Is the 'apparent' phenomena of wave function collapse related to thermodynamics?

Very early in the development of thermodynamics, it was realized that the 2nd Law of Thermodynamics is not a law fundamental to the fabric of our cosmos, but only becomes true in the limit of the number of particles. It was none other than Boltzmann himself who realized and articulated this aspect of the 2nd Law.

A similar, slightly analogous issue arises in the formalism of Quantum Mechanics, regarding the so-called "wave function collapse". The mathematical formalism of QM neither predicts, depicts, nor implies collapse. In the words of Casey Blood, professor emeritus at Rutgers :

"If wave function collapse occurs at all, its mechanism is not by quantum mechanics."

I have recently gained some powerful intuition about how thermodynamically irreversible processes play a key role in why things like human bodies never observe a superposition. My intuition has immediate application to paradoxes such as "Wigner's Friend". My current intuition about such processes may even have testable predictions in the way computers behave. "Never" is a strong word, but vis-a-vis Boltzmann, we can declare that the probability of a human knowing/experiencing a superposition is physically possible, but just terribly unlikely. The probability is non-zero, but vanishingly small.

(Disclaimer : In no shape or form do I mean to imply that wikipedia is an authoritative source.) I was motivated to create this thread here after seeing some clever author on wikipedia post an interesting claim. It goes something like , decoherence occurs whenever an isolated quantum system interacts with a classical system undergoing an irreversible thermodynamic process. Upon reading that, I was struck with a feeling that I was whistling an obscure song while taking a walk in a public park, only to pass a stranger whistling the same song at the same time.

What do you think? Do you have an intuitive link between irreversible thermodynamic processes and the appearance of wave function collapse? What is your intuition?

 

[atyy]

Measurement in quantum mechanics does require irreversibility.

However, this is due to the practical irreversibility of decoherence (it's easier to see this in the Bohmian formulation). I don't think this has anything to do with thermodynamics since we can also perform measurements at T=0 (in principle).

The Valentini variant of Bohmian mechanics has a separate irrevsersibility that establish what Bohmians call "quantum equilibrium" (which is not thermodynamic equilibrium).

 

[akhmeteli]

Summary:: Is the 'apparent' phenomena of wave function collapse related to thermodynamics?

[1107.2138] Understanding quantum measurement from the solution of dynamical models (arxiv.org) (published in Physics Reports).
" Strictly speaking, for finite values of the parameters of the model, the process that we have studied cannot be an ideal measurement in a mathematical sense. However, in a physical sense, the situation is comparable to the solution of the irreversibility paradox, which is found by disregarding correlations between inaccessibly large numbers of particles and by focusing on time scales short compared to the inaccessible Poincare recurrence time. "

 

[hyksos]

Measurement in quantum mechanics does require irreversibility.

However, this is due to the practical irreversibility of decoherence (it's easier to see this in the Bohmian formulation). I don't think this has anything to do with thermodynamics since we can also perform measurements at T=0 (in principle).

The Valentini variant of Bohmian mechanics has a separate irrevsersibility that establish what Bohmians call "quantum equilibrium" (which is not thermodynamic equilibrium).

So I found this preprint, which is authored by Antony Valentini
[1906.10761] Foundations of statistical mechanics and the status of the Born rule in de Broglie-Bohm pilot-wave theory

It looks great so far. For me it is a page-turner, honestly. He talks quite a lot about Boltzmann. Since PDFs are notoriously bad at copy-paste, I have opted for a screen shot.

In general, I think Valentini's understanding of DeBroglie-Bohm Guiding Wave Theory is the correct one. DBGW is really a claim about the realism of trajectories of particles. Formal QM does not have trajectories (!), instead it only has a position operator.

This Valentini paper mentions quantum equilibrium several times, but I was not able to gain any kind of coherent intuition about the concept from this paper alone (it is 41 pages after fall). Similarly, wikipedia has a section titled "Relaxation to equilibrium", in an article ("Quantum non-equilibrium"). Again, I wasn't able to gain any intuition from it, as it all just reads like independent research.

But I'm not complaining. This has opened up many doors for me. Thanks for the reply.

 

[hyksos]

[1107.2138] Understanding quantum measurement from the solution of dynamical models (arxiv.org) (published in Physics Reports).
" Strictly speaking, for finite values of the parameters of the model, the process that we have studied cannot be an ideal measurement in a mathematical sense. However, in a physical sense, the situation is comparable to the solution of the irreversibility paradox, which is found by disregarding correlations between inaccessibly large numbers of particles and by focusing on time scales short compared to the inaccessible Poincare recurrence time. "

201 pages. Okay, that's a whole book. I will try to keep my analysis on the abstract and the TOC.

{ intermission music }
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I have returned from some skimming and post my reaction . I understand that the authors promote the "statistical interpretation", which is fine. However, I was accidentally pulled into the principle text in section 12.4.2. In that section, the authors made a claim which I disagree with on factual grounds.

Many interpretations are motivated by a wish to describe individual systems, and to get rid of statistical ensembles.The consideration of conscious observers was introduced in this prospect. However, the numerous models based on the S+A dynamics show that a measurement is a real dynamical process, in which the system undergoes a physical interaction with the apparatus, which modifies both the system and the apparatus, as can be shown by performing subsequent experiments.

Italics are the authors' not mine. My problem with the above statement is this part right here :

" . . . in which the system undergoes a physical interaction with the apparatus, which modifies both the system and the apparatus. . ."

These authors took a single isolated experiment with a Curie-Weiss magnet and wrote 201 pages about it, which is fine. This gave them the (cough) liberty to make the statement above and be factually correct. However , this idea that measurement somehow is a physical event that "reaches out and switches" the system S is a popular one... but ultimately wrong.

The experiment called a Delayed Choice Quantum Eraser is the central crux. The DCQE denies what these authors have written. Its results are literally in contradiction to the claim above. Perhaps we need to make a new thread about this?