Wavefunction collapse: is that really an axiom

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Discussion Overview

The discussion centers on the nature of wavefunction collapse in quantum mechanics, questioning whether it can be derived or if it is fundamentally an axiom. Participants explore various interpretations of quantum mechanics, the implications of unitary evolution, and the relationship between measurement and wavefunction collapse.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that wavefunction collapse cannot be derived from unitary time evolution, suggesting it is an axiom.
  • Others propose that including the interaction with the measuring device in the quantum model allows for a different interpretation of measurement processes.
  • One participant asserts that there is no unitary evolution that can lead to a collapsed wavefunction, claiming this can be shown through algebra.
  • Another participant expresses confidence that the collapse axiom can be derived from the Schrödinger equation, although they acknowledge that understanding is currently lacking.
  • Some participants highlight that the wavefunction collapse does not exist in a traditional sense, comparing it to concepts like microreversibility.
  • There is a suggestion that the collapse is not a transformation but results in a statistical mixture, raising questions about the meaning of the wavefunction post-collapse.
  • One participant emphasizes that the wavefunction is a probability amplitude, which cannot be described by deterministic unitary evolution, framing this as a fundamental aspect of quantum mechanics.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of wavefunction collapse, with no consensus reached on whether it can be derived or if it is an axiom. The discussion remains unresolved, with differing interpretations and approaches to the measurement problem.

Contextual Notes

Limitations include the dependence on specific interpretations of quantum mechanics and the unresolved nature of the relationship between measurement and wavefunction collapse. The discussion also reflects varying levels of understanding regarding the mathematical foundations involved.

  • #31
Wojciech Zurek is one of the most influencal theorists in the fields of open quantum system and measurement theory (he is actually quite well known in the whole physics community) and he has written a few reviews that I believe are relevant to the discussion in this thread; some of which are freely available on the arXiv

This short review, "Decoherence and the transition from quantum to classical ", from 2003 is an updated version of an article from Physics Today (meaning it is not a "real" paper so it is quite easy to read)

You can download it from
http://arxiv.org/abs/quant-ph/0306072

Higly recommended! I think it gives a good idea of how these problem are handled i nowadays and how we have at least in part solved the measurement problem.
It is also quite interesting to see how much progress was made between 1991 and 2003.

Zurek has also written a more "technical" review that appeared in Reviews of Modern Physics a few years ago. It can also be found on the arXiv.

I have already recommended "The Theory of Open Quantum System" by Breuer and Petruccione. It is a very good book but you need to be familiar with "ordinary" QM in order to understand it (with ordinary I mean the contents of e.g Sakurai, no QFT or relativistic QM needed)
 
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  • #32
vanesch said:
It is not clear to me whether the dynamics generates a natural "subsystem decomposition", or whether one has to introduce that by hand. It could be that the dynamics is such, that certain (local ?) subsystems "factor naturally off" in that they give rise to the only stable Schmidt decomposition. Or it could be that one has to put in by hand what is "an observer subsystem", in the same way as one has somehow to define by hand what is "your body".

I am not certain yet how the relative state should be defined. Your conditions are the natural requirements. I try to obtain that without introducing anything by hand but locally and for the closed systems (just as in CM).

Regards, Dany.
 
  • #33
Hurkyl said:
Facts:

(1) We have a well-tested theory of unitary evolution that fundamental particles obey.
(2) We have an ad-hoc application of non-unitary evolution to produce measurements.
(3) We have evidence that (2) can be a result of the thermodynamic properties of (1).

So which is the appropriate conclusion?

(A) The evolution of the universe is unitary, and (2) is just a simplifying approximation
(B) The evolution of the universe is non-unitary, because (2) is exactly correct.

(A) is my best choice

But an excellent approximation, and not a simplification at all.
 

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