Wavefunction collapse: is that really an axiom

  • Thread starter lalbatros
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  • #26
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In such a universe (with 3 states) there wouldn't be anything like "observation".
My question is not related to any universe or the "observation". I am interesting to know what the physical meaning of Hilbert-Schmidt decomposition is. It is valid in my example also.

Regards, Dany.
 
  • #27
vanesch
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My question is not related to any universe or the "observation". I am interesting to know what the physical meaning of Hilbert-Schmidt decomposition is. It is valid in my example also.
Eh, you have only one single system, so what's the decomposition in tensor products ?
 
  • #28
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Eh, you have only one single system, so what's the decomposition in tensor products ?
That is my question. Whether I need to introduce additional body to define ref frame? For this reason I took example with three levels. I may construct tensor products with let say ground state and still have non-trivial two or three level system. Why not?

Regards, Dany.
 
  • #29
Hurkyl
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And what about the WF collapse then ?
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.
 
  • #30
vanesch
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That is my question. Whether I need to introduce additional body to define ref frame? For this reason I took example with three levels. I may construct tensor products with let say ground state
I see. 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" and what part of the physical universe is "not your body".
But once a certain subsystem (that is, a certain set of degrees of freedom) is defined to be "an observer", then one can hope that decoherence sets in, and brings naturally this "observer state" in a kind of Schmidt decomposition wrt the rest of the universe.
 
  • #31
f95toli
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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)
 
  • #32
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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
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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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