Preferred Basis and Superposition

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  • #51
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Bill the whole point is that you can't apply 'ordinary statistical thinking' and assume 'random systems' with 'random phases' because quantum theory with only Schrodinger evolution doesn't license that. This is the circularity issue.
You mean to say independent systems prior to interacting and becoming entangled cant be considered to have random phases relative to the system they become entangled with?
 
  • #52
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No, not a semantic issue. Applying Born Rule is FAPP collapse, not real physical collapse. Very different things and the distinction is crucial for this issue.
The word apparent means exactly that its not real.

Now precisely what have you against placing actual collapse just after decoherence?

Was Von Neumann wrong in saying it can be placed anywhere?

Placing it right there solves many issues. Its not actual collapse - which is one of the issues that actually remain - but a whole heap of others are resolved.

Thanks
Bill
 
  • #53
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You mean to say independent systems prior to interacting and becoming entangled cant be considered to have random phases relative to the system they become entangled with?
You just said they were independent, which means they have no quantum correlations -- which means they are already presumed as decohered before one starts 'deriving' anything. That's exactly what is circular about the 'derivations'. If there are nothing but quantum correlated systems as implied by only having Schrodinger evolution (with no collapse that could disrupt those correlations) then there are no independent -- as in uncorrelated -- systems, and one can't assume that there are in order to show that things 'decohere' along the desired basis.
 
  • #54
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If decoherence assumes that which it tries to explain, then decoherence is philosophy and just another interpretation(cripped at that).
 
  • #55
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The word apparent means exactly that its not real.

Now precisely what have you against placing actual collapse just after decoherence?
You can't get decoherence unless you have collapse first -- that's what I've been saying.

Was Von Neumann wrong in saying it can be placed anywhere?
Indeed, and it's because he couldn't figure out why anything physically collapses, so he didn't know where to put it. That's the arbitrary 'Heisenberg Cut'. What I've been arguing is that the transactional picture provides a physical, non-arbitrary place for this 'cut'. And that's what the Born Rule actually applies to.

Placing it right there solves many issues. Its not actual collapse - which is one of the issues that actually remain - but a whole heap of others are resolved.
What I've been arguing is that these 'solutions' are illusory, tendentious, and circular. TI gives a genuine solution. Again I really should end my replies now. I do thank you all for the discussion and I hope you will take a look at the material I've mentioned. Happy to answer questions about it via email, see my blog for contact info: http://transactionalinterpretation.org/

Best wishes, RK
 
  • #56
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If decoherence assumes that which it tries to explain, then decoherence is philosophy and just another interpretation(cripped at that).
Ouch. No, it's just a bad argument. You've just defined 'philosophy' as a bad argument here. ;) Believe it or not there can be good arguments in philosophy!
 
  • #57
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You just said they were independent, which means they have no quantum correlations -- which means they are already presumed as decohered before one starts 'deriving' anything.
Come again you lost me there.

You better spell that one out in full detail.

Take two non entangled systems arbitrarily picked, say two photons, its utterly obvious they will have random phase relative to each other. Of course like the factoring problem we need a proof of this but that IMHO is a VERY long bow to pull if you want to disprove the standard textbook treatments of decoherence that way.

I may be wrong, but I cant quite understand why you are arguing this. You have an explanation for actual collapse just prior to decoherence. Explaining actual collapse is a genuine issue and I will one day get your book to check it out. But all this stuff I have been prattling on about is bog standard textbook stuff. You may be like Grete Hermann - a voice crying in the wilderness - but really that's not the most likely situation.

So until you can actually PROVE it to me I think the most reasonable explanation is the textbooks are correct.

Thanks
Bill
 
  • #58
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How do you know they are nonentangled?
 
  • #59
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You can't get decoherence unless you have collapse first -- that's what I've been saying.
And on that I agree. No argument.

Can we move on please where you detail your actual mechanism for collapse.

To me that's much more interesting.

Thanks
Bill
 
  • #60
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How do you know they are nonentangled?
Its a general assumption.

For example do you believe stray photons from the CBMR interacting with a dust particle are entangled?

Thanks
Bill
 
  • #61
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I'm glad! For collapse details, please see fmoldove.blogspot.com, Part 1 (that's last week).
 
  • #62
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Its a general assumption.

For example do you believe stray photons from the CBMR interacting with a dust particle are entangled?

Thanks
Bill
But it's an assumption you're not allowed to make in order to derive decoherence, because it implicitly injects decoherence from the start. Yes, as I've said, of course things like stray photons are decohered, but that's an empirical observation that can't be used in order to theoretically 'derive' our empirical observation from only the Schrodinger evolution without any actual collapse that could really decohere things. That's why it's circular.

Do you know Boltzmann's H-theorem purporting to derive the 2nd Law of Thermo? Same deal there. He put in a 'hypothesis of molecular disorder' which implicitly assumed irreversibility, in order to 'derive' irreversibility from reversible laws. Decoherence 'derivations' have exactly the same kind of circularity fallacy.
 
  • #63
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I'm glad! For collapse details, please see fmoldove.blogspot.com, Part 1 (that's last week).
Yea - that looks valid.

But like all such things we need a way to test it experimentally.

I have said it before, and I will say it again, these discussions about the weirdness of QM, Schrodinger's cat etc leave me cold. To me, the real problem with QM, is pick any issue that annoys you and you can find an interpretation where its not a problem. But we don't have any way to experimentally distinguish them.

Just one point though about Kochen-Specker. Its really a simple corollary to Gleason's Theorem which IMHO presents the issue in a much more general light as to why the Born rule is correct. There are a number of assumptions that go into using Gleason to prove Born, but the most important one is basis independence (ie non contextuality) and IMHO is the central issue.

Mathematically non-contextuality is ugly - if the formalism of QM is correct it more or less implies Born.

Thanks
Bill
 
  • #64
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Do you know Boltzmann's H-theorem purporting to derive the 2nd Law of Thermo?
Don't know that one.

Not deeply into statistical physics right now.

Thanks
Bill
 
  • #65
kith
Science Advisor
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I agree with Ruth to a certain extent but I don't agree that the derivations of decoherence are necessarily useless wrt to fundamental questions.

If you derive decoherence for the system density matrix, you usually assume things like
a) the initial state of system & environment is a product state
b) the environment is in a thermal (decohered) state and
c) the environment isn't influenced by the system because it is much bigger.

It doesn't seem unreasonable to me to say that it is precisely the fact that the environment is assumed to be already in a time-independent decohered state which leads to permanent decoherence in the system. I also think that there is a strong connection to the H-theorem.

The crucial difference between classical and quantum statistical mechanics is that in QM, a change of coherence / entropy of the system is possible with ordinary Schrödinger dynamics for the combined system. So the big question for me is, what happens if we acknowledge permanent decoherence as an approximation? Does the neglected recoherence forbid the application of decoherence to the measurement process or can it be included?

I'd like to stress again that above all, decoherence is a well-confirmed measureable process in open quantum dynamics. The process and its theoretical description are not controversial at all. What is controversial is the relation of this description to the measurement problem.
 
  • #66
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It doesn't seem unreasonable to me to say that it is precisely the fact that the environment is assumed to be already in a time-independent decohered state which leads to permanent decoherence in the system.


So, the decoherence of system X takes place because the environment is decohered. And the environment is decohered because..... err.... it's obvious when one looks at walls and tables and desks. And so the gist of the argument is that the existence of chairs and desks explains the occurrence of permanent decoherence. And those same chairs they are surely not composed of the very same quantum stuff. No, they are not! :)
They are the decoherence chairs, the chairs that bring forth the classical world.
 
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  • #67
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Decoherence is neither instantaneous or non-reversible. The interaction with a macroscopic system however makes it extremely unlikely to be reversible. Think of it like a reversal of a diffusion process.
 
  • #68
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I think this also the reason why the Everett interpretation which is more in need of decoherence to define their structure fails to deliver the goods as outlined in a number of posts.

Demystifier summarized that point when reviewing the Schwindt paper:
To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves. As reasonable possibilities for the additional structure, he mentions observers of the Copenhagen interpretation, particles of the Bohmian interpretation, and the possibility that quantum mechanics is not fundamental at all.
Many Worlds proved inconsistent?
https://www.physicsforums.com/blog.php?b=4289 [Broken]

Ilja summarizing his papers made the same point:
MWI in it's current form simply becomes invalid, with or without Born rule, because it does not have an additional structure which is necessary to fix the preferred basis: The papers prove that different choices are possible, and lead to different physics. The Copenhagen intepretation solves this problem with its association of the operators p, q with classical experimental arrangements, but this solution is not available in the Everett interpretation. Thus, to make MWI a (viable) intepretation, you not only have to derive the Born rule, but also have to add some new structure to fix the canonical preferred basis.
Why MWI?
http://onqm.blogspot.ca/2009/07/why-mwi.html
 
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  • #69
kith
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I think this also the reason why the Everett interpretation which is more in need of decoherence to define their structure fails to deliver the goods as outlined in a number of posts.
I disagree with this and I've outlined in post #29 why I think so.
 
  • #70
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Seems like this thread has reached the end of its useful life.
 

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