Preferred Basis and Superposition

[rkastner]

I'm glad! For collapse details, please see fmoldove.blogspot.com, Part 1 (that's last week).

 

[rkastner]

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 Schrödinger 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.

 

[bhobba]

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, Schrödinger'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

 

[bhobba]

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

 

[kith]

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.

 

[Maui]

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.

 

[Jilang]

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.

 

[bohm2]

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

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

 

[kith]

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.

 

[Dale]

Seems like this thread has reached the end of its useful life.