Zureck's Quantum Darwinism Paper

[atyy]

I 'm not seeing this. Gleason's theorem assumes non-contextuality, which is a strong assumption, hard to reconcile with the practice of QM and a reality that appears to be contextual, But my point is that interpretations like say Bohmian, or even some Copenhagen flavors include contextuality, how is Gleason's non-contextuality assumption compatible with that?

In BM, the Copenhagn interpretation is emergent, so BM is consistent with Copenhagen.

 

[TrickyDicky]

In BM, the Copenhagn interpretation is emergent, so BM is consistent with Copenhagen.

Be that as it may, how does it explain their contextuality being compatible with Gleason's theorem non-contextual assumption?

 

[atyy]

Be that as it may, how does it explain their contextuality being compatible with Gleason's theorem non-contextual assumption?

I don't know how to answer this in a short way, but if BM is comptaible with standard QM, and standard QM is compatible with Gleason's then BM is compatible with Gleason's. It has to do with the definition of "measurement" in QM, and how "measurement" is implemented in BM via decoherence and he way a preferred basis is continuously picked out by the choice of hidden variable and Bohmian dynamics.

 

[TrickyDicky]

I don't know how to answer this in a short way, but if BM is comptaible with standard QM, and standard QM is compatible with Gleason's then BM is compatible with Gleason's. It has to do with the definition of "measurement" in QM, and how "measurement" is implemented in BM via decoherence and he way a preferred basis is continuously picked out by the choice of hidden variable and Bohmian dynamics.

It's the part about measurement in standard QM (that I am identifying here with Copenhagen) compatibilty with Gleason's theorem that I'm not getting, I can see how it is compatible with the formalism of standard QM without measurement-state reduction.

 

[kith]

I also don't see a problem here. dBB is contextual, so Gleason's theorem doesn't apply. You don't need to reconcile the contextuality of dBB with the non-contextuality assumption of Gleason's theorem. I would say that in the context of dBB, you simply can't use it to derive the Born rule.

And if I get dBB right, there is indeed a very different justification of the Burn rule there: Similar to the 2nd law in statistical mechanics, the Born rule is very likely to hold but it isn't a strict condition. See https://en.wikipedia.org/wiki/Quantum_non-equilibrium

 

[atyy]

It's the part about measurement in standard QM (that I am identifying here with Copenhagen) compatibilty with Gleason's theorem that I'm not getting, I can see how it is compatible with the formalism of standard QM without measurement-state reduction.

State reduction can be derived in BM.

 

[TrickyDicky]

Ok, thanks. I simply cofused myself about what "compatible" implied above.

 

[atyy]

Ok, thanks. I simply cofused myself about what "compatible" implied above.

Thinking about it, I like kith's reply in #40 better. I don't know if contextuality can be derived in BM.