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Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) momentum vanishes.) So, doesn't then the decoherence time depend on the motion of the prepared state relative to the environment? And, doesn't the ultimate environment, all particles in the universe, introduce a preferred frame into quantum mechanics in the sense that the decoherence time is relative to this frame? And would this be measureable, at least in principle? I.e. I could go into a frame with high boost relative to the CMB restframe and notice that the decoherence time changes?

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Environmentally induced decoherence makes wave function collapse unnecessary.

As far as I know, that's still a conjecture. I might be wrong about that, though.

But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) momentum vanishes.)

It's the rest frame of the system + reservoir, but it is not "preferred" in the sense that it violates Lorentz invariance.

So, doesn't then the decoherence time depend on the motion of the prepared state relative to the environment?

Only the part of the environment that is directly interacting with your system. If your reservoir is a collection of matter interacting with the system by the exchange of blackbody radiation photons, then the decoherence time will depend on how often the system interacts with one of those photons.

And, doesn't the ultimate environment, all particles in the universe,

What make you think that the universe is finite?

introduce a preferred frame into quantum mechanics in the sense that the decoherence time is relative to this frame?

All decoherence times can be calculated from the decoherence times of the same system in any other inertial frame. The rest frame of the observable universe is in no way "preferred".

And would this be measureable, at least in principle?

That decoherence is affected by time dilation like everything else? Yes.

I.e. I could go into a frame with high boost relative to the CMB restframe and notice that the decoherence time changes?

Long story short: you probably aren't going to be able to use decoherence to find some universal preferred frame and disprove special relativity.

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I agree with the thrust of this answer. However, the part about the CMB rest frame is incorrect. There is no frame in which an individual photon is at rest. However, when you have a collection of photons in some small region of space whose momenta are not all parallel, the collection has an equivalent rest mass that is nonzero, and it has a center of mass frame. The CMB photons in the immediate environment of our solar system do define a rest frame, and the CMB dipole measures our state of motion relative to this frame. The CMB frame is basically the same as the rest frame of the Hubble flow. –  Ben Crowell Jul 21 '11 at 3:18
    
@Ben Crowell: Thanks for the correction. –  Dan Jul 21 '11 at 4:00
    
Thanks, but I don't understand: Forget about the 'whole universe' and just talk about environment. It is thermal in exactly one frame. In each other frame it has a total nonzero momentum. There is thus a special frame if you dislike the word 'preferred.' If I calculate the decoherence time in any other frame the result differs. I don't say it 'disproves' special relativity or anything of that sort - it's still Lorentz-covariant. I'm just saying there is a preferred frame in which decoherence takes place. Thus, I don't see why I'm not able (in principle) to use decoherence to find that frame. –  WIMP Jul 21 '11 at 6:00
    
@WIMP: Maybe you could clarify what you see as the fundamental interest of the question. Any time we have objects A and B, and they're relatively close to one another (not at cosmological distances) we can define whether or not A is at rest in B's frame and whether or not B is at rest in A's. There are lots of easy ways of doing this. Maybe decoherence is one way, but if so, why is that important? –  Ben Crowell Jul 21 '11 at 18:18
    
Can I only ask a question if it's of fundamental interest? I am just confused by the literature on decoherence because I couldn't find a text that addresses the question, and I would like to know if I got it right. For all I know the standard collapse interpretation has no preferred frame. Collapse is instantaneous in any frame (which has never made a lot of sense to me). So I'm wondering if not decoherence solves this problem, on the expense of rather than being instantaneous or almost instantaneous, the process of 'collapse' can be as long as you wish, if you just boost enough. –  WIMP Aug 16 '11 at 7:02
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