Decoherence: is "other states lost to the environment" part?

[nomadreid]

In Wikipedia's outline of the Many Worlds Interpretation of quantum physics https://en.wikipedia.org/wiki/Many-worlds_interpretation, it states "In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence,...", yet I thought decoherence was the idea that the apparently lost information was preserved in the environment (that is, staying in the same universe), as indeed Wikipedia's page on decoherence https://en.wikipedia.org/wiki/Quantum_decoherence states ""Decoherence can be viewed as the loss of information from a system into the environment ... the effect of sharing quantum information with—or transferring it to—the surroundings." What am I missing?"

 

[PeterDonis]

the apparently lost information was preserved in the environment (that is, staying in the same universe)

These two aren't the same. The point of the MWI is that there is no actual collapse; everything is just unitary evolution all the time. And unitary evolution all the time is what preserves information; an actual wave function collapse would destroy information. So "having only one universe" would mean information gets destroyed; preserving all of the different "universes" (the many worlds of the MWI) is what allows all the information to be preserved (by putting the information that an observer in a single "world" can't see, into the other "worlds").

Decoherence doesn't change any of this; all it does is recognize that unitary evolution has to include the environment as well.

 

[nomadreid]

Can't you have, via entanglement of a state with those of the environment to give a new state (encompassing the previous isolated state along with the previously isolated states of the environment with which it becomes entangled), a unitary evolution that redistributes the information of the old states to the new state, so that there is no actual collapse in the old sense of losing quantum information? Wouldn't this version of unitary decoherence render the other worlds unnecessary?

 

[PeterDonis]

Wouldn't this version of unitary decoherence render the other worlds unnecessary?

What you describe isn't a "different version" of decoherence; it's just a description of decoherence. But the part you are missing is that, if the measured system starts out in a superposition, then once it's entangled with the measuring device, the measuring device will be in a superposition, and once the measuring device gets entangled with the environment, the environment will be in a superposition. The different terms in the superposition are the different worlds. Yes, information gets spread around in the environment as part of this process; but none of it gets rid of the superposition, because it can't--unitary evolution is always going to keep spreading the superposition to everything that gets entangled with the original system. That's why unitary evolution ends up leading to many worlds.

 

[nomadreid]

Hm, very interesting. Forgive me for asking you to be a devil's advocate, but is this saying that all other interpretations of quantum mechanics sacrifice the concept of unitary evolution?

 

[PeterDonis]

is this saying that all other interpretations of quantum mechanics sacrifice the concept of unitary evolution?

Any interpretation that says that wave function collapse is a real phenomenon (as opposed to just being a change in our state of knowledge about a system) requires that unitary evolution is suspended during collapse.

 

[nomadreid]

I am starting to understand this better, thanks. So the MWI basically says that the apparent collapse is simply a change in our state of knowledge about a system? The MWI is an epistemological (rather than ontological) statement?

 

[PeterDonis]

So the MWI basically says that the apparent collapse is simply a change in our state of knowledge about a system?

No. Some collapse interpretations do. The MWI says that the apparent collapse is because the observer's state is entangled with the state of the system being observed, so in each branch of the wave function the observer observes a single result of a measurement.

 

[nomadreid]

Many thanks, PeterDonis. This is helping my understanding greatly. I must mull over it some more, and might have further questions, but I must sign out for now. (Perhaps in another world another I has/have more time this morning, but not in the world the I who is typing this is/am presently observing.