Questions concerning Decoherence and Entanglement

[regent]

I think I wrote the above stuff, no ? Did you understand what I said ? (this is not meant to be offensive ; it is necessary for me to know in how much the statements I made are clear to you in order to continue from there, or to clarify)

I believe you said this earlier:

I can comment on this one: decoherence IS in fact "wild" entanglement with the environment, which is practically irreversible. Remember that "entanglement" is only visible when we look at CORRELATIONS between measurements on the two entangled systems. In the particular case of EPR, for instance, the Alice and Bob photons, *when looked at individually*, behave like a statistical mixture and not a superposition. The superposition (the quantum interference effects, distinguishing a superposition from a statistical mixture) are ONLY visible in *correlations* between measurements on the two photons. As such, a pair of entangled photons looks "less quantum-mechanical" than a single photon beam, which can produce local interference effects. Locally, the beams at Alice and at Bob are "white" so to speak, and don't really show as much interference as a "pure" beam. But such an EPR pair is special, in that the entanglement is still limited to just a pair, and that we still have control over ALL THE COMPONENTS OF THE ENTANGLED SYSTEM.

So, if entanglement, or the property that two 'things' have a more uncertain eigenstate, is simply LOOKING for correlations, why is there such a strong influence with entanglement? In other words, you seem to be implying entanglement is human made, but if it such a strong influence in the quantum universe, how does it work? I'm also still a bit confused of how it ties with the

"Entanglement is that set of pure states, when we look at PURE quantum states of systems which consist of (spatially separated) SUBSYSTEMS. That means that *intuitively* we would be tempted to assign individual states to the subsystems, as we think of them as "separated". But mathematically, if we assign a specific state |u> to system 1 and a state |a> to system 2, then the overall state is of the kind |u>|a>. Now, NOT ALL PURE STATES of the combined system can be written in that form ; in other words, we've severely limited the INTUITIVE set of states, and the actual set of pure states is quite larger. All states that are pure states, but NOT of the kind |state 1> |state 2>, are called ENTANGLED states."

definition. Could you please explain? Thanks for your time.

 

[vanesch]

So, if entanglement, or the property that two 'things' have a more uncertain eigenstate, is simply LOOKING for correlations, why is there such a strong influence with entanglement? In other words, you seem to be implying entanglement is human made, but if it such a strong influence in the quantum universe, how does it work? I'm also still a bit confused of how it ties with the

I read, and re-read this, and can't understand what you're aiming at.
Entangled states are not particularly "human-made", nor are they "more uncertain". Entangled states are just what I said they are: pure states which cannot be written as a product of states of their subsystems.
This is a peculiar property of the way quantum states can be, and comes down to the requirement of them to span a linear (projective) space ; iow the superposition principle.

 

[regent]

But why and how do correlations happen?

 

[regent]

Vanesch,

Can you interpret how MWI solves the measurement problem in QM?

 

[vanesch]

Vanesch,

Can you interpret how MWI solves the measurement problem in QM?

It doesn't "solve" it, it just gives an interpretation on it.

The measurement problem in QM comes from two different aspects, which are related. The first is that "physical interactions" are described by a unitary time evolution operator, which is a linear operator. As such, no interaction, no matter how complicated, can "undo" a superposition.
That is, if initial state |a> gives final state |A> (including states of measurement apparatus etc...) and if initial state |b> gives final state |B>, then there's no avoiding that |a> + |b> gives final state |A> + |B>.
Now, if A and B contained macroscopically distinct measurement apparatus states, then the superposition clearly gives us a non-classical state in the end. If we assume that everything that happens during a measurement is just "physics as any other", and if we assume quantum mechanics correct (unitary time evolution), then there's no getting out of this. This is in fact what Schroedinger wanted to illustrate with his cat.

So we've two options on first sight: or we need to say that quantum physics is not exactly correct (modification of the unitary evolution), or we need to say that during an observation, things are different than in "normal" physics.

The first means that quantum mechanics must be modified, the second means that there is some "different kind of physics" going on with specific systems which do "measurements".

The problem on top of this, is that no matter how we are going to modify quantum physics, or introduce "new" physics for measurement apparatus, we are going to have to violate the principle of relativity.

Well, MWI allows us to get out of all these problems (at a conceptual price however). Indeed, unitarity is kept strictly. So no "special physics" for measurement apparatus: same unitary quantum mechanics for everything physical. As such, the "linearity" problem is not a problem anymore, and there mustn't be a special class of objects which are non-quantum. Because we can keep unitarity, we also keep Lorentz-invariance in all of the theory. Relativity is saved.

The price to pay is that we have to say that the stochastic picking of an outcome is "all in the mind", which is indeed conceptually rather odd. In other words, even though the two outcomes exist in superposition, we're simply only aware of one, and which one, is given by a stochastic rule which is the "Born rule" (the standard probability rule in quantum theory). Now, the funny thing with this idea is that at first sight, it seems totally absurd and crazy, but the more you think about it, the more it is difficult to say that it is totally absurd. (that doesn't make it attractive!)