Careful said:
(a) Obviously, the problem concerns isolated substems of a closed system. The only closed system is the entire universe. Jim Hartle has written good stuff on that.
(b) Let me clarify some entanglement issues to you:
(I) CLASSICAL : all matter fields and gauge fiels are REAL. Entanglement between two particles would mean that results of separate, but identical measurements (***) on both particles are correlated due to interactions between the particles in their mutual *causal* past through gauge fields.
(II) Quantum mechanically: nothing is real except the results of measurements. Here entanglement means the same except that it results from processes which are NOT restricted to the mutual causal past (such as the instantaneous collapse of the wavefunction).
(***) A measurement does NOT need to be a binar number due to interaction with a measurement apparatus, but could be the value of a function on phase space (of one particle) at a particular instant in time determined by the trajectory of the particle.
Since (II) is more liberal than (I), QM predicts correlations which cannot be reached by locally causal realist theories in THEORY (the practice is an entirely different matter).
Now, in scenario (I), suppose we want to check a property of a particle by making some measurement which takes about a nano second. Then, we know that if we control the environment in one meter around the experimental setup, we are safe since no events outside this region can influence the experimental outcome. Now, in scenario (II) this would be more troublesome since if our setup were entangled with an object outside this room and a measurement on this object were done between the preparation and registration of the relevant property of our particle, then the outcome of our experiment would have been influenced superluminally. If such superluminal influences were to occur randomly then it would be impossible to find any regularity in the outcome. This was an objection made by Einstein Podolsky and Rosen.
You can find good discussions about the difference between classical and quantum entanglement in the books of Bell - speakable and unspeakable in QM - and Selleri, the EPR paradox.
Of course, quantum physicists could argue that the influence of the environment on the subsystem would miraculously average out and therefore be of no importance. But that is exactly one aspect of the cat problem which they should SHOW and not assume. As you noticed, this issue gets different faces in different approaches (therefore I am not going to expand on this anymore). So, if you are interested in more measurement stuff, then specify your interpretation of QM.
Thanks for the reply Careful. Sorry I intruded on your European Sunday morning. :-)
So far, my interpretation of qm would be the probabilistic one.
I gather from what you wrote above that quantum entanglement doesn't mean the same thing as classical entanglement in that classical entanglement requires some sort of prior physical connection between two particles, A and B, (not necessarily a direct connection between the two such as an interaction, but at least some common influence); and quantum entanglement doesn't require this. This doesn't seem correct to me. Wave function collapse by itself isn't what entangles two particles in qm, afaik. They have to be related in some way prior to the measurement which collapses the wave function in order for their wave functions to be linearly combined prior to the measurement, don't they?
I'm still not sure what you mean by saying that the assumption that isolated systems exist in nature isn't possible in qm.
In a Bell test setup for example, once a pair of disturbances have been produced and are on their way toward the polarizing filters, and before they interact with the polarizing filters, each disturbance is a closed, isolated system. (It's during this interval that their wave functions are combined and interfere via the application of the superposition principle, but this isn't a physical interaction.)
Every particle in the universe isn't quantum entangled with every other particle. They might be classically 'entangled' in some sense (eg. wrt the motion of the universe as a whole -- expansion, rotation, etc.; or wrt gravitational behavior of the macroscopic objects that they're part of), but these aren't quantum correlations.
I don't understand what you're saying about scenario (II) being more troublesome wrt the 1ns measurement example. It seems like you're assuming that quantum entanglement of spacelike separated events implies superluminal influences -- and, afaik, it doesn't. That is, for all anyone knows quantum entangled particles *are* affecting each other superluminally, but that conclusion isn't *required* from observations and qm (or Bell's theorem for that matter).
As for the S-cat problem, or why don't we see macroscopic interference? Well, we do see macroscopic interference, don't we? That's what ponderable objects are -- regions of interference/interaction wrt a hierarchy of various media, aren't they? After all, the idea of interfering *quantum* phenomena came from observing interfering macroscopic phenomena, didn't it?