I How Does Local Measurement Affect an Entangled System?

[Sargon38]

We don't get nervous here.

That's not my impression. Very long ago when I was a mentor here under my real world name, these kinds of discussions where less agressive and more enlightening.

 

[Fra]

My take with entanglement is an MWI like view.

I saw this first now, interpreting is easiser if you see the stance. I now understand why refer to universes below.

But of course, to even say what is meant by a statistical mixture, you need to assume that the different measurements you're going to perform are going to measure in the same "probability universe". So that the probability universe is not ALTERED by the particular measurement you're going to perform.

In contrast, my take on entanglement fits in an "interacting agent/observer" interpretation.

Here the explanation of the correlation is simply a "Reichenbach's Common cause".
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The explanation of why Bell ansatz is wrong (and thus we don't expect it to hold in the first place) is that interactions is understood in a way there each subsystem of the universe, reacts towards it's environment, not based in hidden variables, but randomly based on what it knows. And in the case of the bell experiment, as the entangled pais is explicitly isolated after creation, not only to the phycisists but from ANY inteaction, when the "instruments know" is only the information implicit in the "preparation". Thus to expect that the instrument would interact as if the hidden variable was known, would not be rational.

This is why the bell inequality to me at least is not a mystery per see, the open question for me is to understand find how the hamiltonian och nature and the fundamental interactions emerge in line with this interpretation.

Similarly the explanation for the complex state in this same interpretation is simply that the agent needs a may to merge information coming from several DEPENDENT sampling spaces. For example the simplest case is trying to merge into one "state" information about position and also momentum, and if you define conjugate momenta via fourier transforms, the complex state is the natural solution in compact notation. But it would be possible to consider instead a combination of difference spaces, that are related. But there are still many open issues in trying to make this complete and consistent, and until that is int place I think it's not really understood.

/Fredrik

 

[Morbert]

The essence of entanglement is that you can't have a Kolmogorov probability set for contrafactual measurements a priori

I don't think I understand this claim. By probability set, are you referring to a probability measure? What does it mean to have a sample space for contrafactual measurements?

Given a classical system and classical theory, the sample spaces of two different measurement procedures are always coarse-grainings of a third sample space. This is not true for a quantum system and theory. E.g. The sample space for a measurement of spin-x of a particle, and the sample space for measurement of spin-y of a particle do not imply a third sample space for measuring "spin-x and spin-y" of a particle. Is this what you mean? This is true whether or not there is entanglement.

 

[PeroK]

This is true whether or not there is entanglement.

For example, the double-slit pattern (which is effectively a probability distribution) is not the classical average of the probability distributions of the two single slits. And, again, its classical physical assumptions that fail, rather than classical probability theory itself.

 

[PeterDonis]

Moderator's note: Moved thread to interpretations subforum.