[stevewillie (OP)]

Given that faster-than-light action at a distance has been established experimentally (Aspect and others), SR has been defended by holding that what passes between two parts of a split photon is not information and that non-local effects are "random".
Just what definitions of these terms are being applied? Probably the best definition of "randomness" was given by Kolmogorov paraphrased as follows: Given a character  sting in some descriptive language of length λ, that string is random if and only if there exists no algorithm which can generate that string other algorithms longer than λ. Information content has been defined by Shannon as I(E)= -c log(P(E)) where E is an event, P is a probability, c is a positive constant and the log is usually taken to be base 2. Have these (or similar)definitions been applied to this issue? It would seem to me that "action" that is random is no action at all.



       

[lyner]

I find it easier not to think in terms of a 'split photon' (or anything else which is exhibiting split qualities, I suppose).

The 'information' about whether a photon is on the left or on the right appears in both places at once, granted, and that could imply instantaneous transfer. But when the resolution of the ambiguity occurs and the detector on the left gets the blip, it is not relevant to either Mr Left or to Mr Right which of them got the photon until a time delay equal to the transit time for light between the two. There wasn't an 'action', in as far as neither Mr Left nor Mr Right did anything.  SR isn't violated in any way because there is no transfer of information, 'as such'.

It is easier to think in terms of a probability / wave function to describe what is going on during the  'transit' of the energy (or even of the electron etc.). Once the final interaction has occurred, the wave function collapses and you can then say that the effect could be interpreted as if a particle had traveled between source and detector. Once the final destination had been determined, the whole of space 'gets to know about it, instantly - so it can't happen anywhere else.

It's only an alternative vew, of course but it avoids some of the apparent paradox involved. You don't need to invoke SR and its consequences. If you try to say "what really happens", there be dragons.

[LeeE]

One of the best examples of this is Quantum Entanglement, where two entangled qubits can be prepared and then separated.  Each of the two qubits exists in a number of different states simultaneously until one of them is resolved to a single state.  As soon as one of the entangled qubits is resolved, it's entangled partner also resolves, into a compatible state, without any time appearing to pass i.e. the two qubits resolve simultaneously, giving action at a distance.  However, the state that the qubits resolve into is random and cannot be specified or predicted, so no information can be passed.

[JP]

There is also a bit of subtlety in defining measurements of quantum information.  A quantum bit can be in both states A and B simultaneously, and only has to choose one when it is measured.  A classical bit has a probability of being in A or of being in B, but is definitely not in both simultaneously, even if you haven't measured it yet.  Because of this (and other issues relating to the "weirdness" of quantum mechanics), measurements of quantum information are different than measurements of classical information.  The Shannon entropy you mention is a classical definition of information.

The proposed schemes I know of for using quantum information all work by adding a quantum information channel to an existing classical information channel in order to improve the performance of the classical information channel, or to do nonclassical things, such as teleporting information.  The caveat is that your quantum information has to work alongside a classical information channel in order to do any of this, so you can benefit from quantum information, but your whole system is still limited by the classical information channel.