Hello Steven,
I am fascinated by quantum entanglement, but having no time to study it I will offer no opinion. But I have two questions.
Entanglement is destroyed by measurement, but that tells us nothing about the means to non local interaction. In the double slit experiment single photons do not know where they are until they get there, and this indicates a non local interaction with their source. Interfering with this non local interaction before the single photon must choose which slit to go through, robs it of its ability to go through both, so too any subsequent interaction which robs it of its ability to be in a compromise position. Do you think that this non local interaction with its source, is a form of entanglement, of something else? The other question relates to entropy.
I wonder if you have considered the possibility that the missing element in the relationship between entropy, information and the conservation of energy, is gravity, and that this missing player frustrates our ability to see the Second Law of Thermodynamics within a context which can make sense of "order" and "information" and its relationship with energy. I believe it is possible to establish a context within which SLT can coexist with "order", "information" and "conservation of energy", without seeing everything go down the plug hole we call singularity where information survives as a boundary condition. Everything going down a plug hole and information surviving as a boundary condition is the very scenario which sees the universe as holographic, and everything therein as something projected from the outer boundary.
I have an alternative scenario, one where information can only be conserved in one way, and that way is the conservation of things created, that is, all things do not go down the plug hole, and that means there is no plug hole called singularity. My understanding of this all inclusive alternative scenario demands that I put the following to you, but I will be brief.
If we disassociate entropy from the question of "order" and "information", and in freeing it from that constraint, see entropy as the expression of a balance between domains, say domains A and B, and we see the net entropy of a system as the sum of the entropy in both domains, we open the door to defining gravity as the means to the expression of that balance; domains where the loss of energy in one domain is captured by the other. If you can imagine this, you may be able to imagine the following.
Having associated entropy with gravity, we can say that "order" and "information" are associated with the constriction gravity provides. We can see constriction as the means to the construction of "order" and "information" in a fashion consistent with SLT. That is, constriction brings about the energy needed to do the work which brings about "order" and "information", and all this consistent with SLT and the recirculation of energy within the system made possible by gravity. And in this we see gravity as the means to the recirculation of work, and any given state as an expression of the balance of entropy between domains A and B. Gravity, via constriction, is the means to the creation of "order" and "information", but not their conservation. Of course, this is impossible to imagine without redefining gravity as the means to the recirculation of work, and entropy as the expression of the balance between work in progress in domain A and work held in abeyance in domain B.
If you need more information concerning the nature of these domains, please see my essay, but I don't think you need to read my essay to comment on the scenario I just put.
What do you think?
Zoran.