Dear Eugene,
Thank you for your careful reading and consideration of the implications. I think I can answer you why, on the one hand, you find my solution correct, on the other hand it seems to contradict some other views. My solution takes place within General Relativity, and it makes use of the mathematics of GR - extended to work with degenerate metrics. I did not add other postulates, I just removed one assumption or two, which are made implicit. The things that seem to be contradicted by my findings may be either part of other theories, or consequences of some other assumptions. I will try to address them individually.
> "I got somewhat lost when you gave up orthonormality ..."
In GR orthonormality cannot exist in coordinate systems in general, only in particular cases. It can exist in local frames though. But if the metric becomes degenerate, the length of some vector fields becomes zero, even if they are not zero. Trying to normalize such a vector fields leads to infinities. But GR works fine with non-orthonormal and even non-orthogonal frames.
> "... and when you insist that identical points can exist with no distance between them and still retain their identity."
Geometrically, the simplest example is a 2-dimensional vector space having the inner product given by g=(1,0), not g=(1,1) as in Euclidean geometry, not g=(1,-1) as in Lorentzian geometry.
Having my solution confined to General Relativity (with the small fix I proposed) doesn't exclude QFT, as many work was done in QFT in curved spacetime, which is in my opinion compatible with GR and may very well be enough.
> "For example, in Feynman diagrams..."
Yes, the particles of the same type are identical in QFT. The quantum particles get mixed up, but there is no need to track them back. The evolution is unitary, and here there is no problem with the information, even if we lose track of their identities. The input in a Feynman diagram determines the output - the converse is valid as well.
> "I find the idea that black holes can evaporate and all the 'information inside' be reconstructed ridiculous, but I know that others do not do so, so you are addressing a 'legitimate' problem of current physics."
Of course it is ridiculous, it is like reconstructing the "Total Baseball, The Ultimate Baseball Encyclopedia" from its own ashes. This is not possible in practice, because we don't know the complete information, and even if we do, it may be impossible to calculate from it the original information. The point is that somehow the universe knows all this info, and computes it to find the next state. The laws we know work as well backwards, so they can in principle help reconstructing the past.
> "You seem to imply that both classical and quantum time evolution laws are violated if info is lost."
Maybe in the real world there is no information conservation. But in Quantum Theory the time evolution is unitary, hence the information is preserved. The classical time evolution is deterministic and reversible (once we know the complete configuration), so the information is also preserved. Hawking's paradox states a contradiction between the information conservation and evaporating singularities, and this is what I address.
> "But if, as many fqxi'ers seem to believe, the real nature of time is essentially NOW, and Einstein's block time is an illusion, or at least a mathematical extrapolation that goes beyond reality, then what seems to be necessary is a physics that accurately describes interactions taking place NOW."
Maybe Einstein's block is an illusion, maybe the NOW is an illusion (I think that both are illusions, but it would take many pages to explain how). But General Relativity can be formulated in terms of NOW as well, and you can see in my essay that I addressed the ADM formalism, which does exactly this. So, my solution does not contradict the presentism.
> "Elsewhere Jason Wolfe points out that when photons are red-shifted, they lose information. This seems to me to be true (with a caveat that I'm working on.)"
I don't know, but I think that in a discrete world this should be true.
> "I also have the opinion that, as Feynman said of QM, no one understands information. For example, some big names treat information as if it is a particle. Information is not a particle. In this sense I am not sure what is even meant when one speaks of 'information at a point of space', whether or not there is a zero or finite distance from another point."
In my essay and the articles I referred, I am using the word "information" implicitly as a placeholder for "the complete description of the topology of space, and of the fields defined on the space" - for example the initial data. The fields have definite values at each point, and by this I understand 'information at a point of space'. And by "information loss" I meant the loss of the initial data at a given time.
> "To your knowledge, has anyone proved the 'uniqueness' of the history leading up to NOW?"
No. The 'only' proof is that the laws that seem to us to work best have this property. But I would not exclude the possibility of violation of this 'uniqueness'. The most notable counterexample was the black hole information paradox. And perhaps the state vector reduction in Quantum Mechanics.
--- continued in the following comment ---
