Christian - its fascinating how similarly we think.
In response to your comments/questions:
I will respond by paragraph number:
Paragraph 1:
P1: Concerning your statements that "reversible computation occurs within an entangled system. Only when the entangled system decoheres into the environment of other entangled systems (through the exchange of photons) does time emerge as progressively irreversible, providing persistent evolution of information at the macroscopic scale", don't you think that we could have information loss during the passage from reversibility to irreversibility?
A1: This is how I "currently" think: information is trapped in entanglement, but does indeed escape during decoherence. The question is, where does it escape to? As I suggested in an earlier post, free photons seek out "entanglement" with other atoms. Some find targets nearby, which is why we have condensed matter and the double slit experiment. Intermediate ones create rare reflections in planetary or stellar distances (don't forget entanglement swapping). Yet others fly off in the universe and go forever, perhaps exerting pressure on some distant galaxy to accelerate them away from us.
Paragraph 2:
P2: I think that your "principle of retroactive non-discernability" could have some implication also in the issue of my Essay, i.e. the black hole information loss paradox.
A2: This was what attracted me most to your essay. I hope we will have time after the contest to go into this more deeply.
Paragraph 3:
P3: Concerning Information and Entanglement I would like to bring to your attention another important behavior: in general the term entanglement means that the quantum state of a quantum system composed by two (or more) subsystems depends on the quantum state of each subsystem even if they are spatially separated. When one sums up the information in the two subsystems the result will be less than the information in the original system.The apparent information loss results hidden inside correlations between the subsystems. This should have some implication also for my comment 1).
A3: Thank you for bringing this to my attention. I was aware that the conventional formalism for entanglement provides for two distantly separated quantum systems to be "coupled" via Hilbert space, such that measurement of one can suddenly change the state of the other. Until your paper, I was not aware that there was an apparent information loss hidden inside the correlations between subsystems. This appears to lend credence to the subtime insight as to what form that "coupling" might take.
Paragraph 4:
P4: A recent paper by Pierre Fromholz, Eric Poisson and Clifford M. Will correctly stresses that Einstein's general relativity is built based on the principle of general covariance. This basic principle implies that coordinates are seen like simply labels of space-time events. Thus, one can assign coordinates completely arbitrarily. Therefore, the only quantities that have physical meaning, i.e. the measurables one, are those that are invariant under coordinate transformations. One such invariant is the number of ticks on an atomic clock giving the proper time between two events. Do you think that your idea of "background-free conceptualization of time" could be connected with such a proper time?
A4: I have the paper downloaded and it is on my list to read next. That Schwarzschild geometry can be described in infinitely many coordinate systems appears to be consistent with the background-free conceptualization of time I would like to achieve. In a nutshell, I believe that coordinate systems and labels of space-time events are a figment of our imagination. The reason for the invariance in the number of ticks on an atomic clock providing a "proper time" between them is nothing more than the speed of light being invariant. This does not mean that there is any temporal relationship whatsoever between one atomic clock and another.
I am delighted to have the opportunity to debate this with you and look forward to further discussions down the road.
Best of luck in the contest.
Kind regards, Paul
