While Pentcho struggles to explain the theory of optics without a speed of light constant, let me revive a post of mine from 2013, in this thread:
I find interesting:
"One proposal being studied describes black holes and their environments as a network of Hilbert spaces (a Hilbert space for any quantum mechanical system defines all possible states that the system can be in). In the conventional picture of a black hole, locality prevents the Hilbert space of the interior of the black hole from influencing the Hilbert space of the exterior of the black hole."
For good reason. The quantum configuration space according to Bell's result cannot be mapped onto physical space without a nonlocal model. Therefore, quantum configuration space in the Hilbert space behind the event horizon is assumed simply connected and local, while the Hilbert space outside the event horizon has to be assumed multiply connected and nonlocal. If it seems paradoxical that simply connected space adjoining multiply connected space is not itself multiply connected -- that's because it *is* a paradox. Either the interior quantum configuration space maps nonlocally to the exterior space -- or the exterior space outside the event horizon is simply connected, not multiply conected, and all the space inside and outside the black hole horizon is simply connected.
Giddings chooses nonlocality to resolve the paradox. Does he have to? If one accepts the Hilbert space model of quantum configuration space, there is no way out; the choice is singular and correct.
In the continuous functions of quantum field theory, though, locality is everywhere. The Hilbert space doesn't work to preserve locality except as Giddings has described it: constrained by the boundary of a black hole event horizon. Giddings thinks he has found a way out. The article continues:
"In Giddings' model, however, the Hilbert spaces can exchange information. This allows a black hole to slowly evaporate, but not before it has dumped the information contained within into the environment."
Problem is, this does not resolve the paradox -- "the environment," the space outside the event horizon, is nonlocal. So the mathematical model is accurate; the quantum configuration space of the black hole interior maps onto physical space with a nonlocal model, consistent with Bell's result. There's a catch:
A physical observer sufficiently far from the event horizon has no concept of "fast" or "slow" information leakage. All she sees is on the 2-dimension surface of the event horizon, and those events are suspended in time, not dynamic, with no exchange of information between events inside and outside the horizon.
The article continues:
"The idea is that local quantum field theory can be derived as an approximation of this more fundamental underlying structure, in the same way that non-relativistic Newtonian physics can be derived from relativistic Einsteinian physics."
Except that quantum field theory is everywhere local, not bounded by anything except the speed of light, and nothing physical. It's also inaccurate that non-relativistic Newtonian physics derives from Einstein relativity -- Einstein's relativity is an extension of Newton's physics as Newton is an extension of Galilean relativity. There's no discontinuity, no gap where relativity doesn't apply.
Giddings seems aware of the conundrum, and is willing to eject spacetime from the physics canon: "Spacetime is doomed." If it is, Giddings' model doesn't do the job. The paradox created by the discontinuous dumping of information from the assumed local, simply connected quantum-configured black hole into the classical simply connected space outside the horizon, tells us at least three things:
1. There is no boundary between the quantum configuration space of the black hole, and "the environment." (All the space is simply connected.)
2. If the quantum configuration space cannot map onto the physical space without a nonlocal model, as Bell's result avers, the quantum configuration space behind the black hole event horizon is not local and not simply connected.
3. Nonlocality -- not spacetime -- is doomed.
Spacetime and quantum field theory nicely coexist with a continuum of Euclidean space, generalized to n-dimension topology. We simply don't need assumptions of Hilbert spaces and nonlocality.