Interesting idea, even if it’s just a thought experiment. Photons “experience” everything in an instant, so it’s not that farfetched. I do like the image of time he subscribed. That could be a cool idea for a time travel movie.
Singularities are mathematical concepts based on the flawed theory of relativity. That isn’t to say that Relativity is wrong, but it does not jive with quantum mechanics and a flawless theory of gravity would include QM.
A theory of everything that encompasses Relativity and QM may describe a singularity under a quantum gravity model differently than how they are described currently.
There may be only one “singularity” that is unified due to the extreme spacial topography that defines them. So they aren’t separate volumes, but are one volume holographically projected from one feature to multiple locations, as you posed.
Just as time and space is irrelevant to the photon, and possibly the electron and other particles, space and time would be irrelevant to the singularity. Given that they would operate with indifference to time and space, they may have properties that are a division of a sum total, meaning the properties of the singularity are a derivative of the universe itself. So if our universe had more or less black holes, the properties of the singularity would respond accordingly.
So yes, we may just be watching the shadows on the walls of caves and every different cave’s shadows are all made with one fire that isn’t in a cave.
Think Klein bottle with a number of holes in it instead of one and the diameter of the holes are all the same. The diameter of the holes depend on the mass of the bottle and number of holes.
Then make it a 4 dimensional object and the holes transit time and space as if there was no time or space because the holes will have always existed, despite more holes being added between the time the bottle was created until the atoms of the bottle evaporate into the surface of the bottle itself.
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