Monday, January 01, 2018

New Year's Eve fireworks and spacetime continuity at the event horizon

Happy New Year! Note that 2018 factorizes as 2*1009, the latter is a prime.

Most of you have probably seen and heard some fireworks. In my hometown, most of the havoc looked privatized. The explosions were a Poisson process with the rate around 10 per second – well, assuming an IR distance cutoff so that I could hear them. Millions of crowns had to be spent on these pyrotechnical toys, providing us with some extra evidence of the prosperity right now.

It's really irrational to treat the transition from 2017 to 2018 as a discontinuity. The moment when the year jumps to the new one is a pure human convention. On top of that, the moment is different in different time zones. Lots of skeptics must have always been as skeptical about the celebrations.

But I was led to think about an analogous fact: the black hole event horizon seems to be such a fake discontinuity, too. In classical general relativity, it is a coordinate singularity. It only looks special if you use certain coordinates and those coordinates may only be defined in an invariant way if you also know the full future.

A black hole has lots of microstates and each of them should allow the infalling observer to think that nothing special is happening at the event horizon, just like during New Year's Eve. At least I think that there's no firewall over there. So all the fireworks at the event horizon are fake or they are artifacts of some conventions, gauge choices, duality frames, and so on.

It would be nice to believe that there will be a real discontinuity, a break from 2017 to 2018, and in 2018, your humble correspondent or someone else finally figures out the actual principles and arguments that allow one to understand quantum gravity in the most general context – universal rules that define what the most general dynamical laws in quantum gravity may be, universal rules that allow you to calculate the spectrum and scattering amplitudes in the most general backgrounds.

I feel that the "apparent emptiness" of the event horizon in the most generic complex black hole microstate is actually a very puzzling fact – because a black hole microstate seemingly contains a huge amount of mess. It's one of the "apparent paradoxes" that may be severely underestimated now. There should be some crisp way to formulate this "almost paradox" and to solve it, too. It's possible that, as I have argued before, all the physical degrees of freedom hiding in the choice of the black hole microstate may be reorganized so that one part of them is a choice of the gauge transformation – something that is physically equivalent to nothing from the infalling observer's viewpoint.

On the Hilbert space of large black hole's microstates, all "creation operators" for smaller objects near the event horizon have to exist. The discrete choice of a black hole microstate should be analogous to the choice of the "position eigenstates" in quantum mechanics while the description in terms of "smaller objects falling into a smooth black hole spacetime" have to be analogous to the "momentum eigenstates". There should be some justifiable application of the quantum mechanical complementarity and perhaps a new state-operator correspondence where the operators – basically creation operators for objects – remember what objects do when they fall into each other as if the other were a black hole microstate.

Lots of papers have been written about quantum gravity and some of them are "constructive". They add new hypotheses and assumptions. But I find it plausible that the universal recipes of quantum gravity – so far unknown rules that would include all known descriptions of string/M-theory as subclasses of solutions or Ansätze – could be derivable and provable by a direct argument or a clever choice of the degrees of freedom, some monodromies in the gauge groups, Wilson lines, Schur's orthogonality theorems, and stuff like that.

Some readers are surely annoyed by the technical jargon but I hope that in 2018, someone will be much more technical and penetrating in these matters than I have been above.

Good luck to you, TRF folks, in 2018 and a Happy New Year.

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