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Senior Vice-President for Research and Innovation, Professor of Theoretical Physics, Michigan State University

Tuesday, August 27, 2013

Factorization of unitarity and black hole firewalls

Factorization of unitarity and black hole firewalls
Stephen D.H. Hsu

Unitary black hole evaporation necessarily involves a late-time superposition
of decoherent states, including states describing distinct spacetimes (e.g.,
different center of mass trajectories of the black hole). Typical analyses of
the black hole information problem, including the argument for the existence of
firewalls, assume approximate unitarity ("factorization of unitarity") on each
of the decoherent spacetimes. This factorization assumption is non-trivial, and
indeed may be incorrect. We describe an ansatz for the radiation state that
violates factorization and which allows unitarity and the equivalence principle
to coexist (no firewall). Unitarity without factorization provides a natural
realization of the idea of black hole complementarity.
From the paper:
... An objection to the importance of macroscopic superpositions to the information problem is that there is much less information in the coarse grained position or even trajectory (sequence of positions) of the black hole than in the radiation. From this perspective one should be able to neglect the superposition of spacetimes and demand approximate unitarity branch by branch -- in other words, impose factorization. Below, we show that the firewall argument depends sensitively on the precision of factorization. Once macroscopic superpositions are taken into account, the required deviation of near-horizon modes from the inertial vacuum state becomes extremely small. ...


The quantum evolution of a complex pure state typically leads to a superposition of decoherent semiclassical states. In the case of black hole evaporation one obtains a superposition of spacetime geometries because the Hawking radiation inevitably exhibits fluctuations in energy and momentum density over different regions. Firewall and information paradoxes result from the non-trivial assumption of factorization: approximate unitarity on each decoherent geometry. Global unitarity is a much weaker condition than factorization. Quantum correlations between geometries can plausibly resolve the information paradoxes, although specific dynamical mechanisms are still not understood.


LuboŇ° Motl said...

Nice paper, I completely agree with you: all the potential final microstates are being mixed in the most general way so it's certainly incorrect to assume that the evaporating black hole Hilbert space may be rewritten as a direct sum of many "superselection sectors" that evolve unitarily and independently. This is one of the wrong assumptions constantly made by AMPS and followers - one that effectively amounts to believing that the geometry is purely classical and the gross features of a system like BH are perfectly predictable which they're not.

Just to sure, you're not the first one who pointed out pretty much the same thing but it's nice that you cite Nomura, Varela, Weinberg, and friends for whom this was a key point to point out.

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steve hsu said...

Hi Lubos,

Thanks for your comment and blog post about my paper. Note I cite the Nomura gang as well as P-R. I actually have you (earlier post on your blog) to thank for pointing me to P-R, which I agree is a nice paper.

I was kind of surprised that most people working on BH information take "factorization"for granted, whereas it appears both you and I consider it a nontrivial assumption. It seems obvious to me that if you give up factorization you can avoid firewalls, but I anticipate this claim may turn out the be controversial.

I've also watched many of the KITP talks on firewalls. I wonder if Raju was able to get his points across in offline discussions concerning what is meant by "state dependent operators". To me it's kind of obvious that, e.g, the b, tilde-b operators in the AMPSS notation is state dependent in the sense that it is clearly background geometry dependent!

Michael Bacon said...

Over at Scott Aaronson's blog a commentor in reference to your paper and a comment by Lubos says:

Actually I am worried that Stephen’s argument proves too much. Unitarity is a properity of the S-matrix and if you will the Schroedinger evolution. But every real measurement involves a macroscopic device and at the end we only experience one decohered branch of the wave function.
So does this mean we can never demonstrate unitarity in a real experiment?

Curious what you thought about this.

Michael Bacon said...

Since comments on your paper are being bandied about -- feel free to comment there is you are so inclined.



steve hsu said...

Thanks! I posted the following comment there:


It is quite difficult to demonstrate unitary evolution in an experiment because to do so one would have to detect decohered branches of the "many worlds" wavefunction. This requires either exponential sensitivity (of order exp (-S) where S is the number of dof of the measuring device), or the ability to prepare operators comprised of macroscopic superpositions.

This article clarifies the analogy between unitarity in BH evaporation and unitarity in ordinary QM measurements:

Michael Bacon said...

Thanks Steve.

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