Yesterday Samir Mathur gave a colloquium here on the black hole information paradox. I've known Samir for many years; he was an assistant professor at MIT when I was a postdoc up the river. I've always found him to be a very precise and clear thinker.
On his web page there is a very simple introduction to the paradox. The initial presentation emphasizes the role of negative binding energy in black hole physics, which is related to the question of monsters: configurations in classical general relativity with more entropy than black holes of the same mass. (Slides.)
Here is a recent paper in which Samir discusses the black hole firewall problem and subadditivity of entropy.
Samir in action giving a more technical seminar earlier today:
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I went through Samir's intro. It is very accessible. The nagging question is, in GR, is it possible for one of these composite objects to have a negative effective mass? [and so somehow be inflationary?] Would it be realizable [maybe via some primordial process]?
ReplyDeletei feel ya bother.
ReplyDeleteonce the black hole information problem is solved life expectancy in bolivia will double.
and the boon to humanity that the students of these great minds will bring. it is truly awesome to contemplate.
or is it all just bourgeois degeneracy?
Ha! I was there too and sent his web counter from 132 to 136. Between us we must be 10% of the traffic!
ReplyDeleteinflationary = negative effective pressure, not mass.
ReplyDeleteThere are positivity theorems in GR that don't let the effective mass become negative.
"It is very accessible."
ReplyDeleteYes, thank goodness there were no differential equations!
It seems like the intro cuts off in the middle of the "Entangled states: notation" section. Is there something funny with my browser?
ReplyDeleteI have the Through-The-Wormhole understanding of GR. I was equating negative energy with negative mass, and negative mass implying repulsive 'gravity' [since gravity is just the curvature of the universe due to local mass|energy densities].
ReplyDeleteYES! But no. I don't know how the mc^2 interacts as a field, and my science-fiction-sensibility is that it is GR, so the gravitational potential shouldn't compute based on masses, it should compute based on E/c^2.
ReplyDeleteIt's still a work in progress, I think.
ReplyDeleteIt seems to me that that the usual theoretical methods, including the currently fashionable ones, haven't really come to grips with the implications of gauge theory gravity, as in Lasenby, Doran and Gull's "Gravity, Gauge Theories and Geometric Algebra" (http://arxiv.org/abs/gr-qc/0405033v1)
ReplyDeleteFor some of these applications the predictions of GTG and general relativity are identical, and these cases include all present experimental tests of general relativity. However, on matters such as the role of horizons and topology, the two theories differ. For example, we show that the black-hole solutions admitted in GTG fall into two distinct time asymmetric gauge sectors, and that one of these is picked out uniquely by the formation process. This is quite different to general relativity, which admits eternal time-reverse symmetric solutions.
...
After studying some solutions for the gravitational fields we turn to the properties of electromagnetic and Dirac fields in gravitational backgrounds. For
example, we give field configurations for a charge held at rest outside a black hole. We show how these field lines extend smoothly across the horizon, and
that the origin behaves as a polarisation charge. This solution demonstrates how the global properties of the gravitational fields are relevant to physics outside
the horizon, a fact that is supported by an analysis of the Dirac equation in a black-hole background. This analysis also provides a quick, though physically
questionable, derivation of a particle production rate described by a Fermi–Dirac distribution with the correct Hawking temperature. ... In particular, it is shown that a non-spatially-flat universe does not appear homogeneous to Dirac fields — fermionic matter would be able to detect the ‘centre’ of the universe if k != 0.
In other news Chris Doran and the other former members of the Cambridge geometric algebra group recently sold their successful GA-based dynamic game lighting firm, Geomerics, to ARM for an undisclosed sum .
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One thought that has always bugged me when thinking about the black hole information "paradox" is the antinomy between on one hand the apparent fact that information (such as embodied every brain state that has ever existed) can never be destroyed, and on the other the doctrinaire assertion that there is no possible physical basis for any form of afterlife. / Something about Wick rotations turning the Schrodinger equation into the heat diffusion equation/ imaginary friends naturally live in imaginary time, mumble, mumble.