On Jan 8, 2011, at 1:49 AM, michael ibison wrote:

*My original idea was similar. The problem is that absorption is a very particular event which the de Sitter singularity does not cause. Absorption is not a boundary condition in the usual sense of the word, where some condition is applied to the fields and / or their derivatives on a hypersurface of co-dimension 1. In fact there is no way that I know of to mimic absorption by such means. Absorption connotes cancellation of the incoming radiation in the forward direction (the direction in space and time of incoming light rays). For that to happen requires that there be matter at the boundary to take up the missing energy. There is no such matter at the future Conformal Singularity of de Sitter spacetime. So absorption, at least in its traditional meaning, does not happen at that boundary. In fact the incoming radiation apparently traverses the de SItter boundary unimpeded precisely because it is a singularity in a CONFORMAL factor, to which EM is insensitive. That's why people go to a conformal representation to analyze EM.*

Classically what you say is so of course. Indeed, this was Nick Herbert's objection. However, since the virtual electron-positron pairs of Hawking's mechanism are stuck at the horizon they are static LNIF's that feel an enormous Unruh acceleration temperature. Therefore, they get enough energy to be real electron-positron plasma at the Planck temperature that should absorb any photons that reach it. Lenny Susskind discusses this sort of horizon complementarity in his more technical little book on Fidos and Frefos. So the issue is what do the quantum thermodynamic corrections to your classical calculation entail?

*I do not know if the above argument applies to the BH horizon also. The reason I am not sure is because that horizon cannot be written conformally, as far as I know. Anyhow, though the future de Sitter singularity is not an absorber, it turns out impose a boundary condition due to the symmetry required /imposed by the Friedmann equation across the boundary. The scale factor is anti-symmetric about the horizon, so the universe must evolve on the other side in a time-reversed way. That turns out to imply a boundary condition on the EM fields. Some of that (but not all) is captured by requiring that B = 0 at the boundary. This is a mirror condition. (Physical mirrors generally work by setting E = 0, but a 'magnetic conductor' will do a similar job.)*

On Sat, Jan 8, 2011 at 12:15 AM, JACK SARFATTI <

Ray

The escaping member of the photon pair, which has torn apart by the strong gravitational tidal forces near the event horizon

change to

The escaping member of the photon pair, which has been torn apart by the strong gravitational tidal forces near the event horizon

:-)

So, now I need to understand Ibison's argument in detail as part of the question of how to apply the thermodynamics to our future cosmological horizon.

Ray Chiao writes:

"“Black holes” are “black,” in the sense that they are perfect absorbers of

every kind of particle, including photons at all frequencies [1]. Once particles

have passed through the event horizon of a BH, they can never get out again,

at a classical level of description. For in order for a particle to be able to escape

from the black hole, it would need somehow to acquire an escape velocity which

effectively exceeds the speed of light at the event horizon."

My basic idea that I tried to explain to Roger Penrose at Castiglioncello in 2008 is simply to apply the above idea for the black hole, to our future cosmological horizon. Therefore, trivially we have the Wheeler-Feynman total absorber final boundary condition in our accelerating universe that is heading for the de Sitter solution. We are not de Sitter in the past - an important Arrow of Time asymmetry there.

The only Hawking radiation we can see back-from-the-future is Wheeler-Feynman advanced thermal radiation that may well be the dark energy,

I also tried to explain this to Bernard Carr at King's College London - I think he got it, but Penrose did not because it contradicts his current idea of cyclic big bangs.

We are outside a black hole horizon, but inside our future horizon which is also observer dependent.

I don't yet understand Ibison's

"There is no conflict however if electromagnetic interactions on the advanced cone are principally negative rather

than positive energy interactions. If indeed they were, then the emission of positive energy radiation on the retarded

cone of a local source can be re-interpreted as an increment in the magnitude of negative binding energy propagating

(in forwards time) along the (here, necessarily) advanced cone of that source. No future sinks or sources are then

required. The predominance of retarded radiation as commonly understood then follows from the asymmetry of

advanced Greens functions which are the consequence of the boundary condition associated with a future time-like

mirror."

Ibison has this idea of a "time mirror" to replace the Wheeler-Feynman total absorber future boundary condition.

My original idea was simply this

1) No thermodynamic difference between a black hole horizon and our future cosmological horizon - other differences of course.

2) In both cases the static LNIF near the horizon sees infinite blue shift/Unruh temperature

3) i.e. for black hole

g(r) = (rs/r^2)(1 - 2rs/r)^-1/2

horizon at r = 2rs

4) for cosmological future horizon we are at r = 0 and

g(r) = c^2/\^1/2(1 - /\r^2)^-1/2

horizon at r = /\^-1/2