And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!

When Susskind used the elephant in his gedanken experiment he was bringing us up to date. We are not so blind anymore relying on gut feelings?

Hawking radiation owes its existence to the weirdness of the quantum world, in which pairs of virtual particles pop up out of empty space, annihilate each other and disappear. Around a black hole, virtual particles and anti-particles can be separated by the event horizon. Unable to annihilate, they become real. The properties of each pair are linked, or entangled. What happens to one affects the other, even if one is inside the black hole.

See: The elephant and the horizon

Are we then not exploring the region of quantum gravity?

Best,

(1) there is a different kind of inaccessible subset of space-time that mere light cones and event horizons suggested originally;

(2) there is a discontinuity in what one naively expects to be a continuous function, in a way sharper even than phase change.

The series of refereed papers by myself and professor Philip V. Fellman which cite you and discuss you at length about Quantum Cosmology (one presented next month in Shanghai at Complexity2009) are leading us to search for yet another GR solution, near the end of time / beginning of time, where spacetime has two relatively inaccessible subsets. Another description is that the solution bifurcates, and by what basis do we say that one is physical and the other nonphysical?

This is both a Physics problem, and a metaphysics problem. In the subset of the late Caltech prof Fritz Zwicky on “Ideocosm” — Space of all mathematical theories: What topology?
How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories?

p.s. I like “Whoville” and yes, blogs have an advantage.

I built a naive model once where I treated an EM charge as the cause of the cosmological constant. In that model, the interior volume of the universe was electrically neutral and all the excess charge went to the “surface” of the universe (which I never bothered to define). The like charge on the surface of the universe was repulsive and the surface was pliable, so this caused expansion.

Although horribly interesting, in the end you realize that there is a lot of arbitrary reasoning when building such a model.

I have a lot of reading to do, including lurking rather than posting here. So I need to stop that. But I have to put one more thought out there for disconnected ATMs and/or amateur astronomers. Catching up doesn’t suck; catching up is *wonderful*.

“completely unsurprising” sounds like a bit of an overstatement to me. “is it misleadingly simplistic?” It is if you think it follows from any statement that’s only true in some coordinate systems, as opposed to a coordinate-invariant statement of actual physics. The statement “infalling objects never pass the horizon” is only true in some coordinate systems.

It is worth stressing that in GR you can use any coordinate system you like, and the Schwarzschild coordinates (in which t goes to infinity before a falling object passes through the horizon) are, very clearly, pathological on the horizon. What’s “natural” about the Schwarzschild coordinates is only that (a) far from the black hole, they merge nicely into ordinary flat spacetime polar coordinates, and (b) adding a constant to the t coordinate of every point in spacetime is a symmetry of the spacetime (and even that’s not quite true for real black holes). But they are terrible for making sense of infalling objects. There are other coordinate systems that do a much better job of that.

The surfaces of constant Schwarzschild t that fail to pass through the horizon aren’t really telling you anything “from the POV of my reference frame”. A reference frame is something local; every observer can pick a local reference frame in which they are at rest, but that doesn’t give them any special, “correct” way to put coordinates on distant events in curved spacetime. There’s nothing at all that compels someone far from a black hole to use a time coordinate in which infalling objects never pass through the horizon.

…isn’t it completely unsurprising then that the entropy of the black hole should be proportional to the area of the event horizon since, from my frame of reference, that’s where all the information I toss at the black hole ends up?

Is this a useful way of thinking about the entropy of black holes… or is it misleadingly simplistic?

* Gravity has lots of observable consequences. So does quantum mechanics. Therefore, it would be nice to understand how they work together, and this paper was one of the many small steps in that direction. If you don’t think that’s an especially interesting thing to spend time thinking about, that’s fine; there’s plenty of good physics out there for everyone.

* Charged black holes are not going to occur in nature, it’s too easy to cancel the charge by absorbing some ions. Even if you had an extremal black hole, it wouldn’t absorb any more equal charge, because the repulsion would be too strong.

* Eliot, I’m not sure that it’s right to think of gravity as an entropy sink. More that the extremal BH geometry doesn’t include all the spacetime you might naively have thought, just by thinking of it as a limit of non-extremal black holes, and therefore the entropy might not be continuous.

* Sam C, you are more than welcome to pass on that quote.

A better way to think about things falling into a black hole is to note that if you drop something from anywhere outside the hole, after a certain finite amount of time it becomes physically impossible to chase after it and catch it before it crosses the event horizon (or even to shine a beam of light towards the falling object so the photons will reach it before it crosses the horizon).

What you see of an infalling object (albeit exponentially dimmed, so you don’t really get to see it), and what you can calculate if you use certain natural but potentially misleading coordinates, might suggest that the object “hovers forever” at the horizon. But if you can’t catch something, even at the speed of light, it’s gone.

The standard way of defining the mass of a black hole is to time the orbits of distant objects. You certainly won’t have to wait forever for the mass of an object dropped into the hole to show up in the total mass by that definition. And, after any gravitational waves from the infalling object have dissipated, the whole spacetime geometry outside the hole very rapidly comes to reflect the hole’s new mass.

Is the implication here that gravity seems to be functioning as an entropy “sink” here in some as yet to be identified/quantified way or am I completely missing the point?

Thanks

e.

I can smell some very interesting physics lurking around somewhere here…