Warp wrote:
>   Because you can't have a huge bunch of particles in a space of zero
> volume. 

The math for QM doesn't work out (so I've heard) if you assume particles 
aren't points.

> Hence if all the mass is in a singularity, it cannot be in the
> form of particles, but something else completely (basically something
> that cannot be described with current knowledge of physics).

That's fair. But I would more say "we don't know if they're still particles 
or something else" than I would say "we know they can't be particles because 
the math says there's zero space at the bottom of the well."

>   (Of course I'm assuming here that singularities do exist. It's possible
> that reality is different and they don't.)

Yeah, that's really the only assumption I'm challenging. Lots of folks on 
this thread are making assertions about what actually happens in places 
where, by definition, you cannot observe what actually happens. :-)

>   People don't claim to know what happens in the singularity. They claim that
> the equations say something about what happens *outside* the singularity
> (and that "something" is, basically, "there can't be anything inside the
> event horizon and outside the singularity, hence the only possible place
> where everything must be is in the singularity, because that's where all
> the space-time geodesics are pointing to").

Sure. Except it's a singularity. There's a discontinuity in the mathematics 
there. That's why it has that name. And the theories of gravity don't work 
if space isn't continuous, and the theories of really small stuff don't work 
if the space isn't discontinuous.  So ... I think it's safe to say "we don't 
know."

And, actually, the whole thing with the "holographic universe" bit is that 
stuff really doesn't necessarily disappear when it goes into the black hole.

>   Relativity cannot be applied to the singularity itself, but it can be
> applied to the space between the event horizon and the singularity. (It's
> all really weird there, and greatly complicated by things like rotation
> and electric charge, but calculable.)

*Assuming* that space is continuous. But if there's a lower limit on "the 
shortest distance" that isn't zero, then GR breaks down. And QED seems to 
suggest there is such a limit, because QED breaks down when you assume the 
shortest distance *is* zero.

>   If GR breaks at the singularity, who is to say that QM doesn't?

We know it does, *if* you assume GR. That's exactly why people are looking 
for a quantum version of GR. Because if you assume gravity can compress 
things down arbitrarily small, then QED gives infinite energies for every 
interaction, including those outside the event horizon.

>   Maybe information *is* destroyed at the singularity? After all, it's
> pretty weird in there (being of zero size and all).

That would violate all sorts of symmetry laws. That's why they think it 
doesn't happen. You lose all kinds of things like conservation of charge, as 
well as (if I recall right) conservation of some properties that GR assumes 
in its formulation, like conservation of momentum.

Of course, obviously something is wrong with the theories. We already know 
that. That's why people are looking at string theory and other GUTs. It's 
exactly these border conditions (infinite gravity, zero size) where the 
theories break down. So I'm not convinced anyone can confidently assert what 
*actually* happens, vs what the math implies should happen if the math is 
still isomorphic with reality under those circumstances.

-- 
Darren New, San Diego CA, USA (PST)
    C# - a language whose greatest drawback
    is that its best implementation comes
    from a company that doesn't hate Microsoft.

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