(Submitted September 13, 2009)
My brother has put forth a reasonable-sounding notion that seems to
be in conflict with the usual picture of the 'zero volume and infinite
density' of a gravitational singularity. If the volume is truly zero,
he notes, then the content must also be.
This would mean that the matter in a black hole would have to have some
finite, even if extremely small, volume, so as still to be able to exist.
Also, wouldn't the Heisenberg Principle disallow something with an exactly
measurable -- zero -- volume?
To paraphrase your brother: mass equals volume times density, and since
any number times zero is zero, the singularity must have a non-zero
volume to have any mass. But infinity is no ordinary number, and zero
times infinity can be any number between zero and infinity. So, your
brother is wrong to use that particular line of reasoning.
But you're correct to bring in Heisenberg. The singularity is true
if you just stick to general relativity, which is not a quantum theory.
Nobody has developed a convincing quantum theory of gravity yet, but
when someone does, it's almost certain to modify our concept of the
Koji & Vladimir
for "Ask an Astrophysicist"