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The Question

(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?

The Answer

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 singularity.

Best wishes,
Koji & Vladimir
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