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What does zero volume mean in physics?

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Well, I guess I would answer that by looking at how Stephen Hawking and Roger Penrose,

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when they developed the space-time theorems, recognized there was a singularity.

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That when they were tracing the trajectories of particles back in space and time,

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that they all came to a point where they coalesced and the laws of physics broke down.

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And so, what exactly the nature of the singularity is a little bit unknown,

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but it's a sign that the laws of physics broke down, and that's what they said.

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Looked like a beginning.