For one, wouldn’t that mean they have a volume of zero? how does that work?
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It can’t, it’s just our current model.
We know that this model (general relativity) is wrong, but it is extremely good at making reliable predictions when things do not break down, such as in the singularity.
Most likely, the explanation lies in quantum mechanics and a theory of quantum gravity which will explain why there isn’t actually a point of infinite density.
It means our understanding of physics at that scale breaks down. If applying the math we know yields an absurd conclusion, the only possible answer is that the math itself is different at that scale. Maybe the concept of density doesn’t exist.
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