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More precisely, physicists believe that the presence of the singularity in this solution of the Einstein Field Equation means that GR breaks down there and we w

by pdonis 3y ago

More precisely, physicists believe that the presence of the singularity in this solution of the Einstein Field Equation means that GR breaks down there and we will need some other theory (the best candidate at this point appears to be a quantum gravity theory) to figure out what happens there. But unless and until we discover that other theory, GR is the best we have and the best we can do is to describe what it predicts and acknowledge the limitations.

layer8 3y ago
I’d argue that GR literally provides no prediction for what happens at the singularity: https://physics.stackexchange.com/a/354893 https://physics.stackexchange.com/a/354893
- pdonis 3y ago
  > I’d argue that GR literally provides no prediction for what happens at the singularity That's false; GR does make a definite prediction: that curvature invariants increase without bound as the singularity is approached, but that they are finite everywhere in the actual spacetime (see further comments below). (Actually it's more nuanced than that; there are cases where there are incomplete geodesics, which is how "singularity" is actually defined in GR, but not unbounded invariants. But those are edge cases that aren't relevant to what we're discussing here.) The Stack Exchange thread's claim about geodesic incompleteness is misleading. The actual singularity--heuristically, the "point where things become infinite"--is not included in the spacetime manifold. It is an abstract "boundary point" that is not part of spacetime. What is actually included in the manifold is perfectly well-defined, with nothing infinite anywhere, and is a perfectly self-consistent mathematical model that makes perfectly valid predictions for everything in it. The Stack Exchange commenter basically doesn't like the fact that GR says "sorry, your model ends here, you can't extend it any further", which is fine, but it's not the same as saying GR must be wrong when it says that. It's just something many physicists are uncomfortable with and so they are looking for a model that doesn't have that property, like quantum gravity. But that's no guarantee that they will find one, nor is it a guarantee that GR must end up being overridden in this regime. It's just a best guess of many physicists at our current state of knowledge. Nor does it mean that GR doesn't make definite predictions; it just means GR's predictions are ones that most physicists would not like having to be stuck with if that's how it turns out. But nature doesn't care what humans like or don't like.

by pdonis 3y ago

layer8 3y ago

I’d argue that GR literally provides no prediction for what happens at the singularity: https://physics.stackexchange.com/a/354893 https://physics.stackexchange.com/a/354893

pdonis 3y ago
> I’d argue that GR literally provides no prediction for what happens at the singularity That's false; GR does make a definite prediction: that curvature invariants increase without bound as the singularity is approached, but that they are finite everywhere in the actual spacetime (see further comments below). (Actually it's more nuanced than that; there are cases where there are incomplete geodesics, which is how "singularity" is actually defined in GR, but not unbounded invariants. But those are edge cases that aren't relevant to what we're discussing here.) The Stack Exchange thread's claim about geodesic incompleteness is misleading. The actual singularity--heuristically, the "point where things become infinite"--is not included in the spacetime manifold. It is an abstract "boundary point" that is not part of spacetime. What is actually included in the manifold is perfectly well-defined, with nothing infinite anywhere, and is a perfectly self-consistent mathematical model that makes perfectly valid predictions for everything in it. The Stack Exchange commenter basically doesn't like the fact that GR says "sorry, your model ends here, you can't extend it any further", which is fine, but it's not the same as saying GR must be wrong when it says that. It's just something many physicists are uncomfortable with and so they are looking for a model that doesn't have that property, like quantum gravity. But that's no guarantee that they will find one, nor is it a guarantee that GR must end up being overridden in this regime. It's just a best guess of many physicists at our current state of knowledge. Nor does it mean that GR doesn't make definite predictions; it just means GR's predictions are ones that most physicists would not like having to be stuck with if that's how it turns out. But nature doesn't care what humans like or don't like.