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> GR has singularities. More precisely, GR allows spacetime solutions which are geodesically incomplete. > It's definitely wrong in those regimes. No, that's

by pdonis 2y ago

> GR has singularities. More precisely, GR allows spacetime solutions which are geodesically incomplete. > It's definitely wrong in those regimes. No, that's too strong a claim. Most physicists believe that the solutions that are geodesically incomplete will turn out not to be valid in the regimes close enough to the endpoints of the incomplete geodesics. But that is a belief, not a proven fact. The solutions themselves are perfectly consistent mathematically.

naasking 2y ago
> But that is a belief, not a proven fact. The solutions themselves are perfectly consistent mathematically. Every physical theory with singularities has has broken down in that regime. It's not even clear what it would mean for reality to permit singularities. That's a bit more than just a belief.
- pdonis 2y ago
  > Every physical theory with singularities has has broken down in that regime. Can you give some examples? Note that GR has not even been tested anywhere close to the regime you are talking about. > It's not even clear what it would mean for reality to permit singularities. GR doesn't "permit singularities" in the sense I think you are using that phrase. "Singularity" in GR actually does not mean what I suspect you think it means, that things like spacetime curvature "become infinite". Notice that in my previous post I was careful to use the term "geodesic incompleteness", since that's what "singularity" actually means in the GR literature. And even in particular cases where there are invariants that increase without bound along incomplete geodesics, the limit points, such as r = 0 in Schwarzschild spacetime, are not actually part of the spacetime in GR. All invariants are finite at every point in the actual spacetime.
  - naasking 2y ago
    > Can you give some examples? See Baez's paper, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421 The UV catastrophe is probably the most well known.
    - pdonis 2y ago
      The issue in that paper isn't really limited to "singularities". The basic issue is that we use the continuum in our physical models, and "reality" might not actually be a continuum, so the continuum math we use is just an approximation. But if "reality" isn't a continuum, it isn't a continuum everywhere, not just near "singularities", so the continuum is an approximation everywhere, not just near "singularities". The approximation would just become unworkable near "singularities", while remaining workable in other regimes. Most physicists believe that our best current theories, GR and quantum field theory, are approximations anyway ("effective theories" is the term often used in the literature), so that in itself is not a new idea. Baez's paper points at one fairly common hypothesis for why they are approximations and what the underlying theory they are approximations to might look like. I don't have an issue with that as a hypothesis; it's just something we aren't going to be able to test by experiment any time soon, since the most likely scale for where the approximation will break down, the Planck scale, is some twenty orders of magnitude away from the scales we can currently probe with experiments.
      - naasking 2y ago
        Yes, there are many issues in our theories and even our formalisms. All I was trying to is point out, in the simplest way possible, was at least one way we know that GR is "wrong" (incomplete), which is its singularities.
        pdonis 2y ago
        > we know No, we don't know. Most physicists believe it, but that's not the same as knowing. We won't know unless and until we are able to actually do experiments in the relevant regime.

by pdonis 2y ago

naasking 2y ago

> But that is a belief, not a proven fact. The solutions themselves are perfectly consistent mathematically. Every physical theory with singularities has has broken down in that regime. It's not even clear what it would mean for reality to permit singularities. That's a bit more than just a belief.

pdonis 2y ago
> Every physical theory with singularities has has broken down in that regime. Can you give some examples? Note that GR has not even been tested anywhere close to the regime you are talking about. > It's not even clear what it would mean for reality to permit singularities. GR doesn't "permit singularities" in the sense I think you are using that phrase. "Singularity" in GR actually does not mean what I suspect you think it means, that things like spacetime curvature "become infinite". Notice that in my previous post I was careful to use the term "geodesic incompleteness", since that's what "singularity" actually means in the GR literature. And even in particular cases where there are invariants that increase without bound along incomplete geodesics, the limit points, such as r = 0 in Schwarzschild spacetime, are not actually part of the spacetime in GR. All invariants are finite at every point in the actual spacetime.
- naasking 2y ago
  > Can you give some examples? See Baez's paper, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421 The UV catastrophe is probably the most well known.
  - pdonis 2y ago
    The issue in that paper isn't really limited to "singularities". The basic issue is that we use the continuum in our physical models, and "reality" might not actually be a continuum, so the continuum math we use is just an approximation. But if "reality" isn't a continuum, it isn't a continuum everywhere, not just near "singularities", so the continuum is an approximation everywhere, not just near "singularities". The approximation would just become unworkable near "singularities", while remaining workable in other regimes. Most physicists believe that our best current theories, GR and quantum field theory, are approximations anyway ("effective theories" is the term often used in the literature), so that in itself is not a new idea. Baez's paper points at one fairly common hypothesis for why they are approximations and what the underlying theory they are approximations to might look like. I don't have an issue with that as a hypothesis; it's just something we aren't going to be able to test by experiment any time soon, since the most likely scale for where the approximation will break down, the Planck scale, is some twenty orders of magnitude away from the scales we can currently probe with experiments.
    - naasking 2y ago
      Yes, there are many issues in our theories and even our formalisms. All I was trying to is point out, in the simplest way possible, was at least one way we know that GR is "wrong" (incomplete), which is its singularities.
      - pdonis 2y ago
        > we know No, we don't know. Most physicists believe it, but that's not the same as knowing. We won't know unless and until we are able to actually do experiments in the relevant regime.