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I’ve heard black holes described as “more diameter than the circumference suggests” — to paraphrase Kip Thorne. Is there a point where you’re at “quantum scale

I’ve heard black holes described as “more diameter than the circumference suggests” — to paraphrase Kip Thorne. Is there a point where you’re at “quantum scale” around the singularity but not across the singularity? — like a quantum Einstein ring?

fartsucker69 4y ago
What do you mean by "across the singularity"? The singularity is a single point in the center. There's no being across it really.
- actionfromafar 4y ago
  I'm sure that's right, but on the other hand space itself is getting "denser" nearer to the singularity. I don't know what to make of that.
  - pdonis 4y ago
    > space itself is getting "denser" nearer to the singularity Where are you getting this from? It makes no sense.
- zmgsabst 4y ago
  When the shortest path lies on some sphere around the singularity where the circumference of that sphere is “quantum scale” but chords passing near the center are not. In the 2D example, is there some area where quantum effects happen in an annulus rather than in a disc because that central stretched region is “too big”.
  - pdonis 4y ago
    > some sphere around the singularity There is no such thing. The singularity is a moment of time, not a place in space.
    - zmgsabst 4y ago
      The event horizon is an example of a sphere around the singularity. So is the photon sphere.
      - pdonis 4y ago
        No, this is not correct. The singularity is not a place in space, so it is not possible to have a sphere around it. It makes no sense, just as having a sphere around, say, tomorrow noon makes no sense.
        zmgsabst 4y ago
        Perhaps instead of just saying what standard explanations are “make no sense”, you could try elaborating in any of your posts. Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. What facts specifically are you trying to articulate about spacetime geometry around a black hole?
        pdonis 4y ago
        > you could try elaborating in any of your posts I already have: the singularity is a moment of time, not a place in space. > Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. Yes, it does, for the reason I've already given: because there is no such thing as a sphere around a moment of time. > What facts specifically are you trying to articulate about spacetime geometry around a black hole? The fact that the singularity is not a place in space, it's a moment of time.
        zmgsabst 4y ago
        A singularity is a point on a spacetime manifold where it has a cusp. You can draw a bounding sphere around that, of which I’ve given two examples. What fact about spacetime geometries are you trying to convey? You should try explaining the relevance of what you’re repeating in terms of spacetime geometries rather than just repeating the same statement over and over — which isn’t a constructive reply.
- pdonis 4y ago
  > The singularity is a single point in the center. No, it isn't. It's a spacelike line that is to the future of every event inside the hole. It's a moment of time, not a place in space.
BoGoToTo 4y ago
Are you sure that quote isn't referring to the length dilation that occurs in a gravity well? Space is non-Euclidean so you can have a sphere with a radius larger than the circumference would allow.
- zmgsabst 4y ago
  His quote is exactly referring to that: but my question is, are black holes curved enough that you can have a circumference at quantum scale with a diameter above that scale? — ie, at which quantum effects would happen around but not across the singularity.
pdonis 4y ago
> I’ve heard black holes described as “more diameter than the circumference suggests” — to paraphrase Kip Thorne. I'm not sure where Thorne said whatever you are paraphrasing, but this description does not apply to black holes. It applies to ordinary gravitating bodies like stars and planets, but unlike them, black holes do not have a well-defined "diameter". The singularity inside the hole at r = 0 is not a place in space, it's a moment of time. So there is no well-defined "spatial distance from the singularity"; that would be like having a well-defined "spatial distance from tomorrow", which makes no sense.
- karmakaze 4y ago
  Seems a point in space-time, like a point in (longitude, latitude) where at latitude 90, longitude loses meaning.
  - pdonis 4y ago
    Not really, no. What you are describing is a coordinate singularity; but whether a coordinate singularity has a physical meaning or is just an artifact of the coordinates depends on the situation. In the case of the Earth, the coordinate singularity in longitude at the poles is an artifact of the coordinates: the Earth's poles are perfectly good parts of the Earth's surface and nothing physically goes wrong there. You just need to pick different coordinates if you want to cover the poles. The case of the horizon of a black hole in Schwarzschild coordinates is similar: there is a coordinate singularity, but it's an artifact of the coordinates. You can find other coordinate charts that have no coordinate singularity at the horizon. The black hole singularity at r = 0, however, is not an artifact of coordinates. It is a genuine physical singularity, where the spacetime curvature goes to infinity.
    - karmakaze 4y ago
      Thanks for the explanation of the difference. To be fair we don't know the physical curvature goes to infinity--the math says it does.
      - 4y ago

fartsucker69 4y ago

What do you mean by "across the singularity"? The singularity is a single point in the center. There's no being across it really.

actionfromafar 4y ago
I'm sure that's right, but on the other hand space itself is getting "denser" nearer to the singularity. I don't know what to make of that.
- pdonis 4y ago
  > space itself is getting "denser" nearer to the singularity Where are you getting this from? It makes no sense.
zmgsabst 4y ago
When the shortest path lies on some sphere around the singularity where the circumference of that sphere is “quantum scale” but chords passing near the center are not. In the 2D example, is there some area where quantum effects happen in an annulus rather than in a disc because that central stretched region is “too big”.
- pdonis 4y ago
  > some sphere around the singularity There is no such thing. The singularity is a moment of time, not a place in space.
  - zmgsabst 4y ago
    The event horizon is an example of a sphere around the singularity. So is the photon sphere.
    - pdonis 4y ago
      No, this is not correct. The singularity is not a place in space, so it is not possible to have a sphere around it. It makes no sense, just as having a sphere around, say, tomorrow noon makes no sense.
      - zmgsabst 4y ago
        Perhaps instead of just saying what standard explanations are “make no sense”, you could try elaborating in any of your posts. Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. What facts specifically are you trying to articulate about spacetime geometry around a black hole?
        pdonis 4y ago
        > you could try elaborating in any of your posts I already have: the singularity is a moment of time, not a place in space. > Saying that an event horizon or photon sphere isn’t around the singularity of a black hole doesn’t make sense, either. Yes, it does, for the reason I've already given: because there is no such thing as a sphere around a moment of time. > What facts specifically are you trying to articulate about spacetime geometry around a black hole? The fact that the singularity is not a place in space, it's a moment of time.
        zmgsabst 4y ago
        A singularity is a point on a spacetime manifold where it has a cusp. You can draw a bounding sphere around that, of which I’ve given two examples. What fact about spacetime geometries are you trying to convey? You should try explaining the relevance of what you’re repeating in terms of spacetime geometries rather than just repeating the same statement over and over — which isn’t a constructive reply.
pdonis 4y ago
> The singularity is a single point in the center. No, it isn't. It's a spacelike line that is to the future of every event inside the hole. It's a moment of time, not a place in space.

BoGoToTo 4y ago

Are you sure that quote isn't referring to the length dilation that occurs in a gravity well? Space is non-Euclidean so you can have a sphere with a radius larger than the circumference would allow.

zmgsabst 4y ago
His quote is exactly referring to that: but my question is, are black holes curved enough that you can have a circumference at quantum scale with a diameter above that scale? — ie, at which quantum effects would happen around but not across the singularity.

pdonis 4y ago

> I’ve heard black holes described as “more diameter than the circumference suggests” — to paraphrase Kip Thorne. I'm not sure where Thorne said whatever you are paraphrasing, but this description does not apply to black holes. It applies to ordinary gravitating bodies like stars and planets, but unlike them, black holes do not have a well-defined "diameter". The singularity inside the hole at r = 0 is not a place in space, it's a moment of time. So there is no well-defined "spatial distance from the singularity"; that would be like having a well-defined "spatial distance from tomorrow", which makes no sense.

karmakaze 4y ago
Seems a point in space-time, like a point in (longitude, latitude) where at latitude 90, longitude loses meaning.
- pdonis 4y ago
  Not really, no. What you are describing is a coordinate singularity; but whether a coordinate singularity has a physical meaning or is just an artifact of the coordinates depends on the situation. In the case of the Earth, the coordinate singularity in longitude at the poles is an artifact of the coordinates: the Earth's poles are perfectly good parts of the Earth's surface and nothing physically goes wrong there. You just need to pick different coordinates if you want to cover the poles. The case of the horizon of a black hole in Schwarzschild coordinates is similar: there is a coordinate singularity, but it's an artifact of the coordinates. You can find other coordinate charts that have no coordinate singularity at the horizon. The black hole singularity at r = 0, however, is not an artifact of coordinates. It is a genuine physical singularity, where the spacetime curvature goes to infinity.
  - karmakaze 4y ago
    Thanks for the explanation of the difference. To be fair we don't know the physical curvature goes to infinity--the math says it does.
    - 4y ago