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In our day and age we can calculate the mass and maximum volume of a black hole. With LIGO we can also now calculate by how much is space warped, relative to the distance to a black hole merger, such that we could potentially say something like "with a merger of a approximate total mass of M, and an approximate distance from the earth D, we saw a warping of space itself of W", and then even look at the amount of increase in space warping as D approaches 0.

My question then is, do we have anything in quantum mechanics to tell us 2 things:

  1. how much space itself (in quantum space theory) warps around a body of mass M
  2. how many gravitons are responsible for that amount of warping

Please excuse my lack of knowledge, or if I ask anything silly, I am not a physicist in any way shape or form. My intention was to somewhat get an idea on whether this paper, combined with the answer, can tell us what the quark-to-graviton ratio could be in the universe, since supposedly we could approximate the number of quarks in a black hole.

Cosmin A.
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  • gravity is yet not quantized. I would think even if/when it is the dimensions with respect to h_bar will be such that classical calculations of geodesics will be fine. Also the hypothetical gravitons are bosons, and like photons their number is not conserved. – anna v Oct 15 '19 at 09:06
  • We can quantify how much spacetime is warped near a body of mass $M$. We can quantify how much spacetime near Earth is warping when we detect a gravitational wave. None of this requires any quantum mechanics, only classical General Relativity. – G. Smith Oct 15 '19 at 15:56
  • "we can calculate the mass and maximum volume of a black hole" - Indeed, see p. 6 here: https://arxiv.org/abs/0801.1734 - "There is zero volume inside the black hole in any Schwarzschild time slice of a Schwarzschild black hole spacetime." – safesphere Oct 21 '19 at 16:12
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    "how much space itself (in quantum space theory) warps around a body of mass M" - (1) There is no "quantum space theory".(2) Space doesn't "warp around" a body, but expands in the radial direction: https://en.wikipedia.org/wiki/Schwarzschild_metric - "how many gravitons are responsible for that amount of warping" - Gravitons have not (and likely will never be) observed experimentally and are not a part of any complete or accepted theory. There is no evidence that gravity has a quantum nature. Your whole question is based on a series of misconceptions. – safesphere Oct 21 '19 at 16:28
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    Besides, the paper you quote also is based on misconceptions. "A contradiction exists between the gravitational singularity at the center of a black hole predicted by general relativity and the Pauli exclusion principle" - No such contradiction exists: https://physics.stackexchange.com/questions/366468 - Also: "a gravitational singularity [...] having finite mass within a point sized space inside an event horizon*" - This is an urban legend. A singularity is not a point like object in space, but a moment of time along an infinitely long line: https://math.stackexchange.com/questions/2929400 – safesphere Oct 21 '19 at 16:59
  • @safesphere that makes sense, thank you for you comments. I understand that there is no evidence that gravity has a quantum nature. However from your answer, 'and likely will never be' it would seem you're not a fan of any theories involving gravitons as carriers of the gravitational force, and I would also love to hear the thoughts of someone who is a fan – Cosmin A. Oct 25 '19 at 17:46
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    @CosminA. I did not say "never" in relation to gravity's quantum nature. I am totally fine with the idea of quantum gravity. I only said that gravitons likely will never be observed experimentally (even if they exist).They would be just too small to be detected. "Unambiguous detection of individual gravitons, though not prohibited by any fundamental law, is impossible with any physically reasonable detector" - https://en.wikipedia.org/wiki/Graviton – safesphere Oct 25 '19 at 19:07
  • @safesphere Oh, right, yes then that makes good sense, I've learned this from many sources and in my limited knowledge I completely agree. – Cosmin A. Oct 26 '19 at 08:36
  • @safesphere you also said "Your whole question is based on a series of misconceptions.". That makes sense, and I actually am aware of it hehe. But I guess I am still curious as to whether there is any direct correlation between a mass M and the quantifiable impact on space itself. Are there any readings or papers you could suggest, that are even remotely related to this? – Cosmin A. Oct 26 '19 at 08:43
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    @CosminA. It depends on your level of math. A simple example is the radial Schwarzschild metric: $ d\tau^2 = dt^2\cdot(1-2M/r)-dr^2/(1- 2M/r) $ - This formula shows that near heavy bodies (1) time moves slower and (2) space expands in the radial direction. For example, If I see you 1km from the black hole event horizon, you may see yourself 2km away from it "at the same time". I also would see you moving twice slower while you would see me moving twice faster than yourself. Try posting several narrow questions on this site instead of one broad question. – safesphere Oct 26 '19 at 09:03

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