4 ms·

Is that not what it does?

by chownie 3y ago

mr_toad 3y ago
General relativity requires singularities, QM prohibits them. It’s a puzzle.
- XorNot 3y ago
  Keep in mind in GR singularities don't really make sense either: i.e. when you pass the event horizon of a black hole, under GR the rules say that you must always been traveling towards the singularity. But the corollary of this is that it's not actually possible - mathematically - to arrive at the singularity (because then you'd be moving parallel with it rather then towards it). So while we can define what happens very well under GR for the "most" of the inside of a black hole, we can't actually explain what happens to objects which reach the center. There has to be some type of discontinuity whatever happens - i.e. if the object disappears, that's still a discontinuity even if it would resolve the paradox. EDIT: Which is of course where GR and QM need to reconcile as well - as you get infinitely close to the singularity, the size scale is getting small enough that QM should be well in play.
  - richardw 3y ago
    Can they reach the center? And how long would that take? I ask because time will slow down for them as they accelerate towards the center.
    - XorNot 3y ago
      Your first question is the problem: they must always be moving towards the center - which implies they must be getting closer to it. Because if they can never actually reach the center, then in 4D spacetime they're no longer moving towards it - they'd be traveling parallel with it. Which would imply that singularity isn't a singularity - i.e. the "hole" it makes would in fact be highly curved spacetime in one dimension, but completely flat in another (i.e. it would be a cylinder). Which creates a hole lot of weird infinities in the system: i.e. a black hole becomes a finite bounded volume on the outside, but contains an infinite amount of space on the inside (since no matter how much you distort spacetime, the molecules of whatever falls in can just pull themselves together more tightly provided the distortion doesn't happen too quickly).
    - SpaceManNabs 3y ago
      Time doesnt slow down for them. They reach the center in their time as normal. We never see them reach the center. You can use kruskal coordinates and other tools to understand this.
      - wholinator2 3y ago
        Right, time doesn't slow down for them, but it would appear so for an outside observer. So would the "experience" of a particle sent in to be that it circles closer and closer for some time on the order of years and at some point when it is arbitrarily close to the center it just pops out some billion or trillion years later once the black hole has evaporated? Assuming it isn't destroyed and somehow can experience it's own time.
        SpaceManNabs 3y ago
        It would be more than a few trillion years I think, but that is the thinking unless you are a certain contentious Berkeley astrophysicist. The particle does see itself “reach” the black hole though. And so would an outside observer if they had infinite time. The black hole dissipating sure would make some of the experience odd. I would need to revisit my notes to make a claim about that, but discontinuities like that arent uncommon.
- HardlyCurious 3y ago
  Singularities aren't believed to be real by physicists to my understanding. Which if true, would mean the existence of them in GR is an error of the formulation or an error of comprehension. If you look at the tangent lines facing toward the middle of the torus they would point to a single middle point, a singularity. But if you follow those lines around the surface they would never get to that extrapolated point of singularity. Probably nonsense, but the 2d creatures can't see in 3d and all that philosophy stuff.
  - SpaceManNabs 3y ago
    Singularities arent real in what sense? You can deal with some with penrose diagrams and other tools is what you mean?
    - kahnclusions 3y ago
      They aren't real in the physical sense. Physicists do not believe that the singularity is a real physical phenomena at the centre of a black hole. They are only an artefact of the incomplete maths. When a singularity appears in the math of a theory, it is seen as an error or incompleteness in the theory. GR breaks down and fails to describe what happens at the centre of a black hole. It's like how a "divide by 0" doesn't actually equal "infinity", it's answer is undefined.
      - raattgift 3y ago
        > They aren't real in the physical sense. In the spirit of Oppenheim's CQ (classical gravity, quantum matter) work which is discussed in the fine article at the top, I'll say that your first sentence is a bit too strong. Curvature singularities (in the Kretschmann (or other curvature scalar) divergence sense) aren't ruled out by astronomical observation. Indeed, practically no observational data sheds any light on the question. What is easily ruled out is Schwarzschild black holes (known black hole candidates all have significant angular momentum) and Kerr black holes (Kerr & Schwarzschild are eternal without beginning while our universe appears to have a finite age; they exist in an energy-free and non-fluctuating vacuum rather than in a local region full of at least CMB photons but also gas and dust and nearby stars; and they exist in a larger volume filled with stars, black holes in their host galaxy, galaxies with other black holes, and so on). At the following link is Roy Kerr giving a 2016 invited talk where he points out that despite the success of the metric that carries his name, especially for round spinning bodies (planets, stars) and even the then-current evidence favouring Kerr as a good description of large black holes (evidence since then has also been supportive), nobody should feel comfortable about the Kerr interior solution because there will be matter inside an astrophysical BH that is for practical purposes Kerr for outside observers. <https://youtu.be/nypav68tq8Q?t=2884 https://youtu.be/nypav68tq8Q?t=2884> (around the 48 minute mark). This is not that General Relativity is wrong, merely that GR itself depends on a solution to the Einstein Field Equations (EFEs) for a given spacetime, and black hole spacetimes commonly known by non-specialists (including physicists who aren't relativists) have features which are unphysical and which actually matter. There are lots of somewhat recondite solutions to the Einstein Field Equations (EFEs) which look like Kerr or Schwarzschild black holes to families of observers, but which have very different geometrical structure (these model black holes might have formed a finite time in the past by collapse of matter, for instance, or they might couple to a more realistic expanding spacetime with gravitational radiation from distant souces sloshing around). Known black holes (rather, things that in telescopes etc are for all practical purposes black holes) are in such a complicated environment by comparison that we simply do not have an exact solution for the Einstein Field Equations for any of them. We are stuck with approximations, and those approximations often don't even solve the EFEs (even numerically) but rather some cut-down version. The Raychaudhuri focusing theorem and similar results make it pretty clear that singularities form rather generically in fairly generic curved spacetimes equipped with matter. Penrose has raised comparable arguments. Our actual spacetime is not really generic on the whole, so we look at small pieces at a time and hope we are right in our guesses about how we can assemble multiple small pieces into an improved approximation of our universe. Those small pieces are calculated to be riddled with singularities for reasons related to Raychaudhuri, but that's an artifact of the construction of the small pieces as solutions of the EFEs, how we truncate those solutions, and/or how we stitch them together (e.g. Darmois-Israel). Maybe what singularities arising in commonly-used black hole solutions of the Einstein Field Equations tell us is that our understanding of matter is off. Indeed, the whole article at the top is about a programme to study how quantum matter influences the gravitational field ("back-reaction"). For all we know, real matter that remains outside a black hole and does things like inverse Compton scattering (as well as matter that plunges inward) blocks the formation of a singularity inside. Part of the motivation for quantum gravity (CQ being a flavour thereof) is being able to extract observables that can answer that question. > Physicists do not believe ... I'm pretty sure many physicists hope that nature doesn't produce singularities mostly because that makes it harder to ask how parts of the universe evolve (solutions to the EFEs become infinite at a singularity, but we can sorta work around the supposed singularity with Bowen-York punctures, dynamical excisions, adaptive mesh refinement and other techniques). I'm also pretty sure that anyone with a background that supports the formation of such a belief (or its opposite, or some third choice) knows that today we just don't know how to prove much (even in principle) about the interior of black hole candidate objects in our sky. Conversely, I do not believe there are singularities in those astronomically-observed objects, but that's because there isn't much evidence one way or another. In practice it really doesn't matter because the interior doesn't really matter much in practice, and if singularities are somehow observed we will cope with them. As to "somehow observed", quantum gravity phenomenology researchers will tell you that we would be lucky to catch the leading order quantum correction to GR with present-and-near-future observational ability, while theorists will then tell you that the singularity-or-not answer probably depends on the next-to-the-next-to-the-leading order. Consequently we have practically no way to distinguish among quantum gravity theories (including CQ) which are known to reproduce the successes of General Relativity in the neighbourhood immediately around our own planet. (Indeed, the gravitational field of Earth barely needs General Relativity, let alone quantum corrections to that, and there are lots of things we don't know about the deep interior of our own planet. As far as anyone can tell using a post-Newtonian formalism one only needs the leading order (1PN) to fully describe all present measurements of gravitation around us. Earth's gravity essentially a barely-perturbed Kerr (exterior) metric (see e.g. Soffel & Frutos 2016). And that's only thousands of metres to thousands of kilometres away. So not knowing about the deep interior of things at minimum thousands of light-years away doesn't really disturb me, even as we go up to 3PN+ (see e.g. Clifford Will's 2011 "On the unreasonable effectiveness of the post-Newtonian approximation") based on our long-distance observation of the glowing and/or opaque stuff outside of them).
- GoblinSlayer 3y ago
  General relativity requires infinite time for singularities to form. Fully formed singularity is a mathematical construct which is assumed into existence, it doesn't correspond to anything physical.

Is that not what it does?

mr_toad 3y ago

General relativity requires singularities, QM prohibits them. It’s a puzzle.

XorNot 3y ago
Keep in mind in GR singularities don't really make sense either: i.e. when you pass the event horizon of a black hole, under GR the rules say that you must always been traveling towards the singularity. But the corollary of this is that it's not actually possible - mathematically - to arrive at the singularity (because then you'd be moving parallel with it rather then towards it). So while we can define what happens very well under GR for the "most" of the inside of a black hole, we can't actually explain what happens to objects which reach the center. There has to be some type of discontinuity whatever happens - i.e. if the object disappears, that's still a discontinuity even if it would resolve the paradox. EDIT: Which is of course where GR and QM need to reconcile as well - as you get infinitely close to the singularity, the size scale is getting small enough that QM should be well in play.
- richardw 3y ago
  Can they reach the center? And how long would that take? I ask because time will slow down for them as they accelerate towards the center.
  - XorNot 3y ago
    Your first question is the problem: they must always be moving towards the center - which implies they must be getting closer to it. Because if they can never actually reach the center, then in 4D spacetime they're no longer moving towards it - they'd be traveling parallel with it. Which would imply that singularity isn't a singularity - i.e. the "hole" it makes would in fact be highly curved spacetime in one dimension, but completely flat in another (i.e. it would be a cylinder). Which creates a hole lot of weird infinities in the system: i.e. a black hole becomes a finite bounded volume on the outside, but contains an infinite amount of space on the inside (since no matter how much you distort spacetime, the molecules of whatever falls in can just pull themselves together more tightly provided the distortion doesn't happen too quickly).
  - SpaceManNabs 3y ago
    Time doesnt slow down for them. They reach the center in their time as normal. We never see them reach the center. You can use kruskal coordinates and other tools to understand this.
    - wholinator2 3y ago
      Right, time doesn't slow down for them, but it would appear so for an outside observer. So would the "experience" of a particle sent in to be that it circles closer and closer for some time on the order of years and at some point when it is arbitrarily close to the center it just pops out some billion or trillion years later once the black hole has evaporated? Assuming it isn't destroyed and somehow can experience it's own time.
      - SpaceManNabs 3y ago
        It would be more than a few trillion years I think, but that is the thinking unless you are a certain contentious Berkeley astrophysicist. The particle does see itself “reach” the black hole though. And so would an outside observer if they had infinite time. The black hole dissipating sure would make some of the experience odd. I would need to revisit my notes to make a claim about that, but discontinuities like that arent uncommon.
HardlyCurious 3y ago
Singularities aren't believed to be real by physicists to my understanding. Which if true, would mean the existence of them in GR is an error of the formulation or an error of comprehension. If you look at the tangent lines facing toward the middle of the torus they would point to a single middle point, a singularity. But if you follow those lines around the surface they would never get to that extrapolated point of singularity. Probably nonsense, but the 2d creatures can't see in 3d and all that philosophy stuff.
- SpaceManNabs 3y ago
  Singularities arent real in what sense? You can deal with some with penrose diagrams and other tools is what you mean?
  - kahnclusions 3y ago
    They aren't real in the physical sense. Physicists do not believe that the singularity is a real physical phenomena at the centre of a black hole. They are only an artefact of the incomplete maths. When a singularity appears in the math of a theory, it is seen as an error or incompleteness in the theory. GR breaks down and fails to describe what happens at the centre of a black hole. It's like how a "divide by 0" doesn't actually equal "infinity", it's answer is undefined.
    - raattgift 3y ago
      > They aren't real in the physical sense. In the spirit of Oppenheim's CQ (classical gravity, quantum matter) work which is discussed in the fine article at the top, I'll say that your first sentence is a bit too strong. Curvature singularities (in the Kretschmann (or other curvature scalar) divergence sense) aren't ruled out by astronomical observation. Indeed, practically no observational data sheds any light on the question. What is easily ruled out is Schwarzschild black holes (known black hole candidates all have significant angular momentum) and Kerr black holes (Kerr & Schwarzschild are eternal without beginning while our universe appears to have a finite age; they exist in an energy-free and non-fluctuating vacuum rather than in a local region full of at least CMB photons but also gas and dust and nearby stars; and they exist in a larger volume filled with stars, black holes in their host galaxy, galaxies with other black holes, and so on). At the following link is Roy Kerr giving a 2016 invited talk where he points out that despite the success of the metric that carries his name, especially for round spinning bodies (planets, stars) and even the then-current evidence favouring Kerr as a good description of large black holes (evidence since then has also been supportive), nobody should feel comfortable about the Kerr interior solution because there will be matter inside an astrophysical BH that is for practical purposes Kerr for outside observers. <https://youtu.be/nypav68tq8Q?t=2884 https://youtu.be/nypav68tq8Q?t=2884> (around the 48 minute mark). This is not that General Relativity is wrong, merely that GR itself depends on a solution to the Einstein Field Equations (EFEs) for a given spacetime, and black hole spacetimes commonly known by non-specialists (including physicists who aren't relativists) have features which are unphysical and which actually matter. There are lots of somewhat recondite solutions to the Einstein Field Equations (EFEs) which look like Kerr or Schwarzschild black holes to families of observers, but which have very different geometrical structure (these model black holes might have formed a finite time in the past by collapse of matter, for instance, or they might couple to a more realistic expanding spacetime with gravitational radiation from distant souces sloshing around). Known black holes (rather, things that in telescopes etc are for all practical purposes black holes) are in such a complicated environment by comparison that we simply do not have an exact solution for the Einstein Field Equations for any of them. We are stuck with approximations, and those approximations often don't even solve the EFEs (even numerically) but rather some cut-down version. The Raychaudhuri focusing theorem and similar results make it pretty clear that singularities form rather generically in fairly generic curved spacetimes equipped with matter. Penrose has raised comparable arguments. Our actual spacetime is not really generic on the whole, so we look at small pieces at a time and hope we are right in our guesses about how we can assemble multiple small pieces into an improved approximation of our universe. Those small pieces are calculated to be riddled with singularities for reasons related to Raychaudhuri, but that's an artifact of the construction of the small pieces as solutions of the EFEs, how we truncate those solutions, and/or how we stitch them together (e.g. Darmois-Israel). Maybe what singularities arising in commonly-used black hole solutions of the Einstein Field Equations tell us is that our understanding of matter is off. Indeed, the whole article at the top is about a programme to study how quantum matter influences the gravitational field ("back-reaction"). For all we know, real matter that remains outside a black hole and does things like inverse Compton scattering (as well as matter that plunges inward) blocks the formation of a singularity inside. Part of the motivation for quantum gravity (CQ being a flavour thereof) is being able to extract observables that can answer that question. > Physicists do not believe ... I'm pretty sure many physicists hope that nature doesn't produce singularities mostly because that makes it harder to ask how parts of the universe evolve (solutions to the EFEs become infinite at a singularity, but we can sorta work around the supposed singularity with Bowen-York punctures, dynamical excisions, adaptive mesh refinement and other techniques). I'm also pretty sure that anyone with a background that supports the formation of such a belief (or its opposite, or some third choice) knows that today we just don't know how to prove much (even in principle) about the interior of black hole candidate objects in our sky. Conversely, I do not believe there are singularities in those astronomically-observed objects, but that's because there isn't much evidence one way or another. In practice it really doesn't matter because the interior doesn't really matter much in practice, and if singularities are somehow observed we will cope with them. As to "somehow observed", quantum gravity phenomenology researchers will tell you that we would be lucky to catch the leading order quantum correction to GR with present-and-near-future observational ability, while theorists will then tell you that the singularity-or-not answer probably depends on the next-to-the-next-to-the-leading order. Consequently we have practically no way to distinguish among quantum gravity theories (including CQ) which are known to reproduce the successes of General Relativity in the neighbourhood immediately around our own planet. (Indeed, the gravitational field of Earth barely needs General Relativity, let alone quantum corrections to that, and there are lots of things we don't know about the deep interior of our own planet. As far as anyone can tell using a post-Newtonian formalism one only needs the leading order (1PN) to fully describe all present measurements of gravitation around us. Earth's gravity essentially a barely-perturbed Kerr (exterior) metric (see e.g. Soffel & Frutos 2016). And that's only thousands of metres to thousands of kilometres away. So not knowing about the deep interior of things at minimum thousands of light-years away doesn't really disturb me, even as we go up to 3PN+ (see e.g. Clifford Will's 2011 "On the unreasonable effectiveness of the post-Newtonian approximation") based on our long-distance observation of the glowing and/or opaque stuff outside of them).
GoblinSlayer 3y ago
General relativity requires infinite time for singularities to form. Fully formed singularity is a mathematical construct which is assumed into existence, it doesn't correspond to anything physical.