6 ms·

That's a good question. The tl;dr is that if information hides on the other side of an event horizon and doesn't come back, we can pretend unitarity (and all t

That's a good question. The tl;dr is that if information hides on the other side of an event horizon and doesn't come back, we can pretend unitarity (and all the rest of the physics we've discovered) continues where we can't see it. A non-evaporating black hole forever holds within it the information about what fell into it. A forever-expanding universe causes information to exit observability forever. Partitioning away -- hiding forever -- information is not the same as losing track of it when it comes out of hiding. There are some differences between these two types of horizon because they are generated by different metrics : one for an expanding spacetime and one for a collapsing one. We can see the differences by adapting these theoretical (as opposed to astronomically observed) objects. If an expanding universe's expansion slows and reverses, then eventually all the galaxies that exited from one observer's view return into its view (having evolved with stars forming, aging, dying, galaxies merging, and so forth). If we are talking timescales of a few billion years, then if an us-like observer has detailed information about a galaxy now leaving its view, it can in principle predict what it will look like in billions of years when the galaxy returns back into view. The gentle assumption here is that stellar physics does not stop when the most distant galaxies go out of view. If the timescale is pushed out to trillions and zillions of years, these us-like observers could still maintain the idea that the galaxies which exited from visibility continue to evolve like the closer galaxies which continue to be seen. A star which ends up on the other side of the cosmological horizon continues being that same star, evolving as normal. A black hole is different, precisely because we should expect unknown extremely high energy physics to occur as e.g. protons fall in. What happens as you crush some quarks and gluons together at energies enormously higher than that we get from the LHC, or even from supernovae? We don't know. In fact, when we try to answer that, we lose track because our calculations tend to become singular : https://en.wikipedia.org/wiki/Singularity_(mathematics) https://en.wikipedia.org/wiki/Singularity_(mathematics) We don't know what should pop out of a black hole late in evaporation, but we do know when a star crashes through a black hole event horizon, it will stop behaving like a star very quickly. Indeed, even just on "our" side of the two horizons we can see differences near them. The furthest galaxies, at the edge of what we can see of the cosmos, are filled with normally behaved (young) stars. The shapes of those galaxies are not distorted by proximity to any horizon. We expect that to continue as we see galaxies deeper and deeper into our sky. By comparison we can see gas clouds falling into the black hole in the centre of our galaxy, stars orbiting it, and distortions to these caused by these close approaches to the central black hole. We have even found evidence of stars ripped apart by more distant extragalactic black holes. Crossing a black hole horizon does violence to the bit of the star that has not yet crossed; crossing the cosmological horizon would not change the star's basic behaviour. If the universe were to collapse in the future, we would expect to see disappeared stars returning into view. Those stars stayed in locally gently curved spacetime, just like our local star did. If a black hole were to shrink in the future, we would be surprised if it spat out intact stars, or space probes, or whatever fell in emerging unscathed. Those objects did not stay in locally gently curved spacetime, and indeed would have encountered the locally enormously curved spacetime inside the black hole. That strong curvature spaghettifies things, at the very least. These are just the consequences of our best theories of gravitation and matter applied to situations we have no reason to expect to be able to observe. As far as we know our universe is not accelerating towards a recollapse, it is accelerating towards faster expansion. And as far as we know no astrophysical black hole in our universe is presently shrinking. It's fairly safe to bet that if there is ever to be a reversal of the expanding cosmological metric or the collapsing black hole metric it's not going to be soon, so humanity and its descendants have lots of time to think about evaporating black holes (including those that evaporate in a contracting "anti-de Sitter" universe with a big crunch, which is the setting (sometimes including extra spatial dimensions than the three we're used to) for many approaches like the one in the fine article in Quanta Magazine linked at the top). Now, a more direct answer to your question: in an almost-completely-flat-space universe if we have all the data (position, momentum, particle species, etc) at every point in a time-indexed spatial slice of our universe, we can calculate the entire data in neighbouring slices, and the data in those slices' neighbours, and so forth, into the infinite future and the infinite past. An expanding universe doesn't break this, it just means that we can't choose any arbitrary slice and march forwards and backwards from there, we have to take initial data from the hottest densest earliest part of the universe. From complete initial data and appropriate dynamical laws we can (in principle) describe anything in the future, even if the parts we describe are so separated from one another (in that future) that they can't exchange light with one another. The formation of non-evaporating black holes doesn't change the picture much: we know that things fall into a black hole and stay there in some unknown state, unable to exchange light with things outside the black hole. However, once we introduce black hole evaporation we have the problem that we don't know how the stuff inside the horizon evolved inside the horizon, so we have no idea what should pop out through the last stages of evaporation. In our standard cosmology, we can expect black holes to have evolved from stuff that was close to us in the hot big bang era but which is now almost certainly forever outside our cosmological horizon. A general solution to the black hole information paradox should not create craziness in those so-distant-we-will-never-see-them black holes, much less in the earliest visible quasars. That tends to get forgotten until someone asks what the interviewer asked: Most of the justification for the quantum extremal surface formula comes from studying black holes in “Anti-de Sitter” (AdS) space — saddle-shaped space with an outer boundary. Whereas our universe has approximately flat space, and no boundary. Why should we think that these calculations apply to our universe? That's an excellent question, and it was not answered by the interviewee. (I'd love to be persuaded that it has ever been reasonably answered by anyone).

nerdponx 5y ago
My intuition is failing here. If I put a log through a wood chipper, I can't un-chip it! Why should we expect the same for stars getting torn apart by intense gravitational fields? Does it matter that the gravitational field is literally "spacetime itself" changing shape, versus two pieces of matter interacting with each other as in the wood chipper case? Here's my guess of what's happening based on what you read, please tell me where I'm going wrong: Physics generally assumes that it can be theoretically un-chipped; if somehow I could run time backwards, that I would end up with exactly the same log that I started with. But the results of interacting with with the mathematical singularity in the black hole cannot be "undone" in this way. And so far, all attempts to avoid trying to model "matter that has passed through a singularity in spacetime" with some kind of firewall, etc. have failed.
thriftwy 5y ago
Thank you for the detailed considerations. First I want to say that black hole does not imply extreme conditions. You will not notice when falling into a really large black hole. They are violent only when small. Large black holes are almost as benigh as outer event horizon, shredding-and-tearing-wise. We can't observe singularity, so whatever matter state it is on has no bearing on information paradox. With regards of reappearing from black hole. When the universe is close to big crunch, a lot of very heavy black holes begin to merge. When we are virtually inside a black hole, it may merge with more black holes, and if they are sufficiently large, we will be able to interact with objects (such as stars, even) inside the black holes in which they disappeared from our sight previously. Moreover, we will see that they have evolved during their absense in line with how objects outside of observable universe evolved in absense of observation. This is when talking about very large black holes, the size of our galaxy. These are easier than it sounds due to very fast black hole volume growth. About evaporation, I can't say too much. But I also don't see how it UPD: ...I don't see why it needs introduction of new physics, given that it is a virtual phenomenon - nothing interesting really happens near the event horizon, it only becomes interesting at a distance.
- raattgift 5y ago
  Below, I'll focus on model black holes, immersed in vacuum, isolated in asymptotically flat spacetime, and without regard to initial formation. Yes, you can make such a theoretical black hole arbitrarily large, and thus geodesic deviation[1] can be arbitrarily small just outside the horizon. The region just outside the horizon[2] is still a strange and likely bad place to be, filled with post-Newtonian effects from gravitational redshift and plunging orbits. [aside 3] (Astrophysical black holes must have some upper mass limit, and will generally have accretion structures that produce additional hazards). > black hole does not imply extreme conditions I invite you to calculate the scalar curvatures[4] in any model black hole, including one with an arbitrarily high mass (say about that of the known universe), and the geodesic equations below ~ 6(GM)/(c^2) [5]. If you do that, you'll find that extreme conditions are always manifest, and that in particular even for arbitrarily large mass model black holes, once you are past the point of no return you are inevitably drawn into a caustic, and fairly quickly by your own wristwatch-time. Super-and-ultra-massive black holes are mostly interesting because the curvature very close to the horizon is well within the effective field theory limit of General Relativity, so theorists can be sceptical of the introduction of quantum corrections to gravitation in those regions of (all) theoretical black holes unless the corrections vanish as one takes the black hole mass to a very high limit. > a lot of very heavy black holes begin to merge You should consider that clusters galaxies will begin to reappear from the other side of the horizon well before they get close enough to one another to interact gravitationally. The very late time big crunch is not necessary to demonstrate the difference between switching from an expanding universe to a contracting one and switching from a growing black hole to an evaporating one. Indeed, although late times of black hole evaporation are theoretically interesting (is there a remnant?) even the very earliest stages of evaporation are different: what rushes out from the region around the black hole is greybody radiation, not the stars, rocks, and space probes we threw in while the black hole was still growing. Taking the mass of a black hole to an arbitrarily large value does not change this essential difference. I don't know what you're trying to say in the final two paragraphs. If your "I don't see why it needs introduction of new physics" is a request for information rather than a dismissal of the debate itself, you could start with the late Joe Polchinski's excellent 2013 slide deck https://www.slideshare.net/joepolchinski/firecit https://www.slideshare.net/joepolchinski/firecit and the references at https://en.wikipedia.org/wiki/Firewall_%28physics%29 https://en.wikipedia.org/wiki/Firewall_%28physics%29 There is nothing virtual about Hawking radiation; it appears pretty generically close to all sorts of black holes equipped with a non-vacuum exterior, and has been shown in acoustic analogues. Unruh: http://inspirehep.net/record/775859?ln=en http://inspirehep.net/record/775859?ln=en availabile at https://pos.sissa.it/043/039/pdf https://pos.sissa.it/043/039/pdf If you are perturbed off ISCO by Hawking quanta scattering off you, you likely will care very much that it is not a "virtual" phenomenon, while you are still able to care about anything at all. - -- [1] We can consider the Riemann curvature tensor R^{a}{}_{bcd} u^b u^d X^c, where u^a is the 4-velocity of an object on a geodesic and X is a vector quantity in the tangent space between that geodesic and one nearby (e.g., a different mote of neutral dust in an infalling cloud, with identical 4-velocity) describing these geodesics' tendency to separate or converge. More roughly, this encodes the inwards-squash and the back-to-front stretch of this dust cloud from a macroscopic perspective. It also, in suitable coordinates, describes the spaghettification of extended bodies bound by non-gravitational forces. For spherically symmetric masses, in general X shrinks with distance from the mass. For black holes we take the mass to be highly focused so this obtains practically everywhere in the Schwarzschild interior. The interior oddities arising from breaking the symmetries of Schwarzschild with e.g. a non-negligible spin parameter do not change this statement qualitatively. [2] In the Schwarzschild case the region R_s < r < ~ 3R_s is prone to result in inward plunges for non-massless objects, and of course the size of that region scales with M. Some details: https://hepweb.ucsd.edu/ph110b/110b_notes/node80.html https://hepweb.ucsd.edu/ph110b/110b_notes/node80.html Less symmetrical black hole models also have exterior regions, scaling with M, that are hazardous to any non-massless observer. [3] The region just outside the cosmological horizon is essentially identical to the region just inside the cosmological horizon. There is an important symmetry difference: when someone else recedes past our cosmological horizon, we recede past theirs. We do not notice when we exit someone else's cosmological horizon -- we are doing it right now. We continue on diverging geodesics (cf [1]). Being on the inside of a black hole -- even one with a mass greater than the observable universe -- gives a different view. With the time one has left, one could determine (via e.g. Synge's method) that the spacelike part of the spacetime curvature is curved and thus one is inside a truly enormous vacuum black hole. If we break the vacuum condition Robertson-Walker -> Friedmann-Lemaître-Robertson-Walker & vacuum Schwarzscild -> Lemaître-Tolman-Bondi, we would not see isotropic distance-dependent gravitational redshift of luminous matter inside the LTB black hole as we do in the FLRW expanding universe: there would be an enormous anisotropy. [4] Let's use Schwarzschild (black hole and coordinates) to avoid drowning in calculations for a black hole equipped with an "outer event horizon"; the interior metric is also much easier to reason about, and compared to cases such as Kerr-Newman, much more physically plausible. For a Schwarzschild black hole, the Kretschmann curvature scalar is R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho} = \frac{48M^2}{r^6}, where R is the Riemann curvature tensor. Coupled with the appearance at r = 2M of the Schwarzschild horizon, we can see that as we take M -> \infty your point about "benig[n] ... shredding-and-tearing-wise" holds. However, calculating for the interior, we find that the Kretschmann scalar explodes and becomes irregular at r = 0. This is diagnostic of a gravitational singularity. [5] For example, https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Geodesic_equation https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Geodes... although I'd want to resort to a textbook.

nerdponx 5y ago

My intuition is failing here. If I put a log through a wood chipper, I can't un-chip it! Why should we expect the same for stars getting torn apart by intense gravitational fields? Does it matter that the gravitational field is literally "spacetime itself" changing shape, versus two pieces of matter interacting with each other as in the wood chipper case? Here's my guess of what's happening based on what you read, please tell me where I'm going wrong: Physics generally assumes that it can be theoretically un-chipped; if somehow I could run time backwards, that I would end up with exactly the same log that I started with. But the results of interacting with with the mathematical singularity in the black hole cannot be "undone" in this way. And so far, all attempts to avoid trying to model "matter that has passed through a singularity in spacetime" with some kind of firewall, etc. have failed.

thriftwy 5y ago

Thank you for the detailed considerations. First I want to say that black hole does not imply extreme conditions. You will not notice when falling into a really large black hole. They are violent only when small. Large black holes are almost as benigh as outer event horizon, shredding-and-tearing-wise. We can't observe singularity, so whatever matter state it is on has no bearing on information paradox. With regards of reappearing from black hole. When the universe is close to big crunch, a lot of very heavy black holes begin to merge. When we are virtually inside a black hole, it may merge with more black holes, and if they are sufficiently large, we will be able to interact with objects (such as stars, even) inside the black holes in which they disappeared from our sight previously. Moreover, we will see that they have evolved during their absense in line with how objects outside of observable universe evolved in absense of observation. This is when talking about very large black holes, the size of our galaxy. These are easier than it sounds due to very fast black hole volume growth. About evaporation, I can't say too much. But I also don't see how it UPD: ...I don't see why it needs introduction of new physics, given that it is a virtual phenomenon - nothing interesting really happens near the event horizon, it only becomes interesting at a distance.

raattgift 5y ago
Below, I'll focus on model black holes, immersed in vacuum, isolated in asymptotically flat spacetime, and without regard to initial formation. Yes, you can make such a theoretical black hole arbitrarily large, and thus geodesic deviation[1] can be arbitrarily small just outside the horizon. The region just outside the horizon[2] is still a strange and likely bad place to be, filled with post-Newtonian effects from gravitational redshift and plunging orbits. [aside 3] (Astrophysical black holes must have some upper mass limit, and will generally have accretion structures that produce additional hazards). > black hole does not imply extreme conditions I invite you to calculate the scalar curvatures[4] in any model black hole, including one with an arbitrarily high mass (say about that of the known universe), and the geodesic equations below ~ 6(GM)/(c^2) [5]. If you do that, you'll find that extreme conditions are always manifest, and that in particular even for arbitrarily large mass model black holes, once you are past the point of no return you are inevitably drawn into a caustic, and fairly quickly by your own wristwatch-time. Super-and-ultra-massive black holes are mostly interesting because the curvature very close to the horizon is well within the effective field theory limit of General Relativity, so theorists can be sceptical of the introduction of quantum corrections to gravitation in those regions of (all) theoretical black holes unless the corrections vanish as one takes the black hole mass to a very high limit. > a lot of very heavy black holes begin to merge You should consider that clusters galaxies will begin to reappear from the other side of the horizon well before they get close enough to one another to interact gravitationally. The very late time big crunch is not necessary to demonstrate the difference between switching from an expanding universe to a contracting one and switching from a growing black hole to an evaporating one. Indeed, although late times of black hole evaporation are theoretically interesting (is there a remnant?) even the very earliest stages of evaporation are different: what rushes out from the region around the black hole is greybody radiation, not the stars, rocks, and space probes we threw in while the black hole was still growing. Taking the mass of a black hole to an arbitrarily large value does not change this essential difference. I don't know what you're trying to say in the final two paragraphs. If your "I don't see why it needs introduction of new physics" is a request for information rather than a dismissal of the debate itself, you could start with the late Joe Polchinski's excellent 2013 slide deck https://www.slideshare.net/joepolchinski/firecit https://www.slideshare.net/joepolchinski/firecit and the references at https://en.wikipedia.org/wiki/Firewall_%28physics%29 https://en.wikipedia.org/wiki/Firewall_%28physics%29 There is nothing virtual about Hawking radiation; it appears pretty generically close to all sorts of black holes equipped with a non-vacuum exterior, and has been shown in acoustic analogues. Unruh: http://inspirehep.net/record/775859?ln=en http://inspirehep.net/record/775859?ln=en availabile at https://pos.sissa.it/043/039/pdf https://pos.sissa.it/043/039/pdf If you are perturbed off ISCO by Hawking quanta scattering off you, you likely will care very much that it is not a "virtual" phenomenon, while you are still able to care about anything at all. - -- [1] We can consider the Riemann curvature tensor R^{a}{}_{bcd} u^b u^d X^c, where u^a is the 4-velocity of an object on a geodesic and X is a vector quantity in the tangent space between that geodesic and one nearby (e.g., a different mote of neutral dust in an infalling cloud, with identical 4-velocity) describing these geodesics' tendency to separate or converge. More roughly, this encodes the inwards-squash and the back-to-front stretch of this dust cloud from a macroscopic perspective. It also, in suitable coordinates, describes the spaghettification of extended bodies bound by non-gravitational forces. For spherically symmetric masses, in general X shrinks with distance from the mass. For black holes we take the mass to be highly focused so this obtains practically everywhere in the Schwarzschild interior. The interior oddities arising from breaking the symmetries of Schwarzschild with e.g. a non-negligible spin parameter do not change this statement qualitatively. [2] In the Schwarzschild case the region R_s < r < ~ 3R_s is prone to result in inward plunges for non-massless objects, and of course the size of that region scales with M. Some details: https://hepweb.ucsd.edu/ph110b/110b_notes/node80.html https://hepweb.ucsd.edu/ph110b/110b_notes/node80.html Less symmetrical black hole models also have exterior regions, scaling with M, that are hazardous to any non-massless observer. [3] The region just outside the cosmological horizon is essentially identical to the region just inside the cosmological horizon. There is an important symmetry difference: when someone else recedes past our cosmological horizon, we recede past theirs. We do not notice when we exit someone else's cosmological horizon -- we are doing it right now. We continue on diverging geodesics (cf [1]). Being on the inside of a black hole -- even one with a mass greater than the observable universe -- gives a different view. With the time one has left, one could determine (via e.g. Synge's method) that the spacelike part of the spacetime curvature is curved and thus one is inside a truly enormous vacuum black hole. If we break the vacuum condition Robertson-Walker -> Friedmann-Lemaître-Robertson-Walker & vacuum Schwarzscild -> Lemaître-Tolman-Bondi, we would not see isotropic distance-dependent gravitational redshift of luminous matter inside the LTB black hole as we do in the FLRW expanding universe: there would be an enormous anisotropy. [4] Let's use Schwarzschild (black hole and coordinates) to avoid drowning in calculations for a black hole equipped with an "outer event horizon"; the interior metric is also much easier to reason about, and compared to cases such as Kerr-Newman, much more physically plausible. For a Schwarzschild black hole, the Kretschmann curvature scalar is R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho} = \frac{48M^2}{r^6}, where R is the Riemann curvature tensor. Coupled with the appearance at r = 2M of the Schwarzschild horizon, we can see that as we take M -> \infty your point about "benig[n] ... shredding-and-tearing-wise" holds. However, calculating for the interior, we find that the Kretschmann scalar explodes and becomes irregular at r = 0. This is diagnostic of a gravitational singularity. [5] For example, https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Geodesic_equation https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Geodes... although I'd want to resort to a textbook.