Should be pointed out that this is a critique of common popsci journalism tropes and not a fancy new research result. Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.
I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.
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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
They don't just have the same name, they are the same thing.
A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.
Even without quantum mechanics, black holes are trouble:
Approximately everything in nature rotates. Including black holes. Schwarzschild blockholes do not rotate. Rotating black holes are much more complicated and don't necessarily shield their singularity behind an event horizon.
Rotating black holes are described by Kerr geometries and have more than one event horizon, but still have their singularities hidden from anyone outside behind their inner horizon.
OSM - slight generalization of Schwarzshild BH, where you take evolving spherically-symmetric mass distribution instead of point mass - shows that point singularity in the middle can be naked (aka observable), so it's not just QM that causes worms...
> The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions.
How is this any different than classical? Isn't it still just an ~impossibility hidden behind an event horizon in either model?
With our current understanding, baryon and lepton number are not conserved as a black hole radiates. I think this is a better demonstration of the incompatibility with classical and quantum mechanics.
This is like saying the Riemann zeta function is only defined for real numbers. You can always extend the singularity mathematically by incorporating new axioms.
My point is, it’s not super meaningful to argue whether a black hole has an inside.
> 1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
Well, the Ricci curvature scalar blows up to infinity, which is obviously unphysical.
As someone with basically only popsci knowledge of black holes: people claiming it would be a literal point never made much sense - fundamentally, common sense (as much as it can apply here) dictates that you cannot compress particles to an absolute point.
Common sense cannot be trusted on matters like these. Common sense is calibrated for reasoning over matters encountered in daily life. The further away we get from that, into more and more exotic phenomena, the less common sense can apply. Black holes are very far from the domain of common sense.
I always suggest looking at the quantum eraser experiment to see how bad common sense works with quantum mechanics. It's fairly simple but intuition fails most people when it comes to explaining how it works.
No need for funky stuff, just do the classic (lol) Young's slits experiment which should be more than enough oddness for anyone.
I was shown it at school, using microscope glass slides that we waved over a Bunsen burner running cold, to coat with soot. We then carefully etched parallel lines with a compass by hand. Our (~17 y/o) efforts were a bit random but we did get some smudgy banding results on the screen.
The question of "what holds it up?" is where that leads to. There's an interesting history of answering that question again and again - and the discovery of new types of stars each time.
A kugelblitz is a theoretical astrophysical object predicted by general relativity. It is a concentration of heat, light, or radiation so intense that its energy forms an event horizon and becomes self-trapped. In other words, if enough radiation is aimed into a region of space, the concentration of energy can warp spacetime so much that it creates a black hole. This would be a black hole the original mass–energy of which was in the form of radiant energy rather than matter
Rather than compressing particles, would you have difficulty with converting it to incredibly large amounts of energy that wraps space time into a singularity? If you packed enough photons into one spot, that energy would curve space time enough to form a black hole.
>Rather than compressing particles [...] If you packed enough photons into one spot
I haven't watched the video, but if we're compressing electrons, neutrons, or other fermions, I imagine if we want to keep compressing that down to an arbitrarily small radius, won't we pretty quickly find it favorable to shift those fermions to something else, probably photons, to respect Pauli exclusion?
Really, I don't know enough physics to figure out the reason why it shouldn't always end up in this incorporeal energy-curving-space situation either way, if we're compressing arbitrarily far.
But then you "fill up all the photon slots" too (not literally because they are not fermions, but they do spontaneously convert back into things like electrons at that density) and you can work around the Pauli exclusion principle by stacking your electrons at higher and higher energy levels.
Pauli exclusion isn't an impenetrable force field - as you say, it's just often more favourable to do something else than to work around it. Consider an iron atom with however many electrons though - all those orbitals except the inner one are electrons working around Pauli.
A particle is a region of space where it's probable that a certain kind of interaction will happen. I don't see any reason why they can't overlap infinitely and then squeeze to the Dirac delta function: certain to be here, no error bars. That is, apart from the Pauli exclusion principle. But you have to leave that one behind if you're dealing with masses beyond the TOV limit.
Of course I'm missing something here. I've taken QM and not GR so I would have this interpretation.
My rather pop-sci understanding is that when you start playing around with relativity math, trying various masses and densities you hit something rather worrisome. As you approach some great, but still possible, value the plot goes infinite, the singularity. This is bad for the theory because going asymptotic like that usually indicates a fundamental problem in the math. But relativity does so well everywhere else... What if it could? And thus the black hole was born.
The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.
I believe this is a misunderstanding based on inadequate coordinate systems, and that an astronaut would fall through the event horizon, die, and reach the singularity in finite time.
AFAIK from the outside point of view it takes infinite time. We see the falling object redshift to infinity (blackshift, really) and merge into the black sphere we observe.
But in the object's own time coordinates the math says it does hit the singularity. If you fell in you wouldn't die of old age before you hit it.
Does time accelerate just for the astronaut approaching the black hole (meaning they would be witnessing the future) or does it accelerate for everyone (meaning approaching a black hole is going to make everything end quicker)?
If outside observers could watch the astronaut clearly, the astronaut would look like they're slowing down to a stop at the event horizon. The astronaut would not see themselves freezing in time, but they would see everything outside of the black hole speed up.
You could travel arbitrarily far into the future by getting close to a black hole's event horizon for a while without crossing it and then leaving, assuming you had the energy for it and you didn't get obliterated by all the mass and energy falling into the black hole in that timeframe.
Time acceleration is dependent on the gravitational flux.
All objects within a given radius of the black hole (possibly modulo spin) would experience the same time dilation. Remote objects in the universe would not experience the dilation.
From the perspective of the astronaut falling toward the singularity, the rest of the Universe would age at an ever-increasing rate.
From the perspective of a remote observer, the astronaut falling toward the singularity would be experiencing time at an ever-decreasing rate.
The notion of relativity is that time-perception is relative, and dependent on acceleration, whether from motion (as on a spaceship) or from gravitational acceleration (as near a black hole). Objects in orbit around Earth, further from Earth's centre, and hence subject to reduced gravitational acceleration, age more quickly than objects on Earth's surface. This is actually measurable using atomic clocks, though the effect is quite small. It is sufficient that GPS satellites require time correction.
My rather limited understanding is that. first there is a lot going on and due to the forces and gravitational gradients involved, matter itself probably would not survive the journey that close to the horizon. But ignoring that, When in compressed time, from the point of view of someone freefalling, timewise everything is normal, the rest of the universe has accelerated and in the case of a black hole has just aged out and died but you are fine. from the external point of view they are taking forever to get there.
Where my imagination fails(above my pay grade) is in the face of infinity, what are the implications of infinite time compression?(everything happens at once?)
I can only guess as well, infinite time compression might result in a big bang when it applies to everything. All black holes could lead to the same moment causing the bang.
There are a lot of curious coincidences between properties of black holes and properties of the whole universe that lead some physicists to the idea that they could be connected. There's also that Penrose diagram showing another universe beyond a black hole. (Seems like a copout to me though. Penrose diagrams are drawn in 1D space, so the black hole cuts the universe in half. If you had 2D or better space couldn't you just travel around behind the black hole to the other side of it?)
And if they didn't form a superconductor. I'm not sure why they would but if they did they would violate it. That's actually what makes superconductors superconducting - the really weird state where electron pairs act like bosons.
It's a complete violation of good sense to invoke common sense here. You talk about "particles" but that's not what the world is made of. Also, particle/wave duality. Also, any number of bosons can occupy the same position. Also black holes evaporate. And on and on.
Common sense - the experience gained from your common everyday experience of reality - does not apply in black holes.
Common sense would tell you they can't exist at all because you can't compress atoms - you have lived your entire life with atoms being entirely incompressible for the practical purpose of anything you do.
Leaning on common sense to discuss fundamental physics has been wrong since round about the start of the practice of physics.
Common sense actually says that atoms don't exist and if you squish cheese really hard you just get really hard and slightly smaller cheese, or maybe you invent a new type of dairy product.
If you really treated them as points the theory would blow up because the electrostatic potential energy of a point charge is infinite. This is dealt with by “renormalization” which is roughly: assume the theory isn’t really valid all the way to a zero length scale and that we can average out everything that happens below some cutoff size and that it doesn’t really matter where we place the cutoff because the theory works the same if you change the cutoff and change the other parameters accordingly.
They are, but there are some interesting theories about their internal structure. Be aware that this is probably junk science but I have currently been enjoying this effort to describe them via the em field.
Points are a realist view - there's a real object there.
Although some physicists disagree, QM slants very anti-realist. There are no objects anywhere, no particles, no waves, only probabilistic interactions, some of which can be snapshotted into localised partially definite results.
So there are only interactions between probability distributions in space and time, and "particle-like events."
Wouldn't it be both? Electrons occupy probability clouds, but the overall probabilities of things happening are summed over the whole cloud as if, at each point, the electron was a point particle at that point?
QM slanting anit-realist is because some prominent physicists like Neils Bohr gave the math that interpretation, and they were more persuasive than the realists like Einstein, Schrodinger, Everett.
The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.
Of course treating particles as points is also mathematical.
Kind of, but not really.. though there are simple models with electrons as a point charge, a more accurate model involves the electron field describing the probability of an electron existing at any region in space (not to be confused with the electromagnetic field, the medium in which photons propagate).
Sure the position of an electron is not definite, but neither is that of a buckyball, but a buckyball has a shape we can describe, an internal structure we regard as extended over space, in a way that is separate from the indeterminacy of its center of mass position. This is unlike an electron, for which, if we set aside the uncertainty as to its center of mass, my understanding is that the only internal degrees of freedom it has left (in the Standard Model) are its spin and whether it is left or right handed, with no other structure to it.
It is in this sense that, AIUI, electrons are modeled as point particles.
Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.
But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)
> No complete and precise definition of singularities exist in the theory of general relativity,
So which is it? It can't both be trivial to any grad student but also an open question. And things like naked singularities aren't proven to not exist either.
Also, general relativity is a classical, geometric-only theory. It seems obvious that better understanding what a black hole's singularity is would require quantum mechanics because the singularity is effectively what's "left over" of the physical material once you go beyond a neutron star.
Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surface in time, not space (as the book explains, the space and time coordinates switch places as you cross the event horizon).
> the space and time coordinates switch places as you cross the event horizon
If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.)
The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.
Kruskal-Szeres coordinates indeed get rid of the wonky coordinate stuff at the event horizon, but if you look at the corresponding diagrams, you'll just end up with the same confusion, because the singularity is still a point (or rather surface) in the future instead of a point in space. The issue is that these diagrams are for eternal, static black holes, which cause diagrams to have these weirdly stretched infinite regions that are quite useful for understanding details of the math, but are highly confusing to laypeople. In fact these diagrams make it look like you'll always fall into the black hole at t=infinity, no matter how far you are away, when in reality you could orbit a static black hole pretty close for eternity.
If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis.
The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38)
Still one of the best things you can read if you don't just want the math.
This article is great but the references to gravitational waves as if they were an observed fact (in 1972) was mystifying to me. It led me down a rabbit hole to Joe Weber, who is name-checked at the end of the Penrose article.
> the singularity is still a point (or rather surface) in the future instead of a point in space.
It's a spacelike line on the Kruskal diagram, yes.
> The issue is that these diagrams are for eternal, static black holes
The full Kruskal diagram is, yes. But the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse of a massive body. That includes the singularity being a spacelike line, and there being spacelike curves inside the horizon that are infinitely long.
I agree that Eddington-Finkelstein coordinates can help with intuitions about this spacetime geometry as well.
It also is in Schwarzschild coords, so you've gained nothing with respect to the original issue from switching coordinates. Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
>the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse
The issue is even the limited diagram doesn't really show you that and the full one goes crazy with white holes. So not a good place if you don't want to confuse laypeople.
True--indeed, the statement that it's a spacelike line is an invariant, independent of any choice of coordinates. But it's a lot harder to see that in Schwarzschild coordinates.
> Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
I disagree, and I think many GR physicists would as well. Indeed, both classic GR textbooks, Misner, Thorne & Wheeler (1973) and Wald (1984) discuss Kruskal coordinates and their associated spacetime diagram (MTW in Box 31.2 and sections 31.5 and 31.5, Wald in section 6.4), and those discussions contain a good deal more than just showing that the horizon is "not such a weird place".
This doesn't seem meaningfully different to me? Like the notion that the singularity is always in your future (because you can't escape it anymore past the event horizon) makes sense, the point of confusion is what are the implications?
Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to be in a region of space where all possible directions lead to the singularity.
It's not just that it's always in your future in the sense that you can't avoid it. It's that the reason you can't avoid it is that it's a moment of time, not a place in space. You can't avoid it for the same reason you can't avoid tomorrow. And which direction in space you move has no effect on whether or not you reach the singularity for the same reason it has no effect on whether or not you reach tomorrow.
>the notion that the singularity is always in your future makes sense
But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.
> it is just a mathematical artefact of weirdly chosen coordinates.
No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates.
> the singularity is still just a point in space
No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space.
> There's no need for this whole "space turns into time" notion
That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making.
> the spatial coordinates of the singularity
I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.
Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. Certainly I'd trust what he says rather than me, so sorry if I was misleading.
(If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).
The way Brian Cox puts it, a singularity is a point in time: the end of time.
I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.
The singularity in a non-rotating, non-charged black hole is as you say. It’s like in a finite amount of time you “run out of time”, like there isn’t any more time on that trajectory.
The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says.
And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.
If it signifies the end of time, then all the stuff in the black hole would need to no longer exist no? If anything is happening in the black hole, then time is still progressing, so nothing must be all that exists?
The more interesting component is that black hole physics is almost an anti-free will zone.
Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).
Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places.
Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.
The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.
> Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time
That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.
To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.
To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).
Am I understanding this right by thinking - if I was walking toward the black hole past the event horizon, and then I turned around, I would still be walking toward the black hole?
Once you pass the event horizon, every direction leads to the singularity in your future. Directions "away" from the singularity may still visibly show what things looked like outside of the event horizon before you fell in, but that is from your past. Heading in that direction will not get you back there anymore, you will only find the singularity along that path in your future.
> if I was walking toward the black hole past the event horizon, and then I turned around
Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.
And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.
You can't turn around though. Everything goes toward the black hole. If you turned around, atoms would be moving away from, or at the least changing their direction in respect to the black hole. And that's not possible. You wouldn't even see anything because all light is going toward the center, and it wouldn't go into your eyes.
Unless you went in butt-first, but the path of the photons would have changed and would now be going toward the black hole, and everything would look probably all smushed together.
It's unfortunately misleading shorthand for what actually happens: space becomes timelike. It doesn't become time. All this means is that once you cross the event horizon, you can only ever move toward the center of the black hole, in the same way that outside of a black hole, you can only ever move toward the future. You might not take a direct route to the center, but no matter which way you move, you will be following a track that ends at the center.
The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with.
But it doesn't mean that space and time literally switch places.
it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.
I think it's not even a valid critique of that and it's sort of playing games with what the definition of a singularity is to reach the claim that it's making. I think the topology of the singularity is not even a well defined question and certainly not well understood enough to bear the strong claims in the paper.
Unfortunately you are wrong. Everything the paper is saying about the singularity and its properties in GR, and more generally about the black hole solutions it describes, is well understood and has been for decades. The definition of "singularity" that the paper is using is perfectly fine, and its topology is perfectly well-defined. A good textbook treatment is that of Wald (1984).
Some of the things the paper points out are not emphasized in other sources, which is probably why the authors chose to write it. But there is nothing in the paper that is in the least questionable or ill-defined; it's all standard General Relativity as applied to the Schwarzschild and Kerr black hole solutions.
This is the opinion of most physicists, yes, but it does not in any way justify the GP's claims or cast doubt on anything that is said in the paper. Note that the paper talks explicitly about the limitations of GR as the singularity is approached and how a quantum gravity theory, if we ever find and confirm one, might fix those issues.
Due to my engineering background, I know just enough physics and mathematics to completely misunderstand general relativity and quantum mechanics. However, one pattern I have noticed is that one favorite past time of physicists is looking at the mathematical models, trying to find insane ass edge cases and then trying to interpret them.
With that in mind, do these equations allow black holes whose singularities extend beyond their event horizons?
It's not? Schwarzschild has a space-like singularity. That's the wiggly horizontal line at the top left of the diagram. If you are in the black hole you can't avoid hitting it. Seems to be exactly what the paper is remarking on.
1. The boundary of the black hole which traps light, etc, is called the event horizon, and sits at the Schwarzschild radius. This is a geometric surface.
They do speak of the gravitational singularity (not the event horizon). It's within the horizon, there is a contradiction between the need for two infallers' position to reach the singularity (thus hitting a point) and the causal impossibility of them actually meeting (following General Relativity?). This suggests that the point should maybe be a surface.
No, they are theorizing about the Kerr metric. The Kerr metric describes rotating black holes and instead of a point like singularity predicts a ring of zero thickness with infinite density additional work posits the ring is unstable and collapses to a surface all inside the event horizon, they then proceed to make predictions about the nature and behavior of that surface.
By the way the Kerr metric predicts a ring because the centrifugal acceleration due to the rotation partially counteracts the gravity. As far as I understand, not a physicist.
Off-topic, but it makes me think of "reasoning black holes": you get enough like-minded people together that they start reinforcing each other's logic and beliefs until not only those people get completely detached from reality, but anyone who interacts with them gets sucked in as well unless their own logic ("velocity") is adequate to skirt the edge and escape, forever altered by the experience.
Similar questions arise: how would you know if you were inside one? The laws of logic ("physics") seemingly don't apply, but there's no way to test them in that environment.
I dunno. Those rationalists seem to be in some kind of intellectual black hole which never had any danger of sucking me in. Like I have seen many strands of posthumanism and transhumanism, speculations about an intelligence explosion circa 1970, and figure it would have been just as much fun to sit around the campfire, pass a joint around, and talk about crazy stuff with these guys
Well, the analogy is to something flying by a black hole and having its trajectory altered.[1] It sounds like it fits you, then -- you interacted, and are now forever irritated by them or by things that sound like them, even things that you would not have previously noticed.
[1] This is just gravity, nothing specific to black holes, so the analogy isn't doing a lot of work here.
I know this isn't a new discovery but I fully expect the next major theoretical physics breakthrough to be discovered by a frontier LLM at this point, given their aptitude at solving a lot of the recent mathematical conjectures.
Normally people think of gravity as pulling on objects. You can instead think of it as pulling on the space those objects are in.
A black hole happens when there is enough gravity that space gets pulled inwards somewhere, at at least the speed of light.
Gravity falls off with distance, and the distance where space is being pulled inwards at exactly the speed of light is called the "event horizon".
It has this name because speed of light is the speed of causality: events that happen further in, are "over the horizon" for you, they cannot causally influence you.
> Normally people think of gravity as pulling on objects. You can instead think of it as pulling on the space those objects are in.
(Very uneducated person here) I’ve always wondered if large objects caused gravity, or if maybe large objects form in the places where there is a lot of gravity. This is probably elementary, but I’ve never looked in to it. Maybe today is the day!
Scientists have directly measured the gravity coming from big balls of lead. The gravity didn't make the scientist put the lead there, and the gravity wasn't there before the lead. The lead must have made the gravity.
If you want to take a very large-scale - if poetic - view of things, you could also (very arguably) say something like "Mass is Fate".
Mass represents a zone where probabilities want to be. The more that aggregate, the more they make other things want to glom on. With a high enough density, nothing that's nearby can glom to literally anywhere else, and there's your black hole. The Great Inevitable. In this space, there are no other possibilities. Very Demiurge-y.
I mean, it's kind of both: objects have gravity, which attract them together, which creates more gravity and larger objects. Stars are what happens when the rest of physics disagrees with this (and black holes are when gravity wins anyway).
Why not just say it's something with such strong gravity you can't escape even if you go at the speed of light? Maybe that loses too much accuracy for you?
It's a region of space from where not even light can scape.
You can get a region like that by squashing a lot of mass in a small space, like happens when a star collapses under its own gravity. So here the intuition of "high density" makes sense.
But at the center of galaxies you have the so called "supermassive black holes" which are more or less comparable in size to the solar system and yes, they have a lot of mass but they are not very dense, a pop-sci trope is comparing it's density to cotton candy or even the air we're breathing right now.
So it's a matter of how you distribute mass/energy in a given diameter, not exactly of density.
The problem there is that not even the physicists completely agree on the details, because we know black holes definitely exist, but every explanation breaks one rule or another that should apply from different disciplines. It's part of why they get so much ongoing attention.
Black holes are essentially where our knowledge of spacetime breaks, and we can’t even see into it. It’s hard to really concretely know much about it directly.
Consider a balloon. I don’t imagine in visuals but if you do, either a solid color or a patterned balloon works. Let’s say it’s a cow print design.
Deflate it, then stretch the balloon over a vacuum cleaner tube and put on a rubber band to keep it in place.
If you pour sand on it, you can only get a small bump of sand and then it’ll run off the sides. Reasonable, logical, normal behavior. Clearly it’s a surface — it’s holding sand, it’s pouring sand in different directions over the edge, the sand is not all compacted into a single grain.
Turn on the vacuum cleaner. Assume a balloon stretchier than the strongest vacuum cleaner in the universe. What happens? Several things, each of which are perfectly reasonable:
1) The end of the tube is still a circle, and the balloon is still attached and covering the tube, so it’s still a two-dimensional circle.
2) A single grain of sand can’t block the vacuum tube, so it clearly hasn’t collapsed to a point.
3) The covered end of the vacuum cleaner tube is still the same circle, with the same diameter, as it was before you turned on the vacuum.
4) You can pour buckets more of sand onto that stretched circle of balloon than the handful you could before.
5) If you pour enough sand onto the circle, it’ll behave just like it did before: the sand will form a small mound and then newly-poured sand will run off whichever side the sand was poured on.
6) The rubber band is going to catch some of the overflowing grains of sand and hold onto them (‘accretion’), near but just outside the circle.
Next: Consider a more powerful vacuum cleaner. How much more? Lots. The most. An atomic Dyson powered by nuclear fusion. (This is a bit unrealistic, but that’s astrophysics for you.)
How much sand can you pour onto that two-dimensional, circular, balloon surface?
Lots. The most. Some of it will spill around the edges and get caught in the accretion band, but somehow that circle, that’s still the same size and clearly still blocking the vacuum tube, can hold an entire universe of sand.
That’s how black holes work :)
ps. For those who dislike the crudity of my teaching analogy and want to pop the spherical cow balloon: Topologically, the surface covering the vacuum tube is always a circle, even if you have an infinitely-powerful vacuum cleaner. At no point — pun intended — can a vacuum cleaner apply a transformation applied that reduces the dimensionality of the surface, thus it must remain, topologically, a circle.
pps. So clearly I must choose the circle in front of me! Hahaha! Aaaahahahah!
"A really interesting and cool thing for astronomers to talk about...but you might want to pray that not one of 'em ever comes within a million trillion miles of the Earth."
Astronomical distances are vast, million trillion miles too far, that's over a hundred thousand light years. There are known stellar-mass black holes within just 2000 light years of the Earth. Heck, there might be a primordial black hole in the inner Oort cloud and not only would it not destroy earth, we'd have (are having) trouble detecting it.
Unfortunately, there is a rather large one not one sixth of that distance away (a million trillion miles is actually rather large - 170 kly - approximately double the size of our galaxy)
Yes - I took the grandparent comment's "descr to a non-physicist" as "describe to someone who really isn't into math or hard sciences". Those folks will hear "million trillion" as "a really Really REALLY REALLY big number". Not as "1 x 10^18".
I guess, but "light year" is easy to say, easy to understand, and much less likely to mislead. And most black holes would probably be safe at that distance.
Though the issue of small black holes is worth bringing up. If you scrunch up one cubic kilometer of stone into a black hole, that's heavy to be stable for trillions of years, but light enough to pass between the Earth and the moon without causing serious problems. And we really have no idea what the smallest existing black hole is.
Would this apply also to the singularity at the beginning of the universe? I guess I thought that the singularity was where all matter is compressed so much that it occupies a zero dimension point. I'm not sure if that applies equally to black holes and the singularity at the beginning of the universe. I'm kind of dumb on this stuff even though it fascinates me.
Rolling the clock backwards toward the big bang, it is not matter which is directly compressed, it is the fabric and metric of space itself. Matter being compressed is merely a side effect of the fact that "all of the locations that the matter occupies" are also compressed (though again, remain aware that calling it "compression" only makes sense when you rewind time in our cosmological model backwards).
So it is not as though you and the Andromeda Galaxy are made out of matter that got flung out of a point explosion long ago so that now you have traveled a very long distance away from one another, it is more like "both you and the Andromeda galaxy sat still for 13.8 billion years but space expanded between you in that time, so originally you were right on top of each other along with everything else".
We can rewind the model until the entire observable universe was as small as a Planck volume, but we have abundant evidence that the universe is indefinitely larger than that so even "that time when our 98gly diameter patch of space was almost indistinguishable from a mathematical point" means little when even that "point" was still just one pinprick out of the smooth manifold of a larger universe which could have been stupidly large or infinite even that early on.
The big bang didn't happen at a single point, it happened everywhere. You can look out from anywhere and see the cosmic background radiation having expanded from your location, wherever that location might be.
> The big bang didn't happen at a single point, it happened everywhere.
A bit of an odd thing to say, since "everywhere" implies there are multiple places to be, and at the instant of the big bang, there was only place to be. So it was both everywhere and at a single point: it was at all of the single place there was to be.
But your point (sorry) about expansion being from everywhere isn't specific to the big bang; space was expanding well after the big bang and it doesn't seem like the expansion ever had a "center" (at least, not since not-center places existed). It's expanding from everywhere. (But evenly everywhere? I have no idea. Hey, maybe black holes are like buttons in cloth, and it expanded everywhere except for where the buttons were holding things still at a rate relative to distance from the button. A brilliant hypothesis that explains exactly zero unexplained phenomena, at least none that I know of.)
One theory that might help you visualize an alternative is that the big bang was basically two 3D universes (floating in higher-dimensional space) slapping against each other really hard. That creates an explosion everywhere even if everywhere is quite big or even infinite.
so in theory a spinning black hole that's been around for billions of years has a time drag around it in a path that is billions of years old
(no we can't navigate it because yes that would be time travel to the past and violates causality)
black holes are just so weird with every new detail even more weird
oddly more interesting to me to try to grasp neutron stars (densest objects before black holes and are still visible, our entire solar system in a neutron star would be only 10km 6.2miles across)
Another thing that may blow the minds of some is that M87* is less dense than air at 0.44kg/m³ so if you could bring it to sea level (in a large enough theoretical test area) it would float like a helium balloon (sea level air is 1.2kg/m³).
Of course if you did do that, the air itself would collapse into a black hole larger than M87*...
Yes, magnetars are considerably more rare than black holes and considerably more interesting to study in terms of raw horsepower. Imagine a type-2 civilization using them as engines or launchers for spacecraft to zip around the galaxy.
The can produce Earth masses of gold, but of course not in the form of "chunks". The gold starts as atoms in a highly ionized gas and only much later cools enough to form solids (dust).
It blows my mind that, in the frame of an outside observer, time appears to stop at the event horizon. An observer falling through the horizon (who survived the radiation and tidal forces) would not perceive this.
Assuming they do fall through it. Remember they're about to receive an entire universe lifetime's stellar radiation compressed into a microsecond.
(Which is another reason some people think we might be living inside a black hole. An entire universe of energy released in zero time is literally a Big Bang. It would form into stars and galaxies.)
>what's really going to blow your mind is
while you probably assumed or knew spinning black holes move space around them
spinning black holes also move TIME around them
Well, isn't called space-time for nothing. You can't have one without the other. Like in electromagnetism. I thought it was kinda obvious since Einstein and Minkowsky.
treating a black hole as a point, or ;) pointicle,may be valid as matter may be condensed, to the, I mean ,in such a way that there is NO space left whatsoever, and therefor no room for physical dimensions to exist in, and the entire body functions as
an undiferentiated body of stuff, or giant pointicle that destroys time and space.
Hopefully very soon we will get news about our galaxys central black holes interaction with a star that is orbiting very close but at 8% light speed, which may reveal if our blackhole is spinning, and if that is the case the we would have proof of energy/information/gravity waves? escaping from a black hole, along with gravity which while apparently imune to its self, nothing else is so far.
Well... yeah? That's describing the event horizon. It's a term roughly as widely used as "singularity".
Talking about the inside of a black hole is indeed rather pop-misunderstood though, yes. But it's not like physicists are especially confident about the details either. Theoretical astrophysics changes a lot as time goes on and our instruments improve, and it's a rather hard field to do experiments on to get better data quicker.
No, sorry, the singular surface in a Schwarzschild spacetime is not the event horizon. Nothing particularly interesting (from the GR point of view) happens at the event horizon.
Interesting work. The idea that the singularity is a surface rather than a point was unexpected to me even though it seems to follow logically from the theory of relativity.
I wonder how this reconciles with quantum gravity. If the singularity is truly a two-dimensional surface, perhaps it's related to Hawking radiation and the thermodynamics of black holes?
Should be pointed out that this is a critique of common popsci journalism tropes and not a fancy new research result. Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.
I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.
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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
>The fact that both have the same name
They don't just have the same name, they are the same thing.
A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.
Even without quantum mechanics, black holes are trouble:
Approximately everything in nature rotates. Including black holes. Schwarzschild blockholes do not rotate. Rotating black holes are much more complicated and don't necessarily shield their singularity behind an event horizon.
Rotating black holes are described by Kerr geometries and have more than one event horizon, but still have their singularities hidden from anyone outside behind their inner horizon.
OSM - slight generalization of Schwarzshild BH, where you take evolving spherically-symmetric mass distribution instead of point mass - shows that point singularity in the middle can be naked (aka observable), so it's not just QM that causes worms...
https://en.wikipedia.org/wiki/Oppenheimer–Snyder_model
> The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions.
How is this any different than classical? Isn't it still just an ~impossibility hidden behind an event horizon in either model?
With our current understanding, baryon and lepton number are not conserved as a black hole radiates. I think this is a better demonstration of the incompatibility with classical and quantum mechanics.
We don't actually know if a black hole has an inside. Some theories/hypotheses say spacetime just stops at the event horizon.
This is like saying the Riemann zeta function is only defined for real numbers. You can always extend the singularity mathematically by incorporating new axioms.
My point is, it’s not super meaningful to argue whether a black hole has an inside.
I don't mean the coordinate singularity, I mean there is no more spacetime after that.
> 1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
Well, the Ricci curvature scalar blows up to infinity, which is obviously unphysical.
Why is it unphysical?
As someone with basically only popsci knowledge of black holes: people claiming it would be a literal point never made much sense - fundamentally, common sense (as much as it can apply here) dictates that you cannot compress particles to an absolute point.
Common sense cannot be trusted on matters like these. Common sense is calibrated for reasoning over matters encountered in daily life. The further away we get from that, into more and more exotic phenomena, the less common sense can apply. Black holes are very far from the domain of common sense.
I always suggest looking at the quantum eraser experiment to see how bad common sense works with quantum mechanics. It's fairly simple but intuition fails most people when it comes to explaining how it works.
No need for funky stuff, just do the classic (lol) Young's slits experiment which should be more than enough oddness for anyone.
I was shown it at school, using microscope glass slides that we waved over a Bunsen burner running cold, to coat with soot. We then carefully etched parallel lines with a compass by hand. Our (~17 y/o) efforts were a bit random but we did get some smudgy banding results on the screen.
Using a compass is interesting, use two razor blades taped together is much easier and it’s close enough to perfect parallel lines.
The question of "what holds it up?" is where that leads to. There's an interesting history of answering that question again and again - and the discovery of new types of stars each time.
History of the Universe : What Is Hidden In The Core Of A Neutron Star? - https://youtu.be/YoYjkNQ27T8
That video goes into it... without getting mathy at any point.
One of the bits that you're having trouble with is the compression of matter to a point. There's a theoretical type of black hole known as a kugelblitz - https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)
Rather than compressing particles, would you have difficulty with converting it to incredibly large amounts of energy that wraps space time into a singularity? If you packed enough photons into one spot, that energy would curve space time enough to form a black hole.>Rather than compressing particles [...] If you packed enough photons into one spot
I haven't watched the video, but if we're compressing electrons, neutrons, or other fermions, I imagine if we want to keep compressing that down to an arbitrarily small radius, won't we pretty quickly find it favorable to shift those fermions to something else, probably photons, to respect Pauli exclusion?
Really, I don't know enough physics to figure out the reason why it shouldn't always end up in this incorporeal energy-curving-space situation either way, if we're compressing arbitrarily far.
But then you "fill up all the photon slots" too (not literally because they are not fermions, but they do spontaneously convert back into things like electrons at that density) and you can work around the Pauli exclusion principle by stacking your electrons at higher and higher energy levels.
Pauli exclusion isn't an impenetrable force field - as you say, it's just often more favourable to do something else than to work around it. Consider an iron atom with however many electrons though - all those orbitals except the inner one are electrons working around Pauli.
I'm not a physicist either.
Pauli Exclusion is just another “force” that can be overridden. Nature isn’t a list of rules
Pauli exclusion is a QM thing. Black holes are a GR thing. Famously, we don’t know how to mix the two.
We don't know how to mix the two in general. There are plenty of tame enough special cases where we know how a mixture has to look like.
Finding a tame enough special case was how Hawking discovered his radiation.
As far as anyone knows, electrons are already point masses.
A particle is a region of space where it's probable that a certain kind of interaction will happen. I don't see any reason why they can't overlap infinitely and then squeeze to the Dirac delta function: certain to be here, no error bars. That is, apart from the Pauli exclusion principle. But you have to leave that one behind if you're dealing with masses beyond the TOV limit.
Of course I'm missing something here. I've taken QM and not GR so I would have this interpretation.
Some of the most interesting and fundamental ideas in science are counter-intuitive
My rather pop-sci understanding is that when you start playing around with relativity math, trying various masses and densities you hit something rather worrisome. As you approach some great, but still possible, value the plot goes infinite, the singularity. This is bad for the theory because going asymptotic like that usually indicates a fundamental problem in the math. But relativity does so well everywhere else... What if it could? And thus the black hole was born.
The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.
I believe this is a misunderstanding based on inadequate coordinate systems, and that an astronaut would fall through the event horizon, die, and reach the singularity in finite time.
See https://physics.stackexchange.com/questions/82678/does-someo...
AFAIK from the outside point of view it takes infinite time. We see the falling object redshift to infinity (blackshift, really) and merge into the black sphere we observe.
But in the object's own time coordinates the math says it does hit the singularity. If you fell in you wouldn't die of old age before you hit it.
Does time accelerate just for the astronaut approaching the black hole (meaning they would be witnessing the future) or does it accelerate for everyone (meaning approaching a black hole is going to make everything end quicker)?
If outside observers could watch the astronaut clearly, the astronaut would look like they're slowing down to a stop at the event horizon. The astronaut would not see themselves freezing in time, but they would see everything outside of the black hole speed up.
You could travel arbitrarily far into the future by getting close to a black hole's event horizon for a while without crossing it and then leaving, assuming you had the energy for it and you didn't get obliterated by all the mass and energy falling into the black hole in that timeframe.
Time acceleration is dependent on the gravitational flux.
All objects within a given radius of the black hole (possibly modulo spin) would experience the same time dilation. Remote objects in the universe would not experience the dilation.
From the perspective of the astronaut falling toward the singularity, the rest of the Universe would age at an ever-increasing rate.
From the perspective of a remote observer, the astronaut falling toward the singularity would be experiencing time at an ever-decreasing rate.
The notion of relativity is that time-perception is relative, and dependent on acceleration, whether from motion (as on a spaceship) or from gravitational acceleration (as near a black hole). Objects in orbit around Earth, further from Earth's centre, and hence subject to reduced gravitational acceleration, age more quickly than objects on Earth's surface. This is actually measurable using atomic clocks, though the effect is quite small. It is sufficient that GPS satellites require time correction.
My rather limited understanding is that. first there is a lot going on and due to the forces and gravitational gradients involved, matter itself probably would not survive the journey that close to the horizon. But ignoring that, When in compressed time, from the point of view of someone freefalling, timewise everything is normal, the rest of the universe has accelerated and in the case of a black hole has just aged out and died but you are fine. from the external point of view they are taking forever to get there.
Where my imagination fails(above my pay grade) is in the face of infinity, what are the implications of infinite time compression?(everything happens at once?)
> external point of view
So time is localised? I’m not sure what localised time means but I’m hoping the question makes sense.
I can only guess as well, infinite time compression might result in a big bang when it applies to everything. All black holes could lead to the same moment causing the bang.
There are a lot of curious coincidences between properties of black holes and properties of the whole universe that lead some physicists to the idea that they could be connected. There's also that Penrose diagram showing another universe beyond a black hole. (Seems like a copout to me though. Penrose diagrams are drawn in 1D space, so the black hole cuts the universe in half. If you had 2D or better space couldn't you just travel around behind the black hole to the other side of it?)
Yeah, wouldn't this cause trouble with Pauli exclusion principle?
Only if they all had the same energy level.
And if they didn't form a superconductor. I'm not sure why they would but if they did they would violate it. That's actually what makes superconductors superconducting - the really weird state where electron pairs act like bosons.
It's a complete violation of good sense to invoke common sense here. You talk about "particles" but that's not what the world is made of. Also, particle/wave duality. Also, any number of bosons can occupy the same position. Also black holes evaporate. And on and on.
> … you cannot compress particles to an absolute point.
What do you mean by “particle” here? This kind of handwaving is fundamentally classical, and breaks down in the presence of quantum physics.
Common sense - the experience gained from your common everyday experience of reality - does not apply in black holes.
Common sense would tell you they can't exist at all because you can't compress atoms - you have lived your entire life with atoms being entirely incompressible for the practical purpose of anything you do.
Leaning on common sense to discuss fundamental physics has been wrong since round about the start of the practice of physics.
Funnily enough, technical speaking atoms are a small minority of ordinary matter, that is already excluding dark matter.
That's because a lot of the ordinary mass in the universe is ionised or in other weirder states.
Common sense actually says that atoms don't exist and if you squish cheese really hard you just get really hard and slightly smaller cheese, or maybe you invent a new type of dairy product.
Aren't fundamental particles like electrons and quarks treated as points?
If you really treated them as points the theory would blow up because the electrostatic potential energy of a point charge is infinite. This is dealt with by “renormalization” which is roughly: assume the theory isn’t really valid all the way to a zero length scale and that we can average out everything that happens below some cutoff size and that it doesn’t really matter where we place the cutoff because the theory works the same if you change the cutoff and change the other parameters accordingly.
They are, but there are some interesting theories about their internal structure. Be aware that this is probably junk science but I have currently been enjoying this effort to describe them via the em field.
https://quicycle.com/understanding-electrons/
And the video essay on the subject https://www.youtube.com/watch?v=hYyrgDEJLOA (Huygens Optics: Williamson & Van der Mark electron model | Are electrons made of light?)
Points are a realist view - there's a real object there.
Although some physicists disagree, QM slants very anti-realist. There are no objects anywhere, no particles, no waves, only probabilistic interactions, some of which can be snapshotted into localised partially definite results.
So there are only interactions between probability distributions in space and time, and "particle-like events."
No pointy objects, and no need for them.
Wouldn't it be both? Electrons occupy probability clouds, but the overall probabilities of things happening are summed over the whole cloud as if, at each point, the electron was a point particle at that point?
QM slanting anit-realist is because some prominent physicists like Neils Bohr gave the math that interpretation, and they were more persuasive than the realists like Einstein, Schrodinger, Everett.
The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.
Of course treating particles as points is also mathematical.
Kind of, but not really.. though there are simple models with electrons as a point charge, a more accurate model involves the electron field describing the probability of an electron existing at any region in space (not to be confused with the electromagnetic field, the medium in which photons propagate).
Sure the position of an electron is not definite, but neither is that of a buckyball, but a buckyball has a shape we can describe, an internal structure we regard as extended over space, in a way that is separate from the indeterminacy of its center of mass position. This is unlike an electron, for which, if we set aside the uncertainty as to its center of mass, my understanding is that the only internal degrees of freedom it has left (in the Standard Model) are its spin and whether it is left or right handed, with no other structure to it.
It is in this sense that, AIUI, electrons are modeled as point particles.
Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.
But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)
> Anyone who has taken a graduate level class in General Relativity would have been able to tell you the same.
You say that and yet this thread is full of people arguing about it, and there's an entire Wikipedia article on this: https://en.wikipedia.org/wiki/Gravitational_singularity.
In fact, that article says:
> No complete and precise definition of singularities exist in the theory of general relativity,
So which is it? It can't both be trivial to any grad student but also an open question. And things like naked singularities aren't proven to not exist either.
Also, general relativity is a classical, geometric-only theory. It seems obvious that better understanding what a black hole's singularity is would require quantum mechanics because the singularity is effectively what's "left over" of the physical material once you go beyond a neutron star.
Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surface in time, not space (as the book explains, the space and time coordinates switch places as you cross the event horizon).
> the space and time coordinates switch places as you cross the event horizon
If Susskind's book does in fact say that, it's extremely disappointing to me, because, as a number of other GR textbooks will tell you (e.g., Misner, Thorne & Wheeler and Wald, the two great classic GR textbooks), the "switch places" is an artifact of a particular choice of coordinates (Schwarzschild coordinates), and does not represent anything physical. So it's not something that should be relied on. (Not to mention the confusion it causes when pop science sources repeat the statement and then draw all manner of wrong conclusions from it.)
The part about being "a surface in time" might be all right, assuming that by that he means "a surface representing a moment in time, not a place in space"--in more technical language, a spacelike surface. That is correct, and it's an invariant that does not depend on any choice of coordinates. But that invariant fact can be described without having to talk about the "switch places" thing at all.
Kruskal-Szeres coordinates indeed get rid of the wonky coordinate stuff at the event horizon, but if you look at the corresponding diagrams, you'll just end up with the same confusion, because the singularity is still a point (or rather surface) in the future instead of a point in space. The issue is that these diagrams are for eternal, static black holes, which cause diagrams to have these weirdly stretched infinite regions that are quite useful for understanding details of the math, but are highly confusing to laypeople. In fact these diagrams make it look like you'll always fall into the black hole at t=infinity, no matter how far you are away, when in reality you could orbit a static black hole pretty close for eternity.
If you really want to get a picture of what is happening, you can look at Eddington-Finkelstein coordinates. In particular at a light cone field diagram around a collapsing shell of matter that turns into a black hole. Then this whole stuff suddenly makes sense without even going into the math. You don't just see how an event horizon can form out of nothing, you also see how gravity starts to bend your causal forward light cone (i.e. all points in spacetime with events that you could interact with in the future) inward in such a way that you will necessarily always fall closer to the center of the mass once you pass a certain line (aka the event horizon). No need to deal with those weird infinities or points in time suddenly lying on a different axis.
The great Roger Penrose (the same guy who also came up with some of the most confusing diagrams) published a beautiful, simple overview of exactly this stuff in Scientific American: https://www.wkbpic.com/wkbx/SA/1972/1972-05-01.pdf (starting on page 38)
Still one of the best things you can read if you don't just want the math.
This article is great but the references to gravitational waves as if they were an observed fact (in 1972) was mystifying to me. It led me down a rabbit hole to Joe Weber, who is name-checked at the end of the Penrose article.
A Fleeting Detection of Gravitational Waves
https://physics.aps.org/story/v16/st19
Gravitational wave blues
https://aeon.co/essays/how-joe-weber-s-gravity-ripples-turne...
> the singularity is still a point (or rather surface) in the future instead of a point in space.
It's a spacelike line on the Kruskal diagram, yes.
> The issue is that these diagrams are for eternal, static black holes
The full Kruskal diagram is, yes. But the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse of a massive body. That includes the singularity being a spacelike line, and there being spacelike curves inside the horizon that are infinitely long.
I agree that Eddington-Finkelstein coordinates can help with intuitions about this spacetime geometry as well.
>It's a spacelike line on the Kruskal diagram
It also is in Schwarzschild coords, so you've gained nothing with respect to the original issue from switching coordinates. Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
>the essential features of the black hole portion of that diagram are still there in a black hole that forms by gravitational collapse
The issue is even the limited diagram doesn't really show you that and the full one goes crazy with white holes. So not a good place if you don't want to confuse laypeople.
> It also is in Schwarzschild coords
True--indeed, the statement that it's a spacelike line is an invariant, independent of any choice of coordinates. But it's a lot harder to see that in Schwarzschild coordinates.
> Kruskal-Szeres really is only useful for demonstrating that the event horizon is not such a weird place, but it does nothing for the singularity at the center.
I disagree, and I think many GR physicists would as well. Indeed, both classic GR textbooks, Misner, Thorne & Wheeler (1973) and Wald (1984) discuss Kruskal coordinates and their associated spacetime diagram (MTW in Box 31.2 and sections 31.5 and 31.5, Wald in section 6.4), and those discussions contain a good deal more than just showing that the horizon is "not such a weird place".
This doesn't seem meaningfully different to me? Like the notion that the singularity is always in your future (because you can't escape it anymore past the event horizon) makes sense, the point of confusion is what are the implications?
Roughly the general public (including me) knows that gravity is meant to have some effect on the apparent passage of time, so it seems significant but under explained what it means to be in a region of space where all possible directions lead to the singularity.
> the singularity is always in your future
It's not just that it's always in your future in the sense that you can't avoid it. It's that the reason you can't avoid it is that it's a moment of time, not a place in space. You can't avoid it for the same reason you can't avoid tomorrow. And which direction in space you move has no effect on whether or not you reach the singularity for the same reason it has no effect on whether or not you reach tomorrow.
>the notion that the singularity is always in your future makes sense
But it is just a mathematical artefact of weirdly chosen coordinates. In reality, the singularity is still just a point in space (or a line in spacetime), except that inside the event horizon all paths you are allowed to travel lead to it. There's no need for this whole "space turns into time" notion apart from the fact that you are guaranteed to hit it in *your* future as a local observer. And in Eddington-Finkelstein coordinates you can easily see that globally, things simply hit the spatial coordinates of the singularity at certain slices of coordinate time. Other coordinate systems make this whole process seem much more weird than it is.
> it is just a mathematical artefact of weirdly chosen coordinates.
No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates.
> the singularity is still just a point in space
No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of time, not a place in space.
> There's no need for this whole "space turns into time" notion
That's true; that notion is an artifact of Schwarzschild coordinates. But that does not imply the other claims you are making.
> the spatial coordinates of the singularity
I'm not sure what you mean by this. It's true that, since the singularity is a spacelike line, you can treat a coordinate that varies along it as a "spatial" coordinate marking different spatial points on the singularity. But the singularity itself is a moment of time (as above, a spacelike line), so it is not a "place", and it does not have a particular set of "spatial coordinates". A spatial coordinate marking different points along the singularity is marking different points in space at a moment of time.
Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. Certainly I'd trust what he says rather than me, so sorry if I was misleading.
(If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).
> Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing.
That's good. However:
> Interchange of Space and Time Dimensions at the Horizon
This still seems misleading to me, because "Dimensions" makes it seem like it's not just an artifact of coordinates--but it is.
The way Brian Cox puts it, a singularity is a point in time: the end of time.
I have trouble really conceptualizing black hole physics, I just think of it as a mass so great that nothing, including light, can escape its gravity. Works for me.
The singularity in a non-rotating, non-charged black hole is as you say. It’s like in a finite amount of time you “run out of time”, like there isn’t any more time on that trajectory.
The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says.
And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.
To be honest I really can't get past what "the end of time" even means.
If it signifies the end of time, then all the stuff in the black hole would need to no longer exist no? If anything is happening in the black hole, then time is still progressing, so nothing must be all that exists?
The more interesting component is that black hole physics is almost an anti-free will zone.
Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).
I’m not sure free will has anything to do with it.
If you don’t have enough upward velocity to escape earths gravity, hitting the ground is also inevitable.
> the space and time coordinates switch places as you cross the event horizon
I'm sorry but this is blowing my mind. What???
Because it's very misleading. Time and space do not switch places past the event horizon. What happens is that the direction/path between an object and the singularity becomes a timelike dimension, and the direction that plays the role of time outside of the event horizon becomes a spacelike dimension. That is not the same as them swapping or that time becomes space and space becomes time not to mention that space has 3 dimensions and time has only 1 dimension so how could they even swap places.
Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.
The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.
> Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time
That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.
To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.
To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).
Am I understanding this right by thinking - if I was walking toward the black hole past the event horizon, and then I turned around, I would still be walking toward the black hole?
Once you pass the event horizon, every direction leads to the singularity in your future. Directions "away" from the singularity may still visibly show what things looked like outside of the event horizon before you fell in, but that is from your past. Heading in that direction will not get you back there anymore, you will only find the singularity along that path in your future.
> if I was walking toward the black hole past the event horizon, and then I turned around
Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.
And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.
You can't turn around though. Everything goes toward the black hole. If you turned around, atoms would be moving away from, or at the least changing their direction in respect to the black hole. And that's not possible. You wouldn't even see anything because all light is going toward the center, and it wouldn't go into your eyes.
Unless you went in butt-first, but the path of the photons would have changed and would now be going toward the black hole, and everything would look probably all smushed together.
Sounds like that would be true if you were inside any closed surface.
Not quite: inside a closed surface you can't escape, but things can repeat.
You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly.
A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.
Unless it's a spinning black hole, which contains closed timelike curves that can be reached from and can escape back to the outside universe?
It's unfortunately misleading shorthand for what actually happens: space becomes timelike. It doesn't become time. All this means is that once you cross the event horizon, you can only ever move toward the center of the black hole, in the same way that outside of a black hole, you can only ever move toward the future. You might not take a direct route to the center, but no matter which way you move, you will be following a track that ends at the center.
The reason this phenomenon has a spooky-sounding name is that it also affects whether two objects can be causally connected. If you can only ever move closer to the center of the black hole, then there are (conceivably) other objects inside the event horizon that you can never have a causal relationship with.
But it doesn't mean that space and time literally switch places.
[This video][1] and the one before it on the playlist are a good no nonsense explanation of the topic.
[1]: https://www.youtube.com/watch?v=O_2vnb_eVGE
it might help to think of the singularity as not a point in space but rather a future that cannot be avoided. All possible paths through space and time, no matter what happens, will go towards the singularity.
Yup. It's that weird.
Also read Nick Gorkavyi: The Oscillating Universe: Einsteinian Cosmology of Black Holes and Gravitational Waves
I think it's not even a valid critique of that and it's sort of playing games with what the definition of a singularity is to reach the claim that it's making. I think the topology of the singularity is not even a well defined question and certainly not well understood enough to bear the strong claims in the paper.
Unfortunately you are wrong. Everything the paper is saying about the singularity and its properties in GR, and more generally about the black hole solutions it describes, is well understood and has been for decades. The definition of "singularity" that the paper is using is perfectly fine, and its topology is perfectly well-defined. A good textbook treatment is that of Wald (1984).
Some of the things the paper points out are not emphasized in other sources, which is probably why the authors chose to write it. But there is nothing in the paper that is in the least questionable or ill-defined; it's all standard General Relativity as applied to the Schwarzschild and Kerr black hole solutions.
Singularities suggest incomplete theories.
This is the opinion of most physicists, yes, but it does not in any way justify the GP's claims or cast doubt on anything that is said in the paper. Note that the paper talks explicitly about the limitations of GR as the singularity is approached and how a quantum gravity theory, if we ever find and confirm one, might fix those issues.
I have a question for any physicists here.
Due to my engineering background, I know just enough physics and mathematics to completely misunderstand general relativity and quantum mechanics. However, one pattern I have noticed is that one favorite past time of physicists is looking at the mathematical models, trying to find insane ass edge cases and then trying to interpret them.
With that in mind, do these equations allow black holes whose singularities extend beyond their event horizons?
As is nicely visualised by it's Penrose Diagram, e.g.
https://jila.colorado.edu/~ajsh/insidebh/penrose_schw.gif
Some PBS Space Time episodes featuring the Penrose Diagram (in order - the first two are from 9 years ago, the last from 6)
What Happens at the Event Horizon? - https://youtu.be/mht-1c4wc0Q
Escape The Kugelblitz Challenge - https://youtu.be/v3hd3AI2CAA
Mapping the Multiverse - https://youtu.be/4v9A9hQUcBQ
I enjoyed this Veritasium video on the subject, which includes Penrose Diagrams.
https://youtu.be/6akmv1bsz1M
Sorry man, that's not what this is about.
It's not? Schwarzschild has a space-like singularity. That's the wiggly horizontal line at the top left of the diagram. If you are in the black hole you can't avoid hitting it. Seems to be exactly what the paper is remarking on.
Yes it is?
> Black hole singularity is a surface not a point
Might they be trying to say this?
1. The boundary of the black hole which traps light, etc, is called the event horizon, and sits at the Schwarzschild radius. This is a geometric surface.
2. There is no singularity at this surface.
3. In models of black holes, there is a gravitational singularity at a point in the centre: https://en.wikipedia.org/wiki/Gravitational_singularity which is a topic with nuances.
They do speak of the gravitational singularity (not the event horizon). It's within the horizon, there is a contradiction between the need for two infallers' position to reach the singularity (thus hitting a point) and the causal impossibility of them actually meeting (following General Relativity?). This suggests that the point should maybe be a surface.
I don't follow most of the arguments however.
No, they are theorizing about the Kerr metric. The Kerr metric describes rotating black holes and instead of a point like singularity predicts a ring of zero thickness with infinite density additional work posits the ring is unstable and collapses to a surface all inside the event horizon, they then proceed to make predictions about the nature and behavior of that surface.
By the way the Kerr metric predicts a ring because the centrifugal acceleration due to the rotation partially counteracts the gravity. As far as I understand, not a physicist.
Off-topic, but it makes me think of "reasoning black holes": you get enough like-minded people together that they start reinforcing each other's logic and beliefs until not only those people get completely detached from reality, but anyone who interacts with them gets sucked in as well unless their own logic ("velocity") is adequate to skirt the edge and escape, forever altered by the experience.
Similar questions arise: how would you know if you were inside one? The laws of logic ("physics") seemingly don't apply, but there's no way to test them in that environment.
I believe that's called an echo chamber, and exemplified by a board meeting.
I dunno. Those rationalists seem to be in some kind of intellectual black hole which never had any danger of sucking me in. Like I have seen many strands of posthumanism and transhumanism, speculations about an intelligence explosion circa 1970, and figure it would have been just as much fun to sit around the campfire, pass a joint around, and talk about crazy stuff with these guys
https://en.wikipedia.org/wiki/Russian_cosmism
as it would be to do with anyone contemporary. In their orbit I get periodically annoyed but changed forever, no.
Well, the analogy is to something flying by a black hole and having its trajectory altered.[1] It sounds like it fits you, then -- you interacted, and are now forever irritated by them or by things that sound like them, even things that you would not have previously noticed.
[1] This is just gravity, nothing specific to black holes, so the analogy isn't doing a lot of work here.
Kinda sounds like a "linguistic manifold."
I know this isn't a new discovery but I fully expect the next major theoretical physics breakthrough to be discovered by a frontier LLM at this point, given their aptitude at solving a lot of the recent mathematical conjectures.
scoffs Well yeah everyone and their aunt knows singularities have 5 dimensions.
You need at least 11 for the math to work out but it's okay most can be compacted.
How does one descr blackhole to a non-physicist without losing much accuracy? I just it of a very-dense-object.
Normally people think of gravity as pulling on objects. You can instead think of it as pulling on the space those objects are in.
A black hole happens when there is enough gravity that space gets pulled inwards somewhere, at at least the speed of light.
Gravity falls off with distance, and the distance where space is being pulled inwards at exactly the speed of light is called the "event horizon".
It has this name because speed of light is the speed of causality: events that happen further in, are "over the horizon" for you, they cannot causally influence you.
> Normally people think of gravity as pulling on objects. You can instead think of it as pulling on the space those objects are in.
(Very uneducated person here) I’ve always wondered if large objects caused gravity, or if maybe large objects form in the places where there is a lot of gravity. This is probably elementary, but I’ve never looked in to it. Maybe today is the day!
Scientists have directly measured the gravity coming from big balls of lead. The gravity didn't make the scientist put the lead there, and the gravity wasn't there before the lead. The lead must have made the gravity.
If you want to take a very large-scale - if poetic - view of things, you could also (very arguably) say something like "Mass is Fate".
Mass represents a zone where probabilities want to be. The more that aggregate, the more they make other things want to glom on. With a high enough density, nothing that's nearby can glom to literally anywhere else, and there's your black hole. The Great Inevitable. In this space, there are no other possibilities. Very Demiurge-y.
Dark matter is mysterious enough to be compatible with both at the same time, I think.
(Is a collisionless gas really even an "object"?)
I mean, it's kind of both: objects have gravity, which attract them together, which creates more gravity and larger objects. Stars are what happens when the rest of physics disagrees with this (and black holes are when gravity wins anyway).
Why not just say it's something with such strong gravity you can't escape even if you go at the speed of light? Maybe that loses too much accuracy for you?
It's a region of space from where not even light can scape.
You can get a region like that by squashing a lot of mass in a small space, like happens when a star collapses under its own gravity. So here the intuition of "high density" makes sense.
But at the center of galaxies you have the so called "supermassive black holes" which are more or less comparable in size to the solar system and yes, they have a lot of mass but they are not very dense, a pop-sci trope is comparing it's density to cotton candy or even the air we're breathing right now.
So it's a matter of how you distribute mass/energy in a given diameter, not exactly of density.
The problem there is that not even the physicists completely agree on the details, because we know black holes definitely exist, but every explanation breaks one rule or another that should apply from different disciplines. It's part of why they get so much ongoing attention.
Black holes are essentially where our knowledge of spacetime breaks, and we can’t even see into it. It’s hard to really concretely know much about it directly.
A one-way door in space.
Consider a balloon. I don’t imagine in visuals but if you do, either a solid color or a patterned balloon works. Let’s say it’s a cow print design.
Deflate it, then stretch the balloon over a vacuum cleaner tube and put on a rubber band to keep it in place.
If you pour sand on it, you can only get a small bump of sand and then it’ll run off the sides. Reasonable, logical, normal behavior. Clearly it’s a surface — it’s holding sand, it’s pouring sand in different directions over the edge, the sand is not all compacted into a single grain.
Turn on the vacuum cleaner. Assume a balloon stretchier than the strongest vacuum cleaner in the universe. What happens? Several things, each of which are perfectly reasonable:
1) The end of the tube is still a circle, and the balloon is still attached and covering the tube, so it’s still a two-dimensional circle.
2) A single grain of sand can’t block the vacuum tube, so it clearly hasn’t collapsed to a point.
3) The covered end of the vacuum cleaner tube is still the same circle, with the same diameter, as it was before you turned on the vacuum.
4) You can pour buckets more of sand onto that stretched circle of balloon than the handful you could before.
5) If you pour enough sand onto the circle, it’ll behave just like it did before: the sand will form a small mound and then newly-poured sand will run off whichever side the sand was poured on.
6) The rubber band is going to catch some of the overflowing grains of sand and hold onto them (‘accretion’), near but just outside the circle.
Next: Consider a more powerful vacuum cleaner. How much more? Lots. The most. An atomic Dyson powered by nuclear fusion. (This is a bit unrealistic, but that’s astrophysics for you.)
How much sand can you pour onto that two-dimensional, circular, balloon surface?
Lots. The most. Some of it will spill around the edges and get caught in the accretion band, but somehow that circle, that’s still the same size and clearly still blocking the vacuum tube, can hold an entire universe of sand.
That’s how black holes work :)
ps. For those who dislike the crudity of my teaching analogy and want to pop the spherical cow balloon: Topologically, the surface covering the vacuum tube is always a circle, even if you have an infinitely-powerful vacuum cleaner. At no point — pun intended — can a vacuum cleaner apply a transformation applied that reduces the dimensionality of the surface, thus it must remain, topologically, a circle.
pps. So clearly I must choose the circle in front of me! Hahaha! Aaaahahahah!
ppps. dies
"A really interesting and cool thing for astronomers to talk about...but you might want to pray that not one of 'em ever comes within a million trillion miles of the Earth."
Astronomical distances are vast, million trillion miles too far, that's over a hundred thousand light years. There are known stellar-mass black holes within just 2000 light years of the Earth. Heck, there might be a primordial black hole in the inner Oort cloud and not only would it not destroy earth, we'd have (are having) trouble detecting it.
Unfortunately, there is a rather large one not one sixth of that distance away (a million trillion miles is actually rather large - 170 kly - approximately double the size of our galaxy)
Yes - I took the grandparent comment's "descr to a non-physicist" as "describe to someone who really isn't into math or hard sciences". Those folks will hear "million trillion" as "a really Really REALLY REALLY big number". Not as "1 x 10^18".
I guess, but "light year" is easy to say, easy to understand, and much less likely to mislead. And most black holes would probably be safe at that distance.
Though the issue of small black holes is worth bringing up. If you scrunch up one cubic kilometer of stone into a black hole, that's heavy to be stable for trillions of years, but light enough to pass between the Earth and the moon without causing serious problems. And we really have no idea what the smallest existing black hole is.
Would this apply also to the singularity at the beginning of the universe? I guess I thought that the singularity was where all matter is compressed so much that it occupies a zero dimension point. I'm not sure if that applies equally to black holes and the singularity at the beginning of the universe. I'm kind of dumb on this stuff even though it fascinates me.
Rolling the clock backwards toward the big bang, it is not matter which is directly compressed, it is the fabric and metric of space itself. Matter being compressed is merely a side effect of the fact that "all of the locations that the matter occupies" are also compressed (though again, remain aware that calling it "compression" only makes sense when you rewind time in our cosmological model backwards).
So it is not as though you and the Andromeda Galaxy are made out of matter that got flung out of a point explosion long ago so that now you have traveled a very long distance away from one another, it is more like "both you and the Andromeda galaxy sat still for 13.8 billion years but space expanded between you in that time, so originally you were right on top of each other along with everything else".
We can rewind the model until the entire observable universe was as small as a Planck volume, but we have abundant evidence that the universe is indefinitely larger than that so even "that time when our 98gly diameter patch of space was almost indistinguishable from a mathematical point" means little when even that "point" was still just one pinprick out of the smooth manifold of a larger universe which could have been stupidly large or infinite even that early on.
The big bang didn't happen at a single point, it happened everywhere. You can look out from anywhere and see the cosmic background radiation having expanded from your location, wherever that location might be.
> The big bang didn't happen at a single point, it happened everywhere.
A bit of an odd thing to say, since "everywhere" implies there are multiple places to be, and at the instant of the big bang, there was only place to be. So it was both everywhere and at a single point: it was at all of the single place there was to be.
But your point (sorry) about expansion being from everywhere isn't specific to the big bang; space was expanding well after the big bang and it doesn't seem like the expansion ever had a "center" (at least, not since not-center places existed). It's expanding from everywhere. (But evenly everywhere? I have no idea. Hey, maybe black holes are like buttons in cloth, and it expanded everywhere except for where the buttons were holding things still at a rate relative to distance from the button. A brilliant hypothesis that explains exactly zero unexplained phenomena, at least none that I know of.)
Doesn't that imply that, "everywhere" was, precisely, a single point?
No, why would it imply that?
One theory that might help you visualize an alternative is that the big bang was basically two 3D universes (floating in higher-dimensional space) slapping against each other really hard. That creates an explosion everywhere even if everywhere is quite big or even infinite.
Physicists say a singularity is a classical prediction so most likely wrong.
It could also be an infinite dimensional ball which technically also has 0 surface area & volume even though it has a non-zero radius.
Is there such a thing as a "point" in the universe?
That is the whole question. My gut says no, infinites and infinitesimals are the edges of our understanding not real.
Depends on whether anything less than the Planck length has meaning.
An object sans semantics would be fine.
what's really going to blow your mind is
while you probably assumed or knew spinning black holes move space around them
spinning black holes also move TIME around them
* https://www.science.org/doi/10.1126/sciadv.ady9068
so in theory a spinning black hole that's been around for billions of years has a time drag around it in a path that is billions of years old
(no we can't navigate it because yes that would be time travel to the past and violates causality)
black holes are just so weird with every new detail even more weird
oddly more interesting to me to try to grasp neutron stars (densest objects before black holes and are still visible, our entire solar system in a neutron star would be only 10km 6.2miles across)
Another thing that may blow the minds of some is that M87* is less dense than air at 0.44kg/m³ so if you could bring it to sea level (in a large enough theoretical test area) it would float like a helium balloon (sea level air is 1.2kg/m³).
Of course if you did do that, the air itself would collapse into a black hole larger than M87*...
Consider the magnetar.
https://en.wikipedia.org/wiki/Magnetar
"A magnetar's 10^10 tesla field, by contrast, has an energy density of 4.0×1025 J/m3, with an E/c2 mass density more than 10,000 times that of lead."
Yes, magnetars are considerably more rare than black holes and considerably more interesting to study in terms of raw horsepower. Imagine a type-2 civilization using them as engines or launchers for spacecraft to zip around the galaxy.
the radiation from a magnetar exceeds any other star, overcoming that would seem implausible
still trying to wrap my mind around kilonovas (colliding neutron stars)
ie. they can pop out earth-sized chunks of gold, in theory, and since they aren't black holes that would be VISIBLE, albeit also "in theory" lol
* https://www.nasa.gov/image-article/unfolding-story-of-kilono...
maybe Roman can spot one someday, that would be something
> they can pop out earth-sized chunks of gold
The can produce Earth masses of gold, but of course not in the form of "chunks". The gold starts as atoms in a highly ionized gas and only much later cools enough to form solids (dust).
It blows my mind that, in the frame of an outside observer, time appears to stop at the event horizon. An observer falling through the horizon (who survived the radiation and tidal forces) would not perceive this.
Assuming they do fall through it. Remember they're about to receive an entire universe lifetime's stellar radiation compressed into a microsecond.
(Which is another reason some people think we might be living inside a black hole. An entire universe of energy released in zero time is literally a Big Bang. It would form into stars and galaxies.)
> densest objects before black holes
Not quite, I think a (theoretical) quark star would be higher density?
>what's really going to blow your mind is while you probably assumed or knew spinning black holes move space around them spinning black holes also move TIME around them
Well, isn't called space-time for nothing. You can't have one without the other. Like in electromagnetism. I thought it was kinda obvious since Einstein and Minkowsky.
Or you know there is no such thing as a singularity, and stars collapse to fuzzballs[1]
https://en.wikipedia.org/wiki/Fuzzball_(string_theory)
is hole
treating a black hole as a point, or ;) pointicle,may be valid as matter may be condensed, to the, I mean ,in such a way that there is NO space left whatsoever, and therefor no room for physical dimensions to exist in, and the entire body functions as an undiferentiated body of stuff, or giant pointicle that destroys time and space. Hopefully very soon we will get news about our galaxys central black holes interaction with a star that is orbiting very close but at 8% light speed, which may reveal if our blackhole is spinning, and if that is the case the we would have proof of energy/information/gravity waves? escaping from a black hole, along with gravity which while apparently imune to its self, nothing else is so far.
Isn't that how we're inside one.
Good PBS spacetime episode that looks at this: https://www.youtube.com/watch?v=jeRgFqbBM5E ( Could The Universe Be Inside A Black Hole?) Also, this spacetime episode is interesting the context of the paper and your statement: https://www.youtube.com/watch?v=x4TdColoIu8 (We Thought Black Holes Created Event Horizons. It Might Be the Opposite)
Well... yeah? That's describing the event horizon. It's a term roughly as widely used as "singularity".
Talking about the inside of a black hole is indeed rather pop-misunderstood though, yes. But it's not like physicists are especially confident about the details either. Theoretical astrophysics changes a lot as time goes on and our instruments improve, and it's a rather hard field to do experiments on to get better data quicker.
No, sorry, the singular surface in a Schwarzschild spacetime is not the event horizon. Nothing particularly interesting (from the GR point of view) happens at the event horizon.
Contains 08 rendered frames of a free falling observer's view while crossing the event horizon. This is not reddit, but plz someone animate it :}
Downvoted back to the dark ages.
Interesting work. The idea that the singularity is a surface rather than a point was unexpected to me even though it seems to follow logically from the theory of relativity. I wonder how this reconciles with quantum gravity. If the singularity is truly a two-dimensional surface, perhaps it's related to Hawking radiation and the thermodynamics of black holes?