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Strangeness of Black Holes (nautil.us)
67 points by dnetesn 30 days ago | hide | past | web | favorite | 62 comments

I found these lectures by Leonard Susskind very insightful:

- Leonard Susskind on The World As Hologram (https://www.youtube.com/watch?v=2DIl3Hfh9t)

- Leonard Susskind | "ER = EPR" or "What's Behind the Horizons of Black Holes?" (https://www.youtube.com/watch?v=OBPpRqxY8Uw)

- Entanglement and Complexity: Gravity and Quantum Mechanics (https://www.youtube.com/watch?v=9crggox5rbc)

As a note to the poster: The first video is not available where I live (Netherlands), maybe the link is wrong, the others are however.

This one works for me (UK):


(Leonard Susskind on The World As Hologram)

I think they may have accidentally removed a character from the URL.

The posted URL: https://www.youtube.com/watch?v=2DIl3Hfh9t

The actual URL: https://www.youtube.com/watch?v=2DIl3Hfh9tY

Just adding: it is unavailable for me here in India too.

I would also recommend (8 lectures)

Leonard Susskind Topics in String Theory


Despite the name this is largely about general relativity and black holes and other horizons. The best detailed description of black holes for laymen (assuming you have algebra and basic calculus) I've ever seen.

To add to those

The Perimeter Institute ones

The Royal Institution ones

There's multiple of each devoted to cosmology and black holes in particular.

I find it strange that no one has characterized that boundary layer where light orbits the black hole. We know that massive objects distort space and as a result alter the path of light. At sufficiently close distances, space is so distorted that 'not even light can escape'. Everyone assumes that light 'falls into' a black hole. But for light to do that, it would need a velocity greater than light itself if it is in orbit around the black hole. Thus, any light that is captured by tangential approach to the black hole and goes into orbit around the black hole, has to stay in orbit. Any acceleration that is needed to change the path of light would add to the velocity of light and that should not be possible.

Over time, the only light that is not absorbed by virtue of collision with the singularity at the center of the black hole is the light in orbit around it. This is distinct and different from the light resulting from nuclear fusion of material in the accretion disc which is just outside.

Light that comes within 3/2 of the Schwarzschild radius (Rs hereafter) gets captured by the black hole. Of course I don't mean that it beelines in a direct radial direction to the singularity. Of course it takes a curved path depending on its exact trajectory, but at some point on this trajectory it hits the event horizon. Nothing that hits the event horizon can ever come back out again (according to an observer at sufficient distance).

This magic 3/2 Rs radius is the Innermost Bound Circular Orbit (IBCO), and is the truthfully correct scientific principle that you are grasping for. It is not a stable orbit, but it is an orbit. In a theoretical world, if a photon had the perfect trajectory to enter this orbit, it could orbit there indefinitely, but it is unstable, so in the real world it doesn't happen this way.

If a photon hit outside of the IBCO, then its trajectory is affected by the pull of the black hole, but it escapes the gravity well, and continues on a new trajectory elsewhere into space.

After the photon hits the event horizon, then all statements needs a big asterisk with them. Its behavior might be observer-dependent or undefined. But at least in the conventional view of general relatively equations, it doesn't need to travel directly in the radial direction to the singularity, but it has to travel within a limited cone of possibilities, none of which lead back out. It can change its angular position somewhat as it gets closer to the singularity, but there is no orbit. No light cone within the event horizon allows for increasing the distance between a point particle and the singularity. In these conventional equations, all things that fall into the event horizon _hit_ the singularity within finite time according to a distant observer. Time has some shifty meaning to things inside of the event horizon, and maybe this is all wrong. But I am sure that orbiting the singularity inside the event horizon definitely does not happen.

The perfect orbit geodesic is infinitely thin and therefore unstable due to quantum mechanics. So even if a photon is injected at the perfect orbit it would not stay there, it would fall in or eject. Besides, even without invoking QM, any other matter that actually falls into the hole afterwards would inflate the event horizon, causing those photons caught in the perfect orbit to now exist just infinitesimally within the orbit and fall in.

Do you need quantum mechanics to see that a photon would fall in or eject? Presumably a little movement from the black hole would do the trick too.

Right, but the QM view tells us that even a perfectly stationary chargeless black hole in a perfect vacuum alone in a perfectly smooth universe would still experience fluctuations in its event horizon. Unlike the Classical view, QM reveals that even in principle there exists a degree of instability in the horizon.

thank you for your replies. however, no one addressed the fact that as orbital radius decreases, velocity increases. and that should not be possible for light. In fact, the whole idea of light bending around a gravity well does not seem to follow the rules of orbital mechanics. Masses that come close to a massive body get a velocity boost and a slingshot to their new course. I would suspect that photons are boosted to a higher energy state and thus get a frequency boost as they are accelerated radially since they cannot get a speed boost. And more energetic photons would be more apt to return to a wider orbit-reaching an equilibrium of their orbital path.

In circular motion, acceleration is always perpendicular to the velocity. While the velocity changes, the magnitude of the velocity (aka speed) stays constant.

I'm just a science fan and not an expert by any means but it appears that time simply stops at the event horizon for all intents and purposes. Things/light does not fall into the black hole as it just freezes at the event horizon... forever. There is no time in a black hole. Movement requires time.

I’ve never understood how infinite time dilation jives with black hole evaporation:

> If we take for example the latter observation of unbounded time dilation seriously, we come to the conclusion that in the moment that we spend on the horizon all time passes for anything outside the black hole. The end of all things happens in the rest of the universe, and in fact after the moment in which we enter the black hole, there is no way back.

> However, if we consider a black hole of the same mass, things look rather different. As a (partially) quantum object it radiates and evaporates within a tiny fraction of a second. All its mass converts into energy, which results in an explosion three times stronger than the bomb dropped on Hiroshima.

How do these two things mix? A particle experiences asymptotic time dilation when it crosses the event horizon and the rest of the universe ends in that moment. Then the black hole evaporates and lo and behold the universe is not ended.

Yeah, the particle that went in got annihilated and never actually came back out. Sure. But if the black hole does not survive until the end of the universe, then it seems fundamentally impossible that the particle in question experienced unbounded/infinite/asymptotic time dilation. The particle’s annihilation must have happened by the time the black hole evaporated. And yes, time is relative, but it doesn’t run in reverse.

> How do these two things mix? A particle experiences asymptotic time dilation when it crosses the event horizon and the rest of the universe ends in that moment. Then the black hole evaporates and lo and behold the universe is not ended.

I don't know if that's necessarily correct. From the point of view of an object falling through the event horizon, nothing special happens and they can look outwards normally; whereas an observer some distance from the black hole (and maintaining that distance) sees the falling object fall slower and slower and becoming more redshifted. The falling object also become shorter in the direction of travel (according to the external observer) and end up 'smeared' on the horizon.

Leonard Susskind shows this using a Penrose diagram in lecture 5 or 6 (I think, but they're all worth watching) of the Stanford Topics in String Theory lectures[1]

[1] https://www.youtube.com/watch?v=NZ-ElsvYKyo

Suskind actually has a whole lecture on Youtube devoted to addressing the paradox of falling into a black hole from the perspective of the person falling in versus an outside observer. The outside observer sees the falling observer catastrophically turned into high-entropy soup smeared across the horizon, while the one falling feels nothing particularly special as they cross the event horizon.


Just a note, that’s the case for a very high mass black hole. A “smaller” black hole would shred the astronaut before they even reached the event horizon.

I still don’t see how to reconcile these two things. The observer sees the particle essentially slow to a stop as it crosses the event horizon, right (infinite time dilation)? Then the black hole evaporates. Evaporation happens in finite time, so how is that particle “frozen” indefinitely?

Is characterizing the dilation as “infinite” incorrect? I’ve heard that and equivalent statements from people who studied and seem to actually understand this stuff, and it seems correct per the article here.

The particle goes through the event horizon in finite time according to its own clock (and will then hit the singularity in finite term however it tries to travel).

Think of the view of it by an external observer as being 'frozen' at the event horizon as kind of optical illusion caused by the extreme warping of spacetime. For a non-evaporating black hole (as described by general relativity), the 'last' photon coming off it will indeed be at infinity (or with infinite redshift). If (when) the black hole evaporates, the external observer will see that and of course there will be no more photons from the infalling particle.

These two different views are hard to reconcile from our human perspective of how the world works, but they really do come from the mathematics of general relativity.

Here's a really excellent and short video which attempts to explain this in ten minutes. (His explanation of how a Penrose diagram works is fleshed-out in more detail in the Susskind lectures I mentioned above).

PBS Spacetime - What happens at the Event Horizon


I'm curious about the description of a black hole as a singularity. I'm going to resort to Neoplatonist philosophy to try to understand this.

In the formation of the universe, the notion of a singularity points at an old idea, argued by Plotinus, that everything started with "The One". This is commensurable with the statement that the boltzmann entropy of the start of the universe, prior to inflation, would be equal to "1" -- because that is the total volume of possible phase space. That, to me, is very elegant -- although it is unclear whether there are predictions about how the 1 becomes 2 ("the indefinite dyad"), 3 and then the inflationary myriad. But still, I'm impressed that the logic of ancient philosophy could correspond reasonably with modern physics.

From this perspective, I'm interpreting big bang's "singularity" as =1. What is the nature of the singularity of a blackhole? Is the event horizon itself the singularity, or does it just an effect of a singularity at the center of the blackhole? Is there a "One" at the center of the blackhole?

If one doesn't understand a scientific theory then their understanding of it contains no information. Ancient philosophy rarely contains information. As a result the two often appear to line up.

>Ancient philosophy rarely contains information.

Sounds like you haven't read much, gee. What a strange comment. It has a far higher signal/noise ratio than modern philosophy, I'd say, maybe because usually only the best has survived.

>It has a far higher signal/noise ratio than modern philosophy

You can look at it this way: every possible statement seems to have been made by at least one ancient philosopher, especially once you include the non-western traditions. There were atom-ists, and continuum-ists, and so on. If you view ancient philosophy as one big bucket of sentences, it will fill up sentence space fairly uniformly. You could reconstruct ancient philosophy just by coming up with reasonable-sounding claims about things they were aware of back then until you ran out of possibilities, although that wouldn't produce the historical association of certain views with certain people.

A distribution that uniformly fills space is, in the technical sense of the word, "no information." If you trim it down (for example by doing experiments and discarding whatever doesn't match your newfound knowledge of reality), you get a distribution that "has information."

To put it concretely, finding out that an ancient philosopher said something doesn't help, because ancient philosophers said everything they could think of. Whether that is better or worse than what philosophers are doing now is up to philosophers to decide, I guess.

I haven't actually taken every single statement said by ancient philosophers (if you can even clearly classify philosophers as 'ancient' -- what's the date cutoff?), and put them in a bucket, and checked that the sentence space in that bucket is filled up uniformly.

However, new sentences are made every day, new words made very often. Nobody cares about the technical sense of the words "no information". If your argument was extended from 'ancient philosophy' to 'anything ever said by humans', then anything ever said by humans would fill the sentence space fairly uniformly, so finding out that anyone has said anything doesn't help.

A single human has not considered and thought about every sentence possible. They have their own beliefs and knowledges, and by reading ancient philosophy, they can expand that knowledge base, change those beliefs. Ancient philosophy is not inconsequential, and it certainly contains "information".

I think whatshisface is being overly dismissive of the value/information in ancient philosophy. But the heart of his comment is that you can cherry pick pretty much whatever you want from ancient philosophy because the corpus is so large. If you, e.g., selectively choose statements that vaguely line up with quantum mechanics, you haven’t proven that Ancient Greeks knew quantum mechanics or had some unexpectedly deep understanding of the universe. You did something equivalent to P-hacking to dig meaningless correlations out of the noise.

Right, it would be inappropriate to claim that Plato predicted the big bang!

He did arguably explicitly predict that basic mathematical/geometric forms underlie the structure of the universe. E.g., that atoms would be composed of pyramids, cubes, dodecahedrons and that the behaviour of atoms would be based upon the different geometric properties of basic forms.

That idea is only partially correct, however. Atoms are based on the basic mathematical forms -- but on the spherical harmonics of electron clouds, not point geometries. Whoops! Otherwise, the idea is commensurable with modern atomic understanding.

Earth, water, air and fire correspond not to elements (ice can melt, obviously) but to phases of matter. (Solid, liquid, gas, plasma).

There is a reason Classical Greek philosophy underlies western civilization. They were not dummies and there is still a lot we can learn from them. It's not like all their ideas were examined in the 1800s and we took all the good ones, leaving the classics as a sort of intellectual skin worth shedding. Instead, it is the core we build on. It's worth understanding the core -- and giving them the benefit of the doubt to identify interesting ideas.

Like that the universe begins with "the one" :)

That is some impressively hand-wavy equivalency. Plato predicted something pretty much entirely wrong and you're pretending he was generally correct. Plato believed, without evidence, that there were some indivisible units of matter. That's all he got right (and even that was arguably incorrect given subatomic particles).

>If your argument was extended from 'ancient philosophy' to 'anything ever said by humans', then anything ever said by humans would fill the sentence space fairly uniformly, so finding out that anyone has said anything doesn't help.

That's accurate, though. If I told you a statement and backed it up with the claim that "at some point in history, a human said it" then you really haven't learned very much. Likewise, if a statement is tagged with "and by the way, an ancient philosopher believed it," you may have learned something about history, but the statement itself hasn't gotten any more believable.

This argument could be used pretty much for any field and it's just BS.

If you apply the same principle to all of language then you could say language has no information. Try it with a dictionary, the words are distributed pretty uniformly, does the dictionary have no information?

Same for the whole universe.

So are you saying that "information" only exists when some arbitrary observer (in this case you), applies some sort of filter or boundary to what they are looking at?

>Try it with a dictionary, the words are distributed pretty uniformly, does the dictionary have no information?

That is not true at all: the dictionary is highly concentrated in correctly-spelled English words. If the dictionary was evenly spread over the space of sequences of letters A-Z it would not be useful at all, because next to Cat would be Cas and Cau.

Words are not distributed uniformly in a dictionary at all. They are distributed according to the grammatical structure of the text.

I think you’re reading tea leaves here

Probably just the One tea leaf

Probably a piece of toilet paper they think is a tea leaf.

I think your assumptions are off. Anyway, the event horizon isn’t the singularity itself, it’s the point of no return that surrounds the singularity.

Maybe there is a One. Some physicists think that inside a black hole is a white hole, which would look like expansion. Our cosmological horizon could match up with this

Is this the idea that our observable universe is actually inside of a larger black hole?

That's right

I've never heard of this. Any suggestions on where to read about these theories?

I think you just read everything there is to read about this. To my understanding, the idea that our universe is actually inside a black hole is not a “theory” in the sense that, say, relativity is a theory. It’s pure conjecture, and essentially not falsifiable. It’s more akin to the “theory” that our universe is a computer simulation.

So what happens to stuff falling into the outside black hole?

you probably still hit what looks like a singularity from your perspective and get spagettified

Wouldn't that be additional mass appearing from nothing from the perspective of this universe

Maybe this could be dark energy?

WARNING: This comment contains zero science. I didn't even Google it.

It’s the most intuitive explanation I’ve encountered for why we don’t see other life. (They might be inside of black holes.)

This is not intuitive to me. Why would they be inside black holes and not outside them?

>I'm curious about the description of a black hole as a singularity. I'm going to resort to Neoplatonist philosophy to try to understand this.

Modern physics (with its successful predictions) require complicated mathematics to understand. What makes you think that neoplatonist thought can help you understand a modern scientific theory?

Complicated mathematics doesn't make the singularity more understandable. It just makes more people give up trying to understand. I don't think any physicist would claim that modern physics understands time=1.

Neoplatonist thought holds the belief that the structure of the physical world is based on fundamentally basic mathematical patterns -- which is completely commensurable with modern physics. That they viewed the one as the origin of reality seems to provide a reasonable and human-readable perspective on how the entire universe of 100B+ galaxies could once exist in a volume smaller than the nucleus of an atom.

Math =! understanding. I have faith that the world is fundamentally reasonable and understandable. All models are Wong, some are useful, that sort of thing. So I appreciate the perspective of very smart ancient philosophers on this origin issue.

> Complicated mathematics doesn't make the singularity more understandable.

What do you mean it does not? Limit theory does that in great depths. Some cases are unaccounted for, but that might actually be due to the incompleteness theorem.

I don't mean to be dismissive of complex math, but it can be seen as an excuse by people who expect the universe to NOT make intuitive sense. Usually, powerful mathematical explanations are quite simple (Maxwell's equations, Boltzmann's, etc)

I, for one, don't expect the universe not to make intuitive sense. I just think average folk intuition is waaay to weak for that. Actually, I think the same applies to nearly all people, mathematicians the least of all.

Most physicist probably don't think that black holes actually have a singularity and attribute singularities predicted by general relativity to the fact that the theory is only approximate and breaks down under the conditions at the center of a black hole. Just because the equations say there is a singularity does not mean that there is a real singularity.

Ideally, we'd understand space completely in terms of the relationships between things, and our coordinate geometry would not ascribe any "positions" to events, but only "relations" between events. Singularities are places where our improperly-formed coordinate maps break down. Which means we'd rather like to look at black holes as holes in the coordinate mapping, rather than as singularities, but we don't have the mathematical prowess to do that. Or good enough scientific understanding of the phenomena to know that we've done it correctly.

Coordinate systems are not the primary issue. It's true that coordinates can be problematic but the laws of physics are independent of coordinates because those are of course only a tool we use to perform calculations. But take for example the classical law of gravitation which requires dividing by the square of the distance between the two bodies. The distance is independent of the coordinates you use to describe the positions of the bodies but you still get a divergent force as the distance approaches zero. So the breakdown of the law is not due to a bad choice of coordinates but inherent in the equation and a strong indication that the law is probably only approximate for short distances.

I believe you're just saying the same thing I am in different terms. The fact that zero is even a 'distance' you can divide by is consequence of the fact that you're deriving distance from the coordinates of the bodies. If distance was instead fundamental (and not a function of coordinates), you'd not even have a zero distance, and you'd have no inclination to attempt dividing by it. (But the math for doing that is basically to always account for every part of every body, and that's just entirely intractable.)

This is assuming mostly Newtonian physics, of course. Once you start dealing with fields and quantum mechanics, none of this makes as much sense.

Coordinates and distances are independent concepts. They are function from the space you are working with into the reals assigning each respectively each pair of elements a real number for each coordinate respectively one real number for the distance. You can for various reasons choose coordinates and distances in a way such that they have simple mathematical relationships but that is just an arbitrary choice. The classical law of gravity is only dependent on distances, which is a physical meaningful concept, but not on coordinates, which are not physically meaningful. In that sense distances are fundamental in a way in which coordinates are not and a distance of zero is a meaningful thing, namely two things are at the very same place.

I think what you're aiming for here is the statement: somewhere in a black hole spacetime the Kretschmann scalar goes to infinity.

The Kretschmann scalar is the square of the Riemann tensor, or in notation R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}.

There are no forces or coordinates or anything like that to even consider; it's a curvature invariant. ( https://en.wikipedia.org/wiki/Curvature_invariant_(general_r... )

If the Kretschmann scalar is non-infinite at a point then there is no gravitational singularity there.

If you really want to think about a black hole spacetime in a coordinate system, then in Schwarzschild coordinates for a Schwarzschild black hole, K = \frac{48M^2}{r^6} where K is the Kretschmann scalar. You can see that when r=0, K is undefined.

Other coordinate systems and black hole spacetimes are available.

However, generically, one can distinguish between a coordinate singularity and a gravitational singularity by calculating the Kretschmann scalar at a point. If the Kretschmann scalar is non-infinite then it cannot be the latter, whatever the coordinate basis is.

Continuing to think generically and without choosing coordinates:

"distance" -> it's still interesting for considering non-gravitational body forces of objects as we take the Kretschmann scalar around the objects towards infinity.

Essentially, tossing in one test particle just causes it to free-fall forever; tossing in two classical objects simultaneously (in Schwarzschild coordinates on Schwarzschild black hole spacetime)[1] means at some object- proper-time each object will collide with the other. They will still free-fall forever; there is a notional "down" if we have a gradient in the Kretschmann scalar field. However, the free-falling trajectories available narrow even after contact. For classical objects that are mutually repulsive, pressure[2] builds as they continue on converging free-falling trajectories and eventually classical forces cannot keep the two objects separated; they are forced into each other. The resulting compacted matter, whatever its nature, continues to free-fall forever.

Quantum-mechanically, who knows? Firstly we're way into the ultraviolet completion of the Standard Model, and secondly there's no reason to expect quantum mechanical effects to contribute to the stress-energy tensor in ways that do not look sufficiently classical under averaging or other tricks that let one continue using the geodesics of the black hole background metric or make only small perturbations to them. And we're ignoring quantum-mechanical effects outside the black hole, like Hawking radiation.

- --

[1] The simultaneity condition is a handwavy way of absorbing messy behaviour as we drop two identical charges into a black hole. See Cohen & Wald (1971), http://adsabs.harvard.edu/abs/1971JMP....12.1845C

[2] Pressure here is encoded in the stress-energy tensor T as T^{ii}, i \neq 0. Since the Einstein Field Equations say essentially G = T, we have to deal with pressure as it becomes non-negligible, because as a component of T it must be reflected in the curvature represented here as the Einstein tensor G. This is a practical example of where General Relativity is a dynamical non-linear theory. Two classical objects with identical electric charge within the horizon of a black hole makes a surprising bookkeeping mess! (compare the Schwarzschild metric with the https://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6... and there we are talking about what's outside the black hole and ignoring quantum mechanical effects altogether).

The ancient Greeks put the “Euclid” into “Euclidian geometry”. It took until about 1813 for that to be replaced with non-Euclidian geometry, and everything that makes General relativity really interesting is non-Euclidian.

Keep in mind that the first 28 postulates of Euclid remain valid even in non Euclidean geometry. Even Euclid had to invoke another principle to clarify the 29th, which is now seen as an optional principle.


Keep in mind that this idea of oneness wasn't just some idea of some philosopher -- it was the central idea of Platonic philosophy. Obviously, I disagree with a knee jerk rejection.

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