Strangeness of Black Holes
nautil.us
nautil.us
- 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)
https://www.youtube.com/watch?v=2DIl3Hfh9tY
(Leonard Susskind on The World As Hologram)
The posted URL: https://www.youtube.com/watch?v=2DIl3Hfh9t
The actual URL: https://www.youtube.com/watch?v=2DIl3Hfh9tY
Leonard Susskind Topics in String Theory
https://www.youtube.com/watch?v=NZ-ElsvYKyo
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.
The Perimeter Institute ones
The Royal Institution ones
There's multiple of each devoted to cosmology and black holes in particular.
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.
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.
> 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.
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]
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.
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
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?
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.
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.
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".
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'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.
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?
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.
WARNING: This comment contains zero science. I didn't even Google it.
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?
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.
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.
This is assuming mostly Newtonian physics, of course. Once you start dealing with fields and quantum mechanics, none of this makes as much sense.
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.
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[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).