I saw Luboš Motl’s blog post Most laymen completely misunderstand what a black hole is. When I read the title my irony meter skipped a beat, so I thought I’d take a closer look. Especially since he said this in his opening paragraph:
One of those invalid memes that I want to discuss… is the idea that the point of the black hole is the singularity. That is what makes a black hole a black hole and that’s also where the mysteries of black holes hide.
Ohhh Kaaay. I’m interested. Motl then talks about the density of air, water, iron, and neutron stars, and says this:
In this sequence of material densities, the “black hole” is incorrectly understood to be the final step, bringing you to ρ = ∞, the infinite density. All the matter is concentrated to the point, the layman thinks, and the point is the “singularity”.
Actually, that’s good to hear. I hate point singularities myself. Motl then says black holes have nothing to do with infinite density, and the density isn’t infinite anyway. Hey, this is great stuff. Motl is talking my language. Or is he? Because then he says this:
Instead, black holes aren’t “materials” at all. They are objects in which the whole Newtonian way of thinking about celestial bodies completely breaks down. If you continue to use it, you are bound to produce gibberish.
At this point my eyes narrow, because I’m a big fan of Newton, and because Newton’s description of gravity in query 20 was pretty similar to Einstein’s. But no matter. Motl says when a neutron star merges with another, it collapses, and the resulting object develops a new surface, the event horizon. He also says it’s as finite and spherical as the neutron star’s surface used to be. I can’t argue with that. What’s not to like? And what’s next?
Is the event horizon very different from the surface of a neutron star? Yes, it is very different. The neutron star’s surface is dim; but the black hole’s event horizon is perfectly dark. It can’t radiate at all.
That’s good. Can’t radiate at all means no Hawking radiation. Great stuff! But hang on, then comes this:
Also, the neutron star’s surface is extremely hard, you don’t want to hit it with your skull. On the other hand, the event horizon of a black hole is super soft. In fact, nothing is there at all. You may penetrate it completely smoothly to enter the black hole interior. Unlike the neutron star, the black hole (interior) may be a basically empty volume.
The black hole may be a basically empty volume? Huh? So what’s causing the black hole’s gravity then? Methinks Motl is confusing himself here. Especially since he says this:
So which of the two surfaces, the neutron star’s surface or the black hole’s event horizon, is “more grave”, a bigger separator between two regions? That is a great question (sadly, it is mine). The funny answer is that it depends on the “timescale” in which we observe the effect of the surface.
No, it isn’t a great question, and it doesn’t depend on the timescale. But let’s cut the guy some slack, English isn’t his first language. Moving swiftly on:
In the short term, the neutron star’s surface is a big thing while the event horizon is non-existent. Your head hurts from the former but gets through the latter. In the long run, however, your head may recover from the neutron star collision. But it can’t recover from falling beneath the event horizon.
What? How can you fall beneath the event horizon when a) a gravitational field is a place where there’s a vertical gradient in the speed of light and b) the event horizon is a place where the speed of light is zero? Hasn’t Motl read what Einstein said? You know, stuff like this from 1920: “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. And stuff like this from 1939: “a clock kept at this place would go at the rate zero”. That is, of course, a light clock. So it sounds as if Motl has forgotten about the infinite gravitational time dilation which is really a c=0. What else is he saying?
The event horizon is what actually defines a black hole. It is the surface of no return.
OK, I don’t have a problem with that. But note that Einstein said the event horizon was the singularity. He said “In this sense the sphere r = μ/2 constitutes a place where the field is singular”. However modern physicists tend to dismiss that as a mere “coordinate artifact”, which has to be incorrect because you cannot turn a c=0 into a c≠0 location. People do try to do this, but they’re making a schoolboy error by saying a stopped observer sees a stopped clock ticking normally “in his reference frame”. That’s wrong. The stopped observer doesn’t see a stopped clock ticking normally. He sees nothing, ever. Saying he sees nothing unusual is like a dead parrot sketch, where the shopkeeper insists that a dead customer sees the dead parrot squawking on its perch. Next:
Once you fall beneath that surface, i.e. into the black hole interior, there is no way back. The way back is prohibited by the most universal laws of physics. In particular, it is banned by the condition that material objects never move faster than light because locally, the escape from a black hole is the same thing as a superluminal notion!
I don’t have much of a problem with that either. It’s a pity Motl didn’t spend a little time talking about how gravity works. Or explain that the vertical light beam doesn’t escape from the black hole’s event horizon because that’s a place where the speed of light is zero. But never mind. Like I said, let’s cut the guy some slack because English isn’t his first language.
At some level, it is extraordinarily surprising and disappointing that almost no one gets this basic point. This point is by no means being hidden from the public.
I get it, Luboš. But do you? Let’s see.
A black hole is defined as a region (the black hole interior) from which nothing can escape. Whether there is also a “singularity” somewhere in the region is irrelevant for the black hole’s being a black hole.
That doesn’t square with what Einstein said about “a place where the field is singular”. What else don’t you get?
OK, the event horizon is a characteristic concept that requires general relativity. How should you imagine it? In the Newtonian picture (and in the Schwarzschild-like coordinates), you are probably imagining the event horizon as the spherical surface R=a that is stationary in time, just like the surface of a neutron star. But that is a totally wrong way to think about the event horizon if you want to describe the experiments that are done in the vicinity of that surface.
Oh here we go. Here’s come the physics lesson that’s total garbage. He’s going to tell us about a surface that isn’t stationary in time, forgetting about that infinite gravitational time dilation that’s really a c=0.
To study the local phenomena easily, you should better use very different spacetime coordinates for that vicinity of a point at the event horizon. And indeed, it’s one of the repeating wisdoms of general relativity: you should choose many different coordinates and switch between them all the time.
No, it isn’t wisdom. It’s a schoolboy error and a dead parrot sketch, and it contradicts what Einstein said about “a clock kept at this place would go at the rate zero”. You can’t make a stopped clock tick by switching to “tortoise” seconds that last forever.
That’s not something that you do in Newtonian physics where the Cartesian coordinates are really pretty much great at all times, you know. But this viewpoint assuming “one natural set of coordinates for all situations” is as wrong in general relativity as you can get.
No Lub, it isn’t wrong, because when c=0 light doesn’t move, and nor do you. Nor do your rods and clocks. So there is no coordinate system. This is the crucial point about the event horizon. It’s the end of events, and the end of your coordinate system:
Image from Ethan Siegel’s blog starts with a bang
The vertical light beam cannot escape because it’s at a place where the speed of light is zero, and you can’t change that by changing your coordinate system. Does Motl know this? Actually, I think one of his brain cells does, because he then quickly changes tack, and goes off on one talking about a large black hole where the spacetime curvature is zero:
So when the black hole is large and has characteristic dimensions a, e.g. if the event horizon is a sphere of area 4πa², then the Riemann curvature tensor has components |Rαβγδ|∼C/a².The curvature is inversely proportional to the squared distance scale (squared black hole radius, as measured from the area of the sphere). This scaling follows from the dimensional analysis; the Riemann tensor (which involves second derivatives of the dimensionless metric tensor) has the same units as 1/a² and there is no other dimensionful parameter you could insert here (the “density of the singularity”, even if it could be made meaningful, is infinite so the manifestly finite curvature cannot depend on it!). You may see that if the black hole radius is astrophysical in dimensions, the curvature goes to zero.
That’s totally irrelevant, because spacetime curvature relates to the tidal force, not the force of gravity. More smoke-and-mirrors irrelevance follows:
Because the curvature goes to zero, it becomes increasingly accurate to choose a local Lorentz frame, to describe the spacetime in a vicinity of the event horizon’s point as a region in the Minkowski space.
LOL! Minkowski space does not exist. We live in a world of space and motion. Spacetime models space at all times, and thus there is no motion in spacetime. The map is not the territory. But Motl is treating it like it is, whilst missing the bleeding obvious. He was getting warm when he said locally, the escape from a black hole is the same thing as a superluminal motion. But then he missed the trick with the infinite gravitational time dilation and the zero coordinate speed of light. Which is really the speed of light. Having missed the trick, he attempts to pull a rabbit out of the hat:
It simply has to be the case. So fine, there is some almost flat spacetime with the usual coordinates t,x,y,z over there. What does the event horizon look like? The Newtonian thinking would lead you to think that at the North Pole of the event horizon, the event horizon would look like a z=const surface in the spacetime that is just stationary in time t. But that’s completely wrong.
No, Lub, it doesn’t look like anything because it’s a place where the speed of light is zero. Duh! And because spacetime is an abstract thing that doesn’t actually exist. Duh! And because in chapter 20 of Relativity: The Special and General Theory Einstein said it’s “impossible to choose a body of reference such that, as judged from it, the gravitational field of the Earth (in its entirety) vanishes”. You cannot “transform away” a gravitational field. So it simply doesn’t have to be the case, now does it? Duh!
Instead, the black hole event horizon is (in the local Lorentz coordinates) something like z=ct. Cool. The spatial coordinate is proportional to time, the speed of light (in the vacuum) is the constant of proportionality. Locally, it looks like a surface in the Minkowski space that is moving by the speed of light…
Er no, The speed of light is zero, remember? That’s why the vertical light beam doesn’t get out. Your constant of proportionality went out of the window when Einstein said: “a clock kept at this place would go at the rate zero”. Motl’s article is going seriously downhill now. See how he clutches at straws:
Maybe it’s more pedagogic to describe the black hole event horizon as R=ct. The surface of the black hole seems to grow by the speed of light in the local Lorentz coordinates.
Pedagogic? You wouldn’t know about pedagogic if it jumped up and bit you on the arse. The surface of the black hole doesn’t grow at the speed of light. Here’s pedagogic for you: the speed of light in the local Lorentz coordinates is supposed to be 299,792,458 m/s. Only that’s because those coordinates are defined such that the local motion of light defines your second and your metre, which you then use to measure the local motion of light. It’s a tautology. Only when the local motion of light is zero, it no longer applies. See what Sabine Hossenfelder was saying a couple of weeks back about singular limits.
That’s why you can’t return outside once you are inside. To try to escape is equivalent to chasing a surface that is running away by the speed of light.
Bollocks. That surface isn’t moving at all, and nor are you. Nor is your vertical light beam. Have you never read Oppenheimer and Snyder’s 1929 “frozen star” paper on continued gravitational contraction. Or the 1971 Physics Today article introducing the black hole by Remo Ruffini and John Wheeler? Who said “in this sense the system is a frozen star”.
You have no chance to win. The amazing ability of the spacetime curvature (a basic ingredient or consequence of general relativity) is that this sphere that looks like it is running away by the speed of light (which is highly time-dependent) looks time-independent in other, Schwarzschild (or similar) coordinates.
Now your’e really winging it, Motl. It’s nothing to do with spacetime curvature. Like I said, spacetime curvature relates to the tidal force, not the “force” of gravity.
Yes, the proper area of the event horizon (I mean its 2D section at one moment in this sentence) is constant in time. But the event horizon is still like something that “moves at the speed of light” in all locally pleasant coordinate systems.
Lub, you are lost in maths. Have you never read the Einstein digital papers? Don’t you know that the speed of light is not constant. Don’t you know how gravity works? No, and yet here you are sneering at laymen saying they don’t understand gravity, when you don’t understand it yourself. Buddy, this is horseshit:
The black hole may be imagined as a stationary object similar to stars if you are an observer who is outside the black hole and far enough from the black hole. But for the infalling observer, it is the interior bounded by a surface that runs at the speed of light (and there are no coordinates that allow you to describe the black hole interior as stationary in time; instead, R and t get interchanged so the black hole interior is translationally invariant in a spatial direction). These two pictures may look extremely incompatible within the Euclid-Newton framework but they are totally compatible with one another within the Riemann-Einstein curved framework. To understand why these two perspectives are not only compatible but “derivable from each other” within GR is one of the first tasks you need to solve once you really start to learn GR (and black holes) seriously.
You haven’t got a clue, Motl. Especially since you then pontificate saying “it is completely silly and pretentious to discuss deep problems of quantum gravity… before you understand basic classical general relativity”. Especially since you parrot on about “the information loss puzzle” and AdS/CFT and stringy descriptions, whilst repeating the old canard that “the singularity at the event horizon is just a coordinate singularity”. Then you claim that “there is a quasi-continuous (gradual yet quantized) transition between the light elementary particle species and macroscopic black holes”. Really? And for the cherry on top, you say this:
The main message is “Please don’t send me would-be deep e-mails about black holes if you still believe that the singularity is what is important in a black hole.” Everyone who believes in this misconception is a 100% layman who hasn’t started to understand general relativity (let alone quantum gravity) at all. And that’s the memo.
FFS, you charlatan. You don’t have a f*cking clue. You don’t understand general relativity at all, because you’ve never read Einstein saying the speed of light is not constant, and instead varies with gravitational potential. Einstein said it 1913, in 1914, in 1915, in 1916, and never stopped saying it. Irwin Shapiro said it in 1964, and guys like Don Koks the PhysicsFAQ editor keep saying it: “light travels faster near the ceiling than near the floor”. And yet you have the arrogance to say most laymen completely misunderstand what a black hole is. And the hubris to come out with fairy tales about event horizons moving at the speed of light. Jesus H Christ. To think that we’ve been paying people like you to peddle such nonsense. It fair takes the breath away.