The Black Hole information loss problem is unsolved. Because it’s unsolvable.
Sabine NHossenfelder
[[An extremely clear explanation and very sharp critique of a subject that has been addressed by people who ought to b e experts….]]
Hi everybody, welcome and welcome back to science without the gobbledygook. I put in a Wednesday video because last week I came across a particularly bombastically nonsensical claim that I want to debunk for you. The claim is that the black hole information loss problem is “nearing its end”. So today I am here to explain why the black hole information loss problem is not only unsolved but will remain unsolved because it’s for all practical purposes unsolvable.
First of all, what is the black hole information loss problem, or paradox, as it’s sometimes called. It’s an inconsistency in physicists’ currently most fundamental laws of nature, that’s quantum theory and general relativity.
Stephen Hawking showed in the early nineteen-seventies that if you combine these two theories, you find that black holes emit radiation. This radiation is thermal, which means besides the temperature, that determines the average energy of the particles, the radiation is entirely random.
This black hole radiation is now called Hawking Radiation and it carries away mass from the black hole. But the radius of the black hole is proportional to its mass, so if the black hole radiates, it shrinks. And the temperature is inversely proportional to the black hole mass. So, as the black hole shrinks, it gets hotter, and it shrinks even faster. Eventually, it’s completely gone. Physicists refer to this as “black hole evaporation.”
When the black hole has entirely evaporated, all that’s left is this thermal radiation, which only depends on the initial mass, angular momentum, and electric charge of the black hole. This means that besides these three quantities, it does not matter what you formed the black hole from, or what fell in later, the result is the same thermal radiation.
Black hole evaporation, therefore, is irreversible. You cannot tell from the final state – that’s the outcome of the evaporation – what the initial state was that formed the black holes. There are many different initial states that will give the same final state.
The problem is now that this cannot happen in quantum theory. Processes in quantum theory are always time-reversible. There are certainly processes that are in practice irreversible. For example, if you mix dough. You are not going to unmix it, ever. But. According to quantum mechanics, this process is reversible, in principle.
In principle, one initial state of your dough leads to exactly one final state, and using the laws of quantum mechanics you could reverse it, if only you tried hard enough, for ten to the five-hundred billion years or so. It’s the same if you burn paper, or if you die. All these processes are for all practical purposes irreversible. But according to quantum theory, they are not fundamentally irreversible, which means a particular initial state will give you one, and only one, final state. The final state, therefore, tells you what the initial state was, if you have the correct differential equation. For more about differential equations, please check my earlier video.
So you set out to combine quantum theory with gravity, but you get some something that contradicts what you started with. That’s inconsistent. Something is wrong about this. But what? That’s the black hole information loss problem.
Now, four points I want to emphasize here. First, the black hole information loss problem has actually nothing to do with information. John, are you listening? Really the issue is not loss of information, which is an extremely vague phrase, the issue is time irreversibility. General Relativity forces a process on you which cannot be reversed in time, and that is inconsistent with quantum theory.
So it would better be called the black hole time irreversibility problem, but you know how it goes with nomenclature, it doesn’t always make sense. Peanuts aren’t nuts, vacuum cleaners don’t clean the vacuum. Dark energy is neither dark nor energy. And black hole information loss is not about information.
Second, black hole evaporation is not an effect of quantum gravity. You do not need to quantize gravity to do Hawking’s calculation. It merely uses quantum mechanics in the curved background of non-quantized general relativity. Yes, it’s something with quantum and something with gravity. No, it’s not quantum gravity.
The third point is that the measurement process in quantum mechanics does not resolve the black hole information loss problem. Yes, according to the Copenhagen interpretation a quantum measurement is irreversible. But the inconsistency in black hole evaporation occurs before you make a measurement.
And related to this is the fourth point, it does not matter whether you believe time-irreversibility is wrong even leaving aside the measurement. It’s a mathematical inconsistency. Saying that you do not believe one or the other property of the existing theories does not explain how to get rid of the problem.
So, how do you get rid of the black hole information loss problem. Well, the problem comes from combining a certain set of assumptions, doing a calculation, and arriving at a contradiction. This means any solution of the problem will come down to removing or replacing at least one of the assumptions.
Mathematically there are many ways to do that. Even if you do not know anything about black holes or quantum mechanics, that much should be obvious. If you have a set of inconsistent axioms, there are many ways to fix that. It will therefore not come as a surprise to you that physicists have spent the past forty years coming up with always new “solutions” to the black hole information loss problem, yet they can’t agree which one is right.
I have already made a video about possible solutions to the black hole information loss problem, so let me just summarize this really quickly. For details, please check the earlier video.
The simplest solution to the black hole information loss problem is that the disagreement is resolved when the effects of quantum gravity become large, which happens when the black hole has shrunk to a very small size. This simple solution is incredibly unpopular among physicists. Why is that? It’s because we do not have a theory of quantum gravity, so one cannot write papers about it.
Another option is that the black holes do not entirely evaporate and the information is kept in what’s left, usually called a black hole remnant. Yet another way to solve the problem is to simply accept that information is lost and then modify quantum mechanics accordingly. You can also put information on the singularity, because then the evaporation becomes time-reversible.
Or you can modify the topology of space-time. Or you can claim that information is only lost in our universe but it’s preserved somewhere in the multiverse. Or you can claim that black holes are actually fuzzballs made of strings and information creeps out slowly. Or, you can do ‘t Hooft’s antipodal identification and claim what goes in one side comes out the other side, fourier transformed. Or you can invent non-local effects, or superluminal information exchange, or baby universes, and that’s not an exhaustive list.
These solutions are all mathematically consistent. We just don’t know which one of them is correct. And why is that? It’s because we cannot observe black hole evaporation. For the black holes that we know exist the temperature is way, way too small to be observable. It’s below even the temperature of the cosmic microwave background. And even if it wasn’t, we wouldn’t be able to catch all that comes out of a black hole, so we couldn’t conclude anything from it.
And without data, the question is not which solution to the problem is correct, but which one you like best. Of course everybody likes their own solution best, so physicists will not agree on a solution, not now, and not in 100 years. This is why the headline that the black hole information loss problem is “coming to an end” is ridiculous. Though, let me mention that I know the author of the piece, George Musser, and he’s a decent guy and, the way this often goes, he didn’t choose the title.
What’s the essay actually about? Well, it’s about yet another proposed solution to the black hole information problem. This one is claiming that if you do Hawking’s calculation thoroughly enough then the evaporation is actually reversible. Is this right? Well, depends on whether you believe the assumptions that they made for this calculation. Similar claims have been made several times before and of course they did not solve the problem.
The real problem here is that too many theoretical physicists don’t understand or do not want to understand that physics is not mathematics. Physics is science. A theory of nature needs to be consistent, yes, but consistency alone is not sufficient. You still need to go and test your theory against observations.
The black hole information loss problem is not a math problem. It’s not like trying to prove the Riemann hypothesis. You cannot solve the black hole information loss problem with math alone. You need data, there is no data, and there won’t be any data. Which is why the black hole information loss problem is for all practical purposes unsolvable.
The next time you read about a supposed solution to the black hole information loss problem, do not ask whether the math is right. Because it probably is, but that isn’t the point. Ask what reason do we have to think that this particular piece of math correctly describes nature. In my opinion, the black hole information loss problem is the most overhyped problem in all of science, and I say that as someone who has published several papers about it.
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