These modules are quite interesting.

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

It occurred to me the other day that I’ve never told you

what I did before I ended up in the basement in front of a green screen. So

today I want to tell you why I, as many other physicists, was fascinated by the

black hole paradox that Steven Hawking discovered before I was even born. And

why I, as many other physicists, tried to solve it. But why I, in the end,

unlike many other physicists, decided that it’s a waste of time. What’s the

black hole information paradox? Has it been solved and if not, will it ever be

solved? What if anything is new about those recent headlines? That’s what we’ll

talk about today.

First things first, what’s the black hole information loss

paradox. Imagine you have a book and you throw it into a black hole. The book

disappears behind the horizon, the black hole emits some gravitational waves

and then you have a black hole with a somewhat higher mass. And that’s it.

This is what Einstein’s theory of general relativity says. Yes, that guy again.

In Einstein’s theory of general relativity black holes are extremely simple.

They are completely described by only three properties: their mass, angular

moment, and electric charge. This is called the “no hair” theorem. Black holes

are bald and featureless and you can mathematically prove it.

But that doesn’t fit together with quantum mechanics. In quantum mechanics,

everything that happens is reversible so long as you don’t make a measurement.

This doesn’t mean processes look the same forward and backward in time, this

would be called time-reversal “invariance”. It merely means that if you start

with some initial state and wait for it to develop into a final state, then you

can tell from the final state what the initial state was. In this sense,

information cannot get lost. And this time-reversibility is a mathematical

property of quantum mechanics which is experimentally extremely well confirmed.

However, in practice, reversing a process is possible only in really small

systems. Processes in large systems become for all practical purposes

irreversible extremely quickly. If you burn your book, for example, then for

all practical purposes the information in it was destroyed. However, in

principle, if we could only measure the properties of the smoke and ashes well

enough, we could calculate what the letters in the book once were.

But when you throw the book into a black hole that’s different. You throw it

in, the black hole settles into its hairless state, and the only difference

between the initial and final state is the total mass. The process seems

irreversible. There just isn’t enough information in the hairless black hole to

tell what was in the book. The black hole doesn’t fit together with quantum

mechanics. And note that making a measurement isn’t necessary to arrive at this

conclusion.

You may remember that I said the black hole emits some gravitational waves. And

those indeed contain some information, but so long as general relativity is

correct, they don’t contain enough information to encode everything that’s in

the book.

Physicists knew about this puzzle since the 1960s or so, but initially they

didn’t take it seriously. At this time, they just said, well, it’s only when we

look at the black hole from the outside that we don’t know how reverse this

process. Maybe the missing information is inside. And we don’t really know

what’s inside a black hole because Einstein’s theory breaks down there. So

maybe not a problem after all.

But then along came Stephen Hawking. Hawking showed in

the early 1970s that actually black holes don’t just sit there forever.

They emit radiation, which is now called Hawking radiation. This radiation is

thermal which means it’s random except for its temperature, and the temperature

is inversely proportional to the mass of the black hole.

This means two things. First, there’s no new information

which comes out in the Hawking radiation. And second, as the black hole

radiates, its mass shrinks because E=mc^2 and energy is conserved, and that

means the black hole temperature increases as it evaporates. As a consequence,

the evaporation of a black hole speeds up. Eventually the black hole is gone.

All you have left is this thermal radiation which contains no information.

And now you have a real problem. Because you can no longer say that maybe the

information is inside the black hole. If a black hole forms, for example, in

the collapse of a star, then after it’s evaporated, all the information about

that initial star, and everything that fell into the black hole later, is

completely gone. And that’s inconsistent with quantum mechanics.

This is the black hole information loss paradox. You take quantum mechanics and

general relativity, combine them, and the result doesn’t fit together with

quantum mechanics.

There are many different ways physicists have tried to solve this problem and

every couple of months you see yet another headline claiming that it’s been

solved. Here is the most recent iteration of this cycle, which is about a

paper by Steve Hsu and Xavier Calmet. The authors claim that the

information does get out. Not in gravitational waves, but in gravitons that are

quanta of the gravitational field. Those are not included in Hawking’s original

calculation. These gravitons add variety to black holes, so now they have hair.

This hair can store information and release it with the radiation.

This is a possibility that I thought about at some point myself, as I am sure

many others in the field have too. I eventually came to the conclusion that it

doesn’t work. So I am somewhat skeptical that their proposal actually solves

the problem. But maybe I was wrong and they are right. Gerard ‘t Hooft by the

way also thinks the information comes out in gravitons, though in a different

way then Hsu and Calmet. So this is not an outlandish idea.

I went through different solutions to the black hole information paradox in an

earlier video and will not repeat them all here, but I want to instead give you

a general idea for what is happening. In brief, the issue is that there are

many possible solutions.

Schematically, the way that the black hole information loss paradox comes about

is that you take Einstein’s general relativity and combine it with quantum mechanics.

Each has its set of assumptions. If you combine them, you have to make some

further assumptions about how you do this. The black hole information paradox then

states that all those assumptions together are inconsistent. This means you can

take some of them, combine them and obtain a statement which contracts another

assumption. Simple example for what I

mean with “inconsistent”, the assumption x 1.

If you want to resolve an inconsistency in a set of assumptions, you can remove

some of the assumptions. If you remove sufficiently many, the inconsistency

will eventually vanish. But then the predictions of your theory become

ambiguous because you miss details on how to do calculations. So you have to

put in new assumptions to replace the ones that you have thrown out. And then

you show that this new set of assumptions is no longer inconsistent. This is

what physicists mean when they say they “solved the problem”.

But. There are many different ways to resolve an inconsistency because there

are many different assumptions you can throw out. And this means there are many

possible solutions to the problem which are mathematically correct. But only

one of them will be correct in the sense of describing what indeed happens in

nature. Physics isn’t math. Mathematics is a great tool, but in the end you

have to make an actual measurement to see what happens in reality.

And that’s the problem with the black hole information loss paradox. The

temperature of the black holes that we can observe today is way too small to

measure the Hawking radiation. Remember that the larger the black hole, the

smaller its temperature. The temperature of astrophysical black holes is below

the temperature of the CMB. And even if that wasn’t the case, what do you want

to do? Sit around 100 billion years to catch all the radiation and see if you

can figure out what fell into the black hole? It’s not going to happen.

What’s going to happen with this new solution? Most likely, someone’s going to

find a problem with it, and everyone will continue working on their own

solution. Indeed, there’s a good chance that by the time this video appears

this has already happened. For me, the real paradox is why they keep doing it.

I guess they do it because they have been told so often this is a big problem

that they believe if they solve it they’ll be considered geniuses. But of

course their colleagues will never agree that they solved the problem to begin

with. So by all chances, half a year from now you’ll see another headline

claiming that the problem has been solved.

And that’s why I stopped working on the black hole information loss paradox.

Not because it’s unsolvable. But because you can’t solve this problem with mathematics

alone, and experiments are not possible, not now and probably not in the next

10000 years.

Why am I telling you this? I am not talking about this because I want to change

the mind of my colleagues in physics. They have grown up thinking this is an

important research question and I don’t think they’ll change their mind. But I

want you to know that you can safely ignore headlines about black hole

information loss. You’re not missing anything if you don’t read those articles.

Because no one can tell which solution is correct in the sense that it actually

describes nature, and physicists will not agree on one anyway. Because if they

did, they’d have to stop writing papers about it.

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