Why are we so concerned about quantum mechanics,

as it relates to black holes?

Well, the existence of Hawking radiation

presents an interesting problem to black hole physicists.

Classical black holes can be characterized by three numbers;

their mass, angular momentum, and charge.

This is a concept called the no-hair theorem which is a way of saying that information,

which is what we mean by hair in this instance,

can't escape from a black hole.

But quantum mechanics tells a completely different story,

which has led to one of the biggest unsolved problems of our time,

the black hole information paradox.

In addition to quantum mechanics enabling processes like Hawking radiation,

it also throws a bit of a wrench into theories that

try to combine quantum mechanics with general relativity.

In particular, quantum mechanics requires information to be preserved.

So in order for astrophysicists to have a complete description of a black hole,

they will have to find a way to explain the so-called black hole information paradox.

Information can be defined as something which is an answer to a question.

When physicists talk about information,

they're generally asking questions about the characteristics and state of something.

So when we ask about the mass of a star,

or we measure what its spectral output is, we're generating information.

Now imagine that you're the commander of a scientific research vessel,

that's in orbit around a black hole,

collecting measurements about the properties of the black hole.

You can very easily deduce the mass of the black hole by observing,

measuring, and timing how long it takes to orbit the black hole at a given distance.

You can also measure the spin of the black hole by comparing the size of

the innermost stable circular orbit to the size of the event horizon.

And by dropping a couple of test charges and observing their behaviour,

you can tell the charge of the black hole.

Scientists think that most black holes have zero charge anyway.

So as the commander,

you've collected all this data,

but oh no you've accidentally crossed the event horizon.

Luckily, you and your crew have survived but the future is bleak.

Given the fuel that you have in your reserve,

you can only postpone your collision with the singularity by a few hours,

maybe a few days at most.

Is there any way that you could send what you learned back to

a distant observer or does the event horizon prevent information from escaping?

Classical physics, that is to say general relativity,

has very bad news for you.

There's no way for you to transmit your data across the event horizon.

But being a good spaceship captain,

you are brushed up on your quantum mechanics and you know about two important principles;

quantum determinism and the principle of reversibility.

Let's start by unpacking the easy one, reversibility.

Reversibility is the idea that physical laws can be used to

predict the future or the past of a particular system.

If we look at a comet shooting by,

not only can we predict where it will be decades from now,

but also where it was decades in the past.

In some sense, reversibility also tells us that we can go

backwards from one state just as well as we can go forwards.

In reality, we know that reversibility is more complex than that.

Shattered mugs don't suddenly unshatter themselves.

But we'll address that when we discuss entropy.

On the other hand,

quantum determinism is a much stranger idea.

Determinism, on its own,

is the idea that we can predict the outcome of

any interaction if we have sufficient information.

If I throw a ball and you know its direction and how fast it's going,

where it lands is predetermined.

But quantum mechanics basically deconstructs the notion of

classical determinism because of a concept called the Heisenberg Uncertainty Principle.

Since we have limits on what we can measure,

we also have limits on what we can predict.

Quantum determinism is then telling us a slightly different version of the story.

We can predict with certainty what

the probabilities of outcomes will be in quantum mechanics.

Since the principles of quantum determinism and

reversibility are fundamental to quantum mechanics,

we've run into a problem.

These two principles together mean that information must always be preserved.

But the no-hair theorem for black holes,

says that information falling into

a black hole disappears when it crosses the event horizon.

Many scientists postulate that the information is

destroyed somewhere at the interior of the black hole.

In the next lesson, we'll delve further into this investigation,

examining specific theories which attempt to explain the black hole information paradox.