In the early 1970s, Stephen Hawking discovered that black holes can emit radiation.
This radiation allows black holes to lose mass and, eventually, to entirely evaporate.
This process seems to destroy all the information that is contained in the black hole and therefore
contradicts what we know about the laws of nature.
This contradiction is what we call the black hole information paradox.
After discovering this problem 40 years ago, Hawking spent the rest of his life trying
to solve it.
He passed away last year, but the problem is still alive and there is no resolution
Today, I want to tell you what solutions physicists have so-far proposed
for the black hole information loss problem.
If you want to know more about just what exactly the problem is, please watch my earlier video.
There are hundreds of proposed solutions to the information loss problem, that I cannot
possibly all list here.
But I want to tell you about the five most plausible ones.
The calculation that Hawking did to obtain the properties of the black hole radiation
makes use of general relativity.
But we know that general relativity is only approximately correct.
It eventually has to be replaced by a more fundamental theory, which is quantum gravity.
The effects of quantum gravity are not relevant near the horizon of large black holes, which
is why the approximation that Hawking made is good.
But it breaks down eventually, when the black hole has shrunk to a very small size.
Then, the space-time curvature at the horizon becomes very strong and quantum gravity must
be taken into account.
Now, if quantum gravity becomes important, we really do not know what will happen because
we don’t have a theory for quantum gravity.
In particular we have no reason to think that the black hole will entirely evaporate to
This opens the possibility that a small remainder is left behind which just sits there forever.
Such a black hole remnant could keep all the information about what formed the black hole,
and no contradiction results.
Information comes out very late.
Instead of just stopping to evaporate when quantum gravity becomes relevant, the black
hole could also start to leak information in that final phase.
Some estimates indicate that this leakage would take a very long time, which is why
this solution is also known as a “quasi-stable remnant”.
However, it is not entirely clear just how long it would take.
After all, we don’t have a theory of quantum gravity.
This second option removes the contradiction for the same reason as the first.
Information comes out early
The first two scenarios are very conservative in that they postulate new effects will appear
only when we know that our theories break down.
A more speculative idea is that quantum gravity plays a much larger role near the horizon
and the radiation carries information all along, it’s just that Hawking’s calculation
doesn’t capture it.
Many physicists prefer this solution over the first two for the following reason.
Black holes do not only have a temperature, they also have an entropy,
called the Bekenstein-Hawking entropy.
This entropy is proportional to the area of the black hole.
It is often interpreted as counting the number of possible states that the black hole geometry
can have in a theory of quantum gravity.
If that is so, then the entropy must shrink when the black hole shrinks and this is not
the case for the remnant and the quasi-stable remnant.
So, if you want to interpret the black hole entropy in terms of microscopic states, then
the information must begin to come out early, when the black hole is still large.
This solution is supported by the idea that we live in a holographic universe, which is
currently popular, especially among string theorists.
Information is just lost.
Black hole evaporation, it seems, is irreversible and that irreversibility is inconsistent with
the dynamical law of quantum theory.
But quantum theory does have its own irreversible process, which is the measurement.
So, some physicists argue that we should just accept black hole evaporation is irreversible
and destroys information, not unlike quantum measurements do.
This option is not particularly popular because it is hard to include additional irreversible
process into quantum theory without spoiling conservation laws.
Black holes don’t exist.
Finally, some physicists have tried to argue that black holes are never created in the
first place in which case no information can get lost in them.
To make this work, one has to find a way to prevent a distribution of matter from collapsing
to a size that is below its Schwarzschild radius.
But since the formation of a black hole horizon can happen at arbitrarily small matter densities,
this requires that one invents some new physics which violates the equivalence principle,
and that is the key principle underlying Einstein’s theory of general relativity.
This option is a logical possibility, but for most physicists, it’s asking for too much.
Personally, I think that several of the proposed solutions are consistent, that includes option
1-3 which I just talked about, and other proposals such as those by Horowitz and Maldacena or Maudlin.
This means that this is a problem which just cannot be solved by relying on mathematics alone.
Unfortunately, we cannot experimentally test what is happening when black holes evaporate
because the temperature of the radiation is much, much too small to be measurable for
the astrophysical black holes we know of.
And so, I suspect we will be arguing about this for a long, long time.