Now grab a thermodynamics textbook, locate the laws, and see if you can find true statements when you replace the thermodynamic terms with black hole variables. In many cases you can, and the analogy improves.
Hawking then discovers Hawking radiation, which further improves the analogy. At that point, most physicists start claiming the analogy is so good that it’s more than an analogy—it’s an identity! That’s a super-strong and surprising claim. It says that black hole laws, most of which are features of the geometry of space-time, are somehow identical to the physical principles underlying the physics of steam engines.
Because the identity plays a huge role in quantum gravity, I want to reconsider this identity claim. Few in the foundations of physics have done so.
So what’s the statistical mechanics for black holes?
Well, that’s a good question. Why does ordinary thermodynamics hold? Well, we know that all these macroscopic thermodynamic systems are composed of particles. The laws of thermodynamics turn out to be descriptions of the most statistically likely configurations to happen from the microscopic point of view.
Why does black hole thermodynamics hold? Are the laws also the statistically most likely way for black holes to behave? Although there are speculations in this direction, so far we don’t have a solid microscopic understanding of black hole physics. Absent this, the identity claim seems even more surprising.
What led you to start thinking about the analogy?
Many people are worried about whether theoretical physics has become too speculative. There’s a lot of commentary about whether holography, the string landscape—all sorts of things—are tethered enough to experiment. I have similar concerns. So my former Ph.D. student John Dougherty and I thought, where did it all start?
To our mind a lot of it starts with this claimed identity between black holes and thermodynamics. When you look in the literature, you see people say, “The only evidence we have for quantum gravity, the only solid hint, is black hole thermodynamics.”
If that’s the main thing we’re bouncing off for quantum gravity, then we ought to examine it very carefully. If it turns out to be a poor clue, maybe it would be better to spread our bets a little wider, instead of going all in on this identity.
What problems do you see with treating a black hole as a thermodynamic system?
I see basically three. The first problem is: What is a black hole? People often think of black holes as just kind of a dark sphere, like in a Hollywood movie or something; they’re thinking of it like a star that collapsed. But a mathematical black hole, the basis of black hole thermodynamics, is not the material from the star that’s collapsed. That’s all gone into the singularity. The black hole is what’s left.
The black hole isn’t a solid thing at the center. The system is really the entire space-time.
Yes, it’s this global notion for which black hole thermodynamics was developed, in which case the system really is the whole space-time.
Here is another way to think about the worry. Suppose a star collapses and forms an event horizon. But now another star falls past this event horizon and it collapses, so it’s inside the first. You can’t think that each one has its own little horizon that is behaving thermodynamically. It’s only the one horizon.
Here’s another. The event horizon changes shape depending on what’s about to be thrown into it. It’s clairvoyant. Weird, but there is nothing spooky here so long as we remember that the event horizon is only defined globally. It’s not a locally observable quantity.