In the early 1970s, people studying general relativity, our modern theory of gravity, noticed rough similarities between the properties of black holes and the laws of thermodynamics. Stephen Hawking proved that the area of a black hole’s event horizon—the surface that marks its boundary—cannot decrease. That sounded suspiciously like the second law of thermodynamics, which says entropy—a measure of disorder—cannot decrease.
Yet at the time, Hawking and others emphasized that the laws of black holes only looked like thermodynamics on paper; they did not actually relate to thermodynamic concepts like temperature or entropy.
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Then in quick succession, a pair of brilliant results—one by Hawking himself—suggested that the equations governing black holes were in fact actual expressions of the thermodynamic laws applied to black holes. In 1972, Jacob Bekenstein argued that a black hole’s surface area was proportional to its entropy, and thus the second law similarity was a true identity. And in 1974, Hawking found that black holes appear to emit radiation—what we now call Hawking radiation—and this radiation would have exactly the same “temperature” in the thermodynamic analogy.
This connection gave physicists a tantalizing window into what many consider the biggest problem in theoretical physics—how to combine quantum mechanics, our theory of the very small, with general relativity. After all, thermodynamics comes from statistical mechanics, which describes the behavior of all the unseen atoms in a system. If a black hole is obeying thermodynamic laws, we can presume that a statistical description of all its fundamental, indivisible parts can be made. But in the case of a black hole, those parts aren’t atoms. They must be a kind of basic unit of gravity that makes up the fabric of space and time.
Modern researchers insist that any candidate for a theory of quantum gravity must explain how the laws of black hole thermodynamics arise from microscopic gravity, and in particular, why the entropy-to-area connection happens. And few question the truth of the connection between black hole thermodynamics and ordinary thermodynamics.
But what if the connection between the two really is little more than a rough analogy, with little physical reality? What would that mean for the past decades of work in string theory, loop quantum gravity, and beyond? Craig Callender, a philosopher of science at the University of California, San Diego, argues that the notorious laws of black hole thermodynamics may be nothing more than a useful analogy stretched too far. The interview has been condensed and edited for clarity.
Why did people ever think to connect black holes and thermodynamics?
Callender: In the early ’70s, people noticed a few similarities between the two. One is that both seem to possess an equilibrium-like state. I have a box of gas. It can be described by a small handful of parameters—say, pressure, volume, and temperature. Same thing with a black hole. It might be described with just its mass, angular momentum, and charge. Further details don’t matter to either system.
Nor does this state tell me what happened beforehand. I walk into a room and see a box of gas with stable values of pressure, volume and temperature. Did it just settle into that state, or did that happen last week, or perhaps a million years ago? Can’t tell. The black hole is similar. You can’t tell what type of matter fell in or when it collapsed.
The second feature is that Hawking proved that the area of black holes is always non-decreasing. That reminds one of the thermodynamic second law, that entropy always increases. So both systems seem to be heading toward simply described states.