Preposterous Universe

Friday, July 16, 2004
Hawking on black holes

The cat is out of the bag about Stephen Hawking's new ideas about black holes. Preposterous regulars were in on the ground floor, of course. We can now speculate somewhat more intelligently about what the ideas actually are, since the abstract for his talk (next week at the GR17 conference in Dublin) is online:
The Euclidean path integral over all topologically trivial metrics can be done by time slicing and so is unitary when analytically continued to the Lorentzian. On the other hand, the path integral over all topologically non-trivial metrics is asymptotically independent of the initial state. Thus the total path integral is unitary and information is not lost in the formation and evaporation of black holes. The way the information gets out seems to be that a true event horizon never forms, just an apparent horizon.
(For more scoop see Not Even Wrong, Smijer, By the Way, and this thread on sci.physics.research.)

It seems as if our initial skepticism might be accurate: even if Hawking's proposal is ultimately judged to be a fantastic breakthrough, it won't catch on right away. The Euclidean path integral approach to quantum gravity, which Hawking has been instrumental in developing, is not generally thought to be the most promising approach. One never knows, and it might eventually turn out to be on the right track, but it's not very popular in the quantum-gravity community.

Let's try to explain what is going on. Quantum mechanics tells us that the world is described by wave functions, which give the probability for getting a certain result when we make an observation. A path integral is just a certain way of calculating the wave function. Invented by Richard Feynman, the path-integral approach says that we should attach a certain contribution to every possible path the system can take from one configuration to another, and then sum all of these contributions; the result is the wavefunction for being in the final state, given the initial state we started with. Often this sum (the path integral) is hard to do, and a convenient mathematical trick is to allow the time coordinate to be imaginary; this purely formal manouver turns four-dimensional spacetime into a four-dimensional space (no direction is singled out as "timelike"), and the integral turns out to be much easier to do. In gravity, we would like to sum over all the possible geometries of spacetime itself. So "Euclidean quantum gravity" tells us to calculate the wave function for the geometry of three-dimensional space at some fixed time by summing over all the possible four-dimensional geometries that connect to that spatial geometry.

The problems with this approach include: nobody knows what number to attach to each geometry in the sum, nobody knows how to do the integral, and nobody knows how to interpret the result. Significant problems, in other words. Optimists like Hawking think that they can describe a certain set of approximations in which the path integral makes sense; string theorists, on the other hand, would generally say that the path integral is nonsense if you don't include the fundamentally "stringy" aspects of spacetime on ultra-small scales. In the absence of direct experimental data, we have to judge how well the ideas hang together in their own right; at the moment, Euclidean quantum gravity seems to have serious issues, and hasn't scored many notable triumphs.

Hawking now seems to be saying that the path integral for black holes can help us understand how information that we thought had disappeared into the singularity can actually be lurking close to the horizon, so that it can eventually influence the outgoing Hawking radiation, and thus allow information to be recovered by the evaporating black hole. He'll be met with serious skepticism in the physics community, but let's wait to see how it washes out.

Of course, he'll also be met with serious awe by the media. This can drive other physicists crazy. I often find myself explaining to non-physicists that Hawking is not the very best theoretical physicist out there, but simultaneously defending his reputation to my fellow physicists. It's probably safe to say that Hawking was the leading researcher in theoretical gravitational physics in the second half of the twentieth century, and arguably since Einstein; but gravitational physics was not where the action was during that time (it was in particle physics and quantum field theory). A lot of physicists hurry to point out that Hawking is not doing the most influential work in quantum gravity these days; but the truth is that most sixty-year-old physicists aren't doing the most influential work in their fields, even if they don't have serious neurological disorders. Like anyone else who has made fantastic contributions, Hawking has earned respect for new ideas he might have, but the ideas themselves will be judged on their own merits.

Ideas on culture, science, politics.
Sean Carroll

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