I just noticed that last semester Edward Witten was teaching Physics 539 at Princeton, a graduate topics course. Since he’s now past the age of 70, at the IAS he is officially retired and an emeritus professor (the IAS is the only place I know of in the US with retirement at 70, presumably since it is a non-teaching institution). I don’t know if there are other times Witten has been teaching courses at the university since his move to the IAS in 1987.
Videos of the first few lectures are on Youtube here, problem sets on this web-page. It seems like the course started out covering issues with causality in general relativity, following these lecture notes, then later moved on to topics in quantum information theory.
Are you sure they still have mandatory retirement and it’s not just a tradition? I can’t see why IAS would have any kind of special exception. I guess it’s also possible that just no one has bothered to sue?
Noah,
Legally, there is an exception for high-level executives, who can be required to retire at age 65. I had heard that the IAS argues that the positions of its faculty are more akin to high-level executives than to university faculty, since they don’t teach. I’d also heard that people are well aware this might not stand up in court if challenged, but that so far no one has been interested in challenging it.
In any case, given the nature of the IAS positions, and that there’s not much practical ifference between an emeritus and non-emeritus position there, it would be hard to make an argument on fairness grounds that the IAS should keep paying people very high salaries indefinitely.
Ha, a bit surprised (in a good way) that he’s teaching those particular topics, and to particle physicists, I presume.
In my years reading papers, I think it has become the custom for some people with a background in (Minkowski, perturbative, path integral) QFT to simply launch into a research career in topics like QFT in curved spacetimes, the information paradox, and quantum gravity, without even knowing basic elements from causality theory in GR, like global hyperbolicity and Cauchy hypersuperfaces. These two things are key to give the correct physical interpretation in QFT in curved spacetimes to things like transitions from pure to mixed states. In normal, inertial frame Minkowski QFT, where all relevant time slices are Cauchy, that would certainly be a red flag, but in QFT in curved spacetimes, you can be evaluating the second state in a non-Cauchy time slice, and its nonpure character is a consequence of that. In fact, that’s exactly what happens in the typical Schwarzschild evaporation scenario. As Wald has been stressing for decades, the problem is not the pure to nonpure transition, since that’s explained by the second hypersurface not being Cauchy, but by the resulting “evaporating spacetime” not being/not appearing to be globally hyperbolic, in violation to Penrose’s second cosmic censorship hypothesis.
Alex
There’s an ( important) implicit assumption, though, that black holes have to evaporate completely, so that after the ‘final moment’ of the evaporation, for external asymptotic observers the trapping horizon disappears and nothing remains but empty flat spacetime.
In that case, there’s a Cauchy horizon and spacetime is indeed non globally hyperbolic, as you said.
That seems problematic , not only due to the violation of the weak cosmic censorship; there’s also the issue with the huge ( of order M^5 during the final stages of the evaporation, where M is the initial mass of the hole ) internal ” maximal volume” of the black hole, that ( in the case of full evaporation) is disconnected ( and disappears? who knows?) in a way that seems unphysical when the throat shrinks as the horizon area goes to zero.
Another possibility is that some kind of a slowly decaying remnant is left behind, that disappears gradually ( with soft gravitons/ photons, perhaps…).
In such cases spacetime may be globally hyperbolic after all:
No violation of CC, no information loss. This is an open possibility.
so is Piet Hut emeritus now?
clayton,
He turned 70 last fall, I’m guessing under their usual policy he’d retire after this academic year. But, given his history there, if anyone were to challenge their policy, it might be him.