The buzz is that Hawking has a new idea about how to resolve the “Black Hole Information Paradox”, the well known incompatibility between standard ideas about black holes and the unitary time evolution of the wave function that is fundamental to quantum mechanics. Evidently Hawking has asked to give a talk about this at GR17, a big conference on general relativity that will be held July 18-23 in Dublin.

The abstract for his talk goes like this:

“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.”

I can’t tell exactly what that means either, so I guess we’ll have to wait for the talk. My own prejudice about quantum field theory is that the relation between the Euclidean and Minkowski space formulations of quantum field theory is actually much more interesting and subtle than people think. It’s not just a technical trick. So I’ll be interested to see what Hawking has to say about this.

Something else at the conference that may be interesting will be Sir Roger Penrose’s public talk entitled “Fashion, Faith and Fantasy in Modern Physical Theories”. Guess what he is referring to by “Fashion”.

Another subtlety about Minkowskian signatures is the embedding theorem. Not usually mentioned, but worth to have it at the back of some neuron.

Wick rotation in QFT on a fixed background is certainly deep. But for quantum gravity it is for the obvious reason very problematic, as has been discussed at great length on s.p.r. for instance.

Hawking has worked a lot on Euclidean path integrals for cosmology in the past, and he even goes as far as introducing his ‘Universe in a nutshell’ book with saying that our universe is essentially a Euclidean 4-sphere in a sense. (I think he should have mentioned that this is more of a personal view, a hunch, which is not necessarily shared by the community or even demonstrated by results, I’d think.) Maybe it is just due to my ignorance of the literature, but I am having trouble coming up with past results or even hints that the Euclidean path integral for gravity is the thing to look at. Now, maybe Hawking’s new idea about black hole information is just that hint which I am looking for, I don’t know. But currently I am a little sceptical.

I saw Sir Roger when he gave the same talk(s) at Princeton on Oct. 17, 20, and 22. On that occasion, Fashion, Faith, and Fantasy were each the subject of one night’s talk.

I thoroughly enjoyed what he had to say, but Princeton is a hub for string theory, and I got the distinct feeling that my position was in the minority.

You can watch them at the following address:

http://www.princeton.edu/WebMedia/lectures/

Peter,

Could you give some information about it?

To me the signature seems physical, and I don’t see how it is possible to alter it.

Complex structures that arise naturally out of geometry are another matter. (Think for example of the circular points at infinity in plane projective geometry.)

The french girls did a good work to introduce the subtleties of path measuring, at the end of their geometry manual.

Quote : “My own prejudice about quantum field theory is that the relation between the Euclidean and Minkowski space formulations of quantum field theory is actually much more interesting and subtle than people think.”

Well, it is exactly what we think. And by the way, certain questions raised by S.H. are developed in our “Topological field Theory of the Initial Singulariry of Space time” paper (CQG) that was extensively discussed but not really understood as a new formulation regarding the transition between lorentzian metric (real time, still valid et Planck scale) to euclidean metric imaginary time, only valid at 0 scale). In our model, this transition becomes effective between Planck scale and 0 scale and is characterized by quantum fluctuations of lorentzian and euclidean metrics (superposition (KMS) state of metrics). In this model, the “apparent horizon” evoked by Hawking could be the result of an “euclidean evolution” of events in the black hole whose final singularity does not exist in real (lorentzian time) but in imaginary (euclidean) time.

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