Hearing a drum's shape as approach to quantum gravity (Kempf)

[marcus]

"Hearing a drum's shape" as approach to quantum gravity (Kempf)

Achim Kempf and his students have coded an ITERATIVE procedure for finding the shape that when struck has a given sound spectrum. He shows brief movie clips of the computer finding the correct shape by successive approximations, as part of his QG seminar talk.

Google "kempf pirsa" to get the video.

You get http://pirsa.org/13120064
the talk was given yesterday 12 December.

They have addressed the problems of doing this in 3 and 4 dimensions, but so far have had success mainly in 2D.

This is an excellent talk. Very clear and cogent. He makes a convincing case that "spectral geometry" namely being able to describe an arbitrary compact shape by its vibration spectrum can be a useful tool in quantum geometry. I suppose, since the vibration spectrum reflects a web of correlations or entanglements, this program could even influence how we think about space and spacetime. Here is the abstract of yesterday's talk:
Curvature in terms of entanglement
Speaker(s): Achim Kempf
Abstract: The entanglement of the quantum field theoretic vacuum state is affected by curvature. I ask if or under which conditions the curvature of spacetime can be expressed entirely in terms of the spatial entanglement structure of the vacuum. This would open up the prospect that general relativity could be formulated in quantum theoretic terms, which should then be helpful for studies in quantum gravity.
Date: 12/12/2013 - 2:30 pm

 

[Ben Niehoff]

I thought it was already well-established that the shape corresponding to a given spectrum is not unique? There is a famous pair of shapes, constructed from triangles, which are different, yet have the same spectrum.

 

[marcus]

I thought it was already well-established that the shape corresponding to a given spectrum is not unique? There is a famous pair of shapes, constructed from triangles, which are different, yet have the same spectrum.

You should watch the talk. He talks about the nonuniqueness issue quite a bit. It's a fascinating talk and I'd value your reaction to it.

 

[nicoo]

I see some similarities with Connes's approach via non-commutative geometry.
Connes says you can actually completely reconstruct the shape if in addition of its spectrum you also have additional invariants given by non-commutative geometry.

Have a look at this talk (the issue of the spectral model discussed at the end was solved in a few months after this conference)
http://www.cacocu.es/static/CacocuElementManagement/*/alain-connes-conferencia-duality-between-shapes-and-spectra-the-music-of-shapes/ver#.UqxFcdLuKSo

Edit: Connes' explanation about non-uniqueness and its resolution starts at 19'00

Unfortunately the website does not let the video to be played in full-screen.
Here is the direct link to the video to download or play full-screen within browser
http://video.cacocu.es/UGR/CONFERENCIA/ALAIN_CONNES/UGR_CONFERENCIA_ALAIN_CONNES__1-5671ab.mp4