[math-fun] A Jewel at the Heart of Quantum Physics
From: Ray Tayek <rtayek@ca.rr.com> Subject: [math-fun] A Jewel at the Heart of Quantum Physics
https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-qua...
Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.
--the underlying huge (about 140 pages) paper this came from appears to be http://arxiv.org/abs/1212.5605 it is difficult for me to tell quickly whether this paper is worthless, or worth a lot. They only did their stuff in unphysical fake quantum field theories in lower-than-actual dimensions. Can it be made to work for field theories anybody actually cares about? Are their underlying profundities really profound and useful? Can they quantify their quality by using computational complexity? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
On Wed, Sep 18, 2013 at 5:10 PM, Warren D Smith <warren.wds@gmail.com> wrote:
From: Ray Tayek <rtayek@ca.rr.com> Subject: [math-fun] A Jewel at the Heart of Quantum Physics
https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-qua...
Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.
--the underlying huge (about 140 pages) paper this came from appears to be http://arxiv.org/abs/1212.5605
it is difficult for me to tell quickly whether this paper is worthless, or worth a lot.
It's worth a lot.
They only did their stuff in unphysical fake quantum field theories in lower-than-actual dimensions. Can it be made to work for field theories anybody actually cares about?
There's work to do, but as far as they can tell, there's no reason why it shouldn't.
Are their underlying profundities really profound and useful?
Absolutely. Watch Arkani-Hamed's Messenger lectures for a wonderfully clear exposition of the problems and the ideas leading up to this paper. http://www.sns.ias.edu/~arkani/
Can they quantify their quality by using computational complexity?
Yes, if they cared to. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Better yet, watch Arkani-Hamed explain the amplituhedron: http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_4-3.html On Sep 18, 2013, at 7:31 PM, Mike Stay <metaweta@gmail.com> wrote:
Are their underlying profundities really profound and useful?
Absolutely. Watch Arkani-Hamed's Messenger lectures for a wonderfully clear exposition of the problems and the ideas leading up to this paper. http://www.sns.ias.edu/~arkani/
Better yet, watch Arkani-Hamed explain the amplituhedron: http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_4-3.html
Apparently Arkani-Hamed's partner in crime, Jaroslav Trnka, did a talk one week earlier. Here are the slides (which mirror Arkani-Hamed's exposition closely): http://www.staff.science.uu.nl/~tonge105/igst13/Trnka.pdf
I was going to write a review of Arkani-Hamed's lecture Havermann pointed out on video, but gmail deleted it. After 26 minutes of watching I quit -- let's just say I'd be amazed if a single human being comprehended it, and this is not a "lecture" but rather a "comedy sketch about how not to present a lecture." A few random observations: at one point he says he has "conformal invariance" and goes on about some related stuff like "dual conformal invariance" and "the Yang yin" (whatever those are) as though they matter a lot... if conformal invariance really is needed then that excludes the actual laws of physics from consideration via these methods. At another point he says he has (which is central to his work) "a new way of thinking about permutations" -- a remark which seems on its face absurd. But he does not reveal what that new way might be (at least not in the first 26 minutes), and waves his hand at 2 diagrams plus a permutation on the screen, where there seems to be little or no logical connection between them although supposedly the connection is central. Anyhow, if the main goal/claim of his work is (which he never said in the first 26 min, so this is just a total guess -- he felt no need to state his goal or main claims, if any, during the first 26 min): MAIN GOAL (?): Any physics Feynman-diagram complex amplitude (or perhaps |amplitude|^2 or something?) can be written as the volume of a certain polytope in an infinite dimensional space If that really is the claim, yes that sounds important. (It by the way is quite amazing for such a polytope to have finite volume, but it is possible, e.g. hyperbricks have volume corresponding to any infinite product.) Re computational complexity, we have the following remarkable contrast: Imre Barany and Zoltan Furedi: Computing the volume is difficult, Discrete and Computational Geometry 2 (1987) 319-326. shows no deterministic polytime algorithm can approximate the volume of a convex polytope to within an exponential(dimension) factor, contrasting with M.Dyer, A.M.Frieze, R.Kannan: A random polynomial time algorithm for approximating the volume of convex bodies, Journal of the ACM 38,1 (1991) 1-17 which shows you can approximate volume within a factor (1+epsilon) in time polynomial in #dimensions and 1/epsilon, using a randomized algorithm with success probability >=3/4. The fact that Arkani-Hamed's polytope is "in an infinite dimensional space" seems however to exclude any such algorithm, the above results were in finite dimensional spaces. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
MAIN GOAL (?): Any physics Feynman-diagram complex amplitude (or perhaps |amplitude|^2 or something?) can be written as the volume of a certain polytope in an infinite dimensional space
The fact that Arkani-Hamed's polytope is "in an infinite dimensional space" seems however to exclude any such algorithm, the above results were in finite dimensional spaces.
--actually the usual Feynman diagram formulation yields an algorithm to evaluate any diagram to within epsilon via numerical integration, which I think can be shown to be in the complexity class #P. But the infinite-dimensional polytope formulation (if any) does not seem to lead to any algorithm at all. If the dimension can be made finite, then there would be an algorithm. So on the face of it, this seems a step in the wrong direction. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Warren D Smith: I was going to write a review of Arkani-Hamed's lecture Havermann pointed out on video, but gmail deleted it. After 26 minutes of watching I quit -- let's just say I'd be amazed if a single human being comprehended it, and this is not a "lecture" but rather a "comedy sketch about how not to present a lecture." It is obvious from Arkani-Hamed's looking at his watch several times that he is under some time constraint in his presentation, but you are right. It is not a lecture. His talk at the 21st International Conference on Supersymmetry and Unification of Fundamental Interactions was however preceded by a 4-day school open to students and young researchers.
participants (3)
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Hans Havermann -
Mike Stay -
Warren D Smith