New Directions in the Foundations of Physics Conference in Washington DC 2013 (part 3)
“What is the alternative to quantum theory” by John Preskill
As promised, here is the second story from the subsequent discussions following Preskill’s talk.
After the talk I was listening in a discussion between John Preskill and Chris Fucks and at some point John asked the question: “is there anything else besides classical and quantum mechanics?” Later in the day I approached John and I told him that I know the answer to his question and I started to present my ideas captured in http://arxiv.org/abs/1303.3935 The basic idea is simple. Suppose I have on my left side a physical system A subject to the laws of nature. Also suppose I have on my right side a physical system B subject to the same laws of nature. Then if I perform the tensor product composition of system A with system B, I would get the larger system “A tensor B” subject to the same laws of physics. From this I can extract very hard constraints on the allowed form of the laws of nature. In fact it can be shown that there are only 3 such consistent solutions. One is an “elliptic” solution which corresponds to quantum mechanics, one is a “parabolic” solution which corresponds to classical mechanics, and there is a third “hyperbolic” solution which corresponds to something we do not fully understand at this time. Another way to look at the 3 solutions is by Plank’s constant: positive, zero, or imaginary.
Mathematically the whole thing can be naturally expressed in terms of category theory, and physically it corresponds to the invariance of the laws of nature under tensor composition. Now when I explain this to different people, I usually get a polite nod followed by a polite excuse to end the discussion. However, I did not get this reaction from Preskill who asked cogent clarification questions. Also he told me to look up the recent preprint of an Anton Kapustin. I did not remember the name, and the next day I asked John to type it for me on the archive search field and lo and behold I found out this preprint: http://arxiv.org/abs/1303.6917 titled: “Is there Life beyond QM?” Now the core inspiration for my result was a 70s paper by Grgin and Petersen: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103900192 and Kapustin had the same inspiration. Reading his preprint it struck me that we had independently discovered the same thing and I only managed to upload my preprint 11 days before him. Then the mystery of John’s reaction evaporated. Preskill is colleague with Kapustin at Caltech.
So now I had good news and bad news. The good news was that I am right and my credibility got a boost. The bad news is that I have competition in an area where I thought I worked alone. When I uploaded my preprint, I left out a piece of it, related to the unitary realization of the collapse postulate. So I rushed to package this result as a separate paper and I uploaded a few days after the conference: http://arxiv.org/abs/1305.3594
The problem is that any violation of unitarity is fatal to QM as shown by the QM reconstruction project. This includes the collapse during measurement even though it can be interpreted as Bayesian information update. There is an easy remedy to this though suggested by this composability/category theory formalism and it is based on the Grothendiek group construction. (I’ll explain how this works in detail in a subsequent post). As a side benefit this solves the measurement problem and eliminates the MWI interpretation as well.
The QM reconstruction projects is an area coming of age and Luca Bombelli maintains a page keeping tabs on all such projects: http://www.phy.olemiss.edu/~luca/Topics/qm/axioms.html I believe that such approaches will eventually lead to the elimination of all known QM interpretations as QM will be just as easily and naturally be derivable as special relativity. After all, how many conferences dedicated to the “correct” interpretation of special relativity and “ict-imaginary time” do you know?