From commenter Hendrik, there’s the news that USC has put out a press release claiming that String Theory Could Be the Foundation of Quantum Mechanics. These claims are based on this paper, which argues that finding the Heisenberg commutation relations in a string field theory calculation means string field theory can be the foundation of quantum mechanics.
In my quantum mechanics course this semester, I’m now up to around chapter 13 or so of the notes available here. Last class I was pointing out that one already sees the Heisenberg commutation relations in classical Hamiltonian mechanics. The functions on phase space are a Lie algebra, satisfying commutation relations given by the Poisson bracket. These relations are determined by knowing what happens on linear functions, together with the Leibniz rule. On linear functions, the commutation relations are Heisenberg’s.
So, I think the discovery out of USC is an even greater one: string field theory can explain not only quantum mechanics, but classical mechanics too.
Update: I should have realized that this thing already had one wave of hype earlier this year, courtesy of Tom Siegfried, which I wrote about here. This new wave comes courtesy of Physics Letters, which thought this worth publishing, and USC, which thought a press release was a good idea.
You know, string theory actually is quite important for understanding the (mathematical) foundations of quantum mechanics:
http://arxiv.org/abs/0809.0305
http://arxiv.org/abs/q-alg/9709040
It’s a shame that serious ideas like this hardly ever get discussed on this blog.
Bob Jones,
There has been some blogging here about the mathematical foundations of quantum mechanics. I’ve been teaching and writing about the topic, expect more blogging, this spring a finished draft of a book, and more to come after that. Sorry, but claiming that those two papers you reference show that string theory is important for understanding the foundations of QM is utter hype. I don’t believe the authors of those papers would agree with that claim.
Peter,
I’m glad to hear that more serious content is on the way.
Regarding the papers I mentioned, the formality theorem proved in the second one is really one of the most fundamental results in the mathematical theory of quantization. I don’t think I’m exaggerating when I say that string theory is important here; in the second paragraph, Kontsevich himself writes, “The solution presented here uses, in an essential way, ideas of string theory”.
Bob Jones,
Actually, it seems to me that all Kontsevich is really saying is that in order to prove a certain technical conjecture, he used calculational techniques developed in studying topological string theory (which has nothing to do with physical string theory). He then writes the proof without using any string theory. Quite interesting work and great mathematics, but, sorry, “string theory actually is quite important for understanding the (mathematical) foundations of quantum mechanics” is just hype.
Ah, so mathematical work on two-dimensional sigma models and topological string theory doesn’t count as string theory. Got it.