John Baez
Quantum Quandaries: A Category-Theoretic Perspective
discussion at SPR
https://www.physicsforums.com/showthread.php?t=18633&highlight=quandaries
To appear in a book called
Structural Foundations of Quantum Gravity
eds. Steven French, Dean Rickles and Juha Saatsi, Oxford U. Press.
preprint:
http://www.arxiv.org/abs/quant-ph/0404040
exerpts from the abstract:
"General relativity may seem very different from quantum theory, but work
on quantum gravity has revealed a deep analogy between the two. ...We show how this accounts for many of the famously
puzzling features of quantum theory: the failure of local realism, the
impossibility of duplicating quantum information, and so on. We argue
that these features only seem puzzling when we try to treat Hilb as
analogous to Set rather than nCob, so that quantum theory will make
more sense when regarded as part of a theory of spacetime..."
he argues that since there are still things that puzzle people about QM it is possible that a better understanding of Quantum Theory itself could come out of quantum gravity. And he explores an analogy between GR and QM that shows up in taking a category-approach to each. why does QM use Hilbert space and why does GR use cobordisms (space time continua connecting one geometry to another) and what is in common between hilbertspaces and cobordisms as abstract categories
dont get the idea that I am advocating this, but it is a good balance to a more commonsense view.