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In quite a few countries, string theorists (and usually GR people too) are far more likely to be in mathematics departments than in physics. Pretty much for the

In quite a few countries, string theorists (and usually GR people too) are far more likely to be in mathematics departments than in physics. Pretty much for the reasons you describe -- GR was seen in the 60s as an exotic mathematical playground, not quite real physics.

mikorym 7y ago
This is also true of QM (not just because of QM computational sciences). My MSc thesis has application to quantum mechanics. I wrote a short summary of the generalisation that I made here [1], which generalises what the Nijmegen group calls quotient comprehension chains to sets. The authors of the latter QC-chains did not seem much interested when I emailed them. In any case, ideally the framework should touch on geometry eventually as well, but I am not aware of concrete ways to do it. Toposes are considered geometric, but I don't know whether geometric in the sense of GR. The eventual or at least, hopeful, end point is something like [2] where your mathematical framework should ideally in the language of categorical or functorial duality express physical dualities. I don't know how to get to GR, as I say, and should read maybe this [3] but there are many ways to get to QM. One example is through entropy: the generalised abstract set subobjects are partitions and partitions encode entropy through "distinctions", i.e, elements in separate equivalence classes of the partition. The category of sets itself is a model for QM theories via it's inspiration for (symmetric) monoidal categories so perhaps one would want to express in the self-dual language that as well. It's one thing to point to multiple uses of category theory in physics, but it is another to keep track of it in your personal, internal intuition strategy. [1] https://arxiv.org/abs/1808.01350 https://arxiv.org/abs/1808.01350 [2] https://en.wikipedia.org/wiki/AdS/CFT_correspondence https://en.wikipedia.org/wiki/AdS/CFT_correspondence [3] https://ncatlab.org/nlab/show/duality+in+string+theory https://ncatlab.org/nlab/show/duality+in+string+theory

mikorym 7y ago

This is also true of QM (not just because of QM computational sciences). My MSc thesis has application to quantum mechanics. I wrote a short summary of the generalisation that I made here [1], which generalises what the Nijmegen group calls quotient comprehension chains to sets. The authors of the latter QC-chains did not seem much interested when I emailed them. In any case, ideally the framework should touch on geometry eventually as well, but I am not aware of concrete ways to do it. Toposes are considered geometric, but I don't know whether geometric in the sense of GR. The eventual or at least, hopeful, end point is something like [2] where your mathematical framework should ideally in the language of categorical or functorial duality express physical dualities. I don't know how to get to GR, as I say, and should read maybe this [3] but there are many ways to get to QM. One example is through entropy: the generalised abstract set subobjects are partitions and partitions encode entropy through "distinctions", i.e, elements in separate equivalence classes of the partition. The category of sets itself is a model for QM theories via it's inspiration for (symmetric) monoidal categories so perhaps one would want to express in the self-dual language that as well. It's one thing to point to multiple uses of category theory in physics, but it is another to keep track of it in your personal, internal intuition strategy. [1] https://arxiv.org/abs/1808.01350 https://arxiv.org/abs/1808.01350 [2] https://en.wikipedia.org/wiki/AdS/CFT_correspondence https://en.wikipedia.org/wiki/AdS/CFT_correspondence [3] https://ncatlab.org/nlab/show/duality+in+string+theory https://ncatlab.org/nlab/show/duality+in+string+theory