# Unification of general relativity and quantum mechanics.

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Hello,

This thread concerns a physical notion, but its origins go back to the

emergence of the theory of mathematical unification. In mathematics, two

theories are identical, if their corresponding topos (i.e. categories) are

equivalent.

I would like in this thread to discuss the unification of quantum mechanics,

and general relativity. What do we mean, mathematically speaking, by unifying

quantum mechanics and general relativity?

From a few readings that I had done several times in the past, the General

Theory of Relativity is a geometric theory. On the other hand, quantum

mechanics is an algebraic theory. So, finally, we seek to unify an algebraic

theory and a geometric theory. What would that mean?

Classically, I have seen how we unify an algebraic theory and a geometric

theory, via functors: differential geometry is identified in part with the

theory of commutative algebra,

because, the category of real differential varieties, are identified to a

subcategory of commutative algebras.

Is that, to unify the theory of general relativity, and the theory of quantum

mechanics consists in exhibiting a functor through which, we identify a

category of geometric objects within general relativity, and a category

of algebraic objects within quantum mechanics?

Thanks in advance for your help.
asked Aug 23
edited Aug 23

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