Is EM theory in curved spacetime the same as unification ?
If anyone wants to read Eddington's description of the Weyl theory and discuss it, I'd be interested in talking about it. One thing that seems odd to me about it is the following. He posits that parallel transport around a closed path can change a vector's length. This seems to me to be different in an important way from the usual GR idea that transport around a closed path can change a vector's direction. Let's call the length effect L and the direction effect D. D works the same for all vectors, regardless of what type of vector it is. But it seems to me that the same can't be true for L. L involves changing a scalar. Suppose every scalar were to change by the same amount on transport around a given loop -- regardless of the type of scalar. This rapidly leads to a mathematical contradiction, since for any scalar x, 1/x is also a scalar, but you can't have x and 1/x both scale the same way. As far as I can tell, L can therefore apply only to norms of spacetime displacement vectors, i.e., to meter-sticks and clocks. To me, this seems ugly and contrary to the purely geometrical spirit of parallel transport in normal GR.