so, i've decided to watch every video at the stanford youtube site in the order it was uploaded (with minor corrections to ensure series are in order), and the first thing in the list is an introduction to quantum mechanics. he first goes through a review of what was, for me, first year linear algebra (although it may have been a higher level course for non-honours students, or physics students, especially engineering physics students). and, there's an immediate problem that jumps up.

i never took a dedicated course in quantum mechanics like this (i did take a dedicated course in relativity theory), so it's somewhat of a different presentation, and seeing it plopped down on the table like this really exposes the nature of the problem i've been trying to draw attention to all of these years.

it's the geometry of space that's at the heart of these contradictions. he's building the whole thing up over orthogonal vector spaces, when we know damned well from relativity that space is curved (and probably hyperbolic). there's even an axiom of orthogonality, which is ridiculous, in context.

the point i keep trying to draw attention to is that the general field theory may very well come out in the wash if you stop doing relativity in hyperbolic space and quantum physics in euclidean space. so, how do you adjust? well it's actually a job for a mathematician, right?

in theory, these ideas ought to generalize if you just do them right. but, a hilbert space is going to be associative by assumption, and a corresponding vector space in a hyperbolic geometry isn't. so, that right there is going to screw up the math.

i've asked this question here a few times: if you were trying to understand space (which is both expanding and curved) using euclidean geometry (which is fixed and orthogonal) wouldn't you expect your reference frame to see an illusory multitude of non-existent dimensions?

i just have this nagging feeling that this is actually a lot easier than anybody realizes.