physicists should get this better than the internet seems to suggest they do, too. but, reading through threads full of poorly thought out reasoning is also useful in better articulating my own.

so, what i'm saying is that the vector space should be reflective of reality, which is curved. i'm not talking about "curved vectors". the vectors would be straight, in the curved vector space.

"woah", you say "how can something be straight in a curved space? crazy mathematician."

but, i must interject that you're a bad physicist, because every straight-line you've ever seen in your life has existed in reality, which is a curved spaced. this is not crazy. it's a first principle.

listen: i can empathize, but you need to relent. i went through this, too. they teach you it wrong every year, starting in like grade 11, until you get to the end and realize there isn't even such thing as a straight line. it turns kant and descartes on their respective heads. and, it's enough to make you give up and just fucking play guitar.

hyperbolic geometry isn't just some set of silly escherian drawings. it's the correct way to describe the space that particles move through, and thus necessary to understand in modelling their behaviour. you have to adjust to the point, even if it makes the math almost impossible.

but, you do this: you bring in these awful correcting terms to do basic newtonian mechanics, and you might grit your teeth, but you know you need to take it, like the bad medicine it is.

you need to start doing it in quantum physics, too. you need to discard the childish myth of orthogonality. you need to move completely out of the classical world.