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It is possible that the particles we see are all actually massless, their apparent masses corresponding to extra-dimensional momentum components we can't as yet detect.

Interesting, but I don't get it. (Not an uncommon event when I read about this stuff). So you have a bunch of massless particles in a 3d space, presumably moving in straight lines except when they collide. If you project them onto a 2d space, aren't they still going to appear to move in straight lines? Or is the projection somehow a nonlinear function that can map straight lines to orbits and other curved paths? Even if so, if the particles in the 3d space move independently of each other, how would any projection create the appearance of dependency?

I don't know if that made any sense; I find this stuff fascinating but am missing a lot of the theoretical background. Trying to get through Penrose's Road to Reality, but I start spacing out on calculus on manifolds...

If you project them onto a 2d space, aren't they still going to appear to move in straight lines? Or is the projection somehow a nonlinear function that can map straight lines to orbits and other curved paths?

I'm not talking about gravity, here, I'm talking about straight Newtonian mechanics. Billiard balls. F=ma.