Try this: take a bunch of massless, interacting particles and let them fly around in three dimensions, crashing into each other and bouncing off as they may. Now take their trajectories, and project them onto a two-dimensional plane. As viewed in the two-dimensional plane, the particles interact as if they had masses, the apparent masses being proportional to their momenta in the direction perpendicular to the plane.
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.
Thanks for your 2D/3D projection post: most intriguing thing I've read today.
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...
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.
Sounds like a great simplification, but I'm having difficulty visualizing this. Can you direct me to a website that might have some diagrams of what that 2D projection might look like? All I can think of is a Mercator projection, and I'm sure that's not even in the ballpark.