[PatrickHenry]

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.

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.

[Physicist]

Can you direct me to a website that might have some diagrams of what that 2D projection might look like?

Picture a rod with a kink in it. Picture two of them, meeting at the kinks. Now imagine their shadow on a bright, sunny day.