Ok, I might get it now. So in the hypothetical 3d space all particles have the same resistance to acceleration, but because they have differering velocities in the z direction, their projections on the xy plane will appear to accelerate at different rates given the same force. Is that the idea? If it is, then two further questions:
- Wouldn't observers in the xy plane sometimes see two particles seemingly occupying the same location (because they'd have the same x and y coordinates but different z)?
- How would this model account for gravity? It eliminates inertial mass by making it a function of velocity in the z direction, but what about gravitational mass?
Just so.
Wouldn't observers in the xy plane sometimes see two particles seemingly occupying the same location (because they'd have the same x and y coordinates but different z)?
[Geek alert: Well, for one thing, the extra dimension would likely be curled up into a very tiny circle, too small to be noticed at our scale. (Call it "periodic boundary conditions", if you prefer.) Alert readers might have wondered why, say, an electron couldn't just have any old momentum in the 5th dimension, and therefore any old mass. It's obviously not that way: electrons all have the same mass. The answer is because, in the tiny extra dimension, the quantum wavefunction of the electron would have to have an integer number of wavefunctions along the circle, to match the boundary conditions. [Super Geek Alert: This means only certain masses would be allowed. Could the higher harmonics represent the muon and the tau? The argument has been made, but we still don't know why only three.] ANYWAY, the wavefunction covers the entire space, so the Pauli Exclusion Principle still applies. [Super Geek Alert: Some theorists postulate that there are LARGE extra dimensions. In such models, it actually is theoretically possible (using polarization) to get electrons to "pass through" each other with a head-on trajectory, because they miss each other in the 5th dimension!]]
How would this model account for gravity? It eliminates inertial mass by making it a function of velocity in the z direction, but what about gravitational mass?
Rather than snow you under with handwaving about Kaluza-Klein towers of gravitons, I'll admit that that's a very technical question, which I'm not qualified to answer. I can tell you that the whole model has not been worked out.