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.
Thanks, I actually understood a decent portion of that :)
Wavelengths. An integer number of wavelengths.
Not to belabor what is probably obvious, but I assume the "mystery dimension" is orthogonal to the sub-space in which we observe the particles, yes?
You lose me when it comes to advance theoretical physics, but isn't it possible that we know of ONLY three particle families because we haven't developed particle accelerators capable of imparting sufficient energies to particles to produce a more massive 4th family (or higher) of particles? I assume that any hypothetical fourth family of particles would be more massive than the known three. I am sure it would throw the standard model for a loop, but it is pretty much a consensus view among physicists that the standard model is not a complete theory of elementary particles, isn't it?