Well, what’re the smallest particles we know of? Quarks, last time I checked. Now, I’m no mathmatician, but I think in the current theory they’re 0-dimensional, they just have mass and other quark-y properties, but otherwise they’re just points. So they don’t have sides to move 
Quarks, being described by a wave equation, would be subject to the Uncertainty Principle, so even if you considered them to be of defined volume (which would be a mistake), you wouldn’t be able to locate them accurately and know how fast they were moving accurately at the same time. At any rate, it would be a mistake to refer to a quark as “particle”, even though they are often called “elementary particles”. They aren’t really “particles” any more than an electron (also an elementary particle) is a “particle”-- ie, a little round thingy like a tiny, tiny ball.
“Stuff is made of particles. Therefore, particles can not be made of stuff.” [right]–Raymond Hall[/right]
So there’s no discrete dimension to quarks or leptons. However, it is entirely possible–and even essesntial to the indeterminacy principle–that these particles can, in fact, move faster than light. Actually, it’s not so much that they move in the classical Newtonian sense as that one minute they’re at Point A, and the next time you look they’re way over at Point Q, which is much futher than light would have travelled at the same time. However, in the aggregate, fundamental particles don’t go faster than light and are otherwise well behaved in populations large enough to be useful.
It would be really useful, conceptually, if we could come up with a unique term for fundamental “particles” than distinguishes them from the kind of particles that we see flying through the air or filter out of drinking water. People sometimes get the idea that we actually know something about quantum mechanics because the language is familiar, when in fact all we know are some seemingly arbitrary rules that just happen to work for no explicable reason whatsoever.
Stranger
Every time this topic pops up, the issue of rigidity comes up. What is the measure of rigidity?. How much more rigid is the theoretical limit imposed by relativity over the most rigid materials known to us?
Not to mention that fact that they can pop into being out of, seemingly, nothing if even for just short periods of time. Maybe we could call them “elementons”, but I don’t think that would solve the fundamental problem (no pun intended)-- ie, that quantum physics is not intuitive. As one of my physics profs used to like to say… No one really understands this stuff, they just become more comfortable with it over time.
The basic measure of rigidity (or stiffness, or elasticity, or whatever you like) is Young’s modulus. Relativity tells us (among other things) that material objects can achieve the speed of light: ~2.9979x10[sup]8[/sup] m/s. The speed at which an axial vibration can propogate through a steel rod–that it, the “speed of sound” in the rod–is about 5100 m/s. There are materials that are more rigid than steel, but not five orders of magnitude more rigid; at some point, the speed of propogation is going to be such that the momentum transfer between one molecule and the next will exceed intermolecular forces and cause any real world material to shatter. Even if you ignore that problem, there’s an inherent amount of “elasticity” in any electrical bond that will limit propogation speed, even in solid state, to significantly less than c.
Stranger
Well, if he’s just sleeping then I’ll just poke him a few times with this infinitely rigid device to wake him up.
Admittedly, a line like that seems more “nudge nudge wink wink” then “dead parrot”.
I think you meant “cosmic string” there, not “superstring”. They’re probably two completely different things. I don’t know much about superstrings (a trait I have in common with the vast majority of physicists), but the mechanical wave speeds associated with cosmic strings are all exactly c (which, among other things, makes them very interesting as potential sources of gravitational waves). Current theory strongly suggests that they don’t have endpoints, being instead either infinite or loops (the distinction being irrelevant, for long enough loops). If, of course, they exist at all, which nobody is certain of.
Is it possible to set up an apparatus to test the OP, or is it so basic that it wouldn’t be worth testing? I’m not talking about the propagation of vibration or current, but asking about the point of the OP.
Take a one meter crystalline rod, e.g.–whatever might be very rigid. If one end is accelerated, does the other end begin accelerating well after a photon would have traveled a meter in a vacuum tube parallel to the rod, or is the movement of both ends of the rod simultaneous? If it is not simultaneous, is it the case that this is because of “flexibility” of the molecular bonds, so to speak, and if so, is there any physically definable smaller item than a rod where both sides can be said to move simultaneously? I am all good with the notion that when you get to the quantum level all bets are off and deliberately did not use the term quark instead of particle earlier.
Quoting from the latest NCLB textbooks are you, John?
BTW, the other classic example of this kind of thing is an enormous pair of scissors made out of the same theoretical magic substance. If the jaws of the scissors were sufficiently long, they should move together at a speed faster than light, right?
The speed of sound has been measured in many different materials, and I suspect that it’s a standard thing measured for any new material developed. In all cases, the measured speed of sound has been far, far below the speed of light.