madaco wrote:if a particle is moving at the plank speed (c), then one plank time later, it should have moved the plank length,
but if the particle is moving at less than c, then how far does it move is one plank time?
so if both time and space are quantized in the plank length and the plank time, that to me it seems like that would suggest that things would have to move at a integer multiple of c
and of course it cant move faster than c,
so that would mean that all particles at any instant must be either moving at c or at rest?
That's actually a very good question and I don't think science can answer it conclusively at this point. My understanding is that both Planck length and Planck time are hypothesized to be indivisible units of space and time, respectively - but this doesn't mean that both hypothesis have to be true. If the grain of space is the Planck length and time is infinitely divisible - no problem, and vice versa. On the other hand, when space and time are viewed as just dimensions of the pseudo-Riemannian manifold that spacetime is so it wouldn't feel natural for just one of them to be infinitely divisible.
If both are true then indeed motion with speeds of less than c are problematic. This can be covered by the uncertainty principle - the universe is probably not even theoretically observable at such scales.
I can understand Zeno's frustration with the apparent impossibility of motion. No matter how you look at it, it doesn't seem possible to complete an infinite number of steps in finite time. If the number of steps is finite, then, we run into the other Zeno paradox.
Even nowadays, if we assume finite divisibility we run into all kinds of counter-intuitive implications, even if it's at finer grain than the Planck units. If both space and time are finitely divisible, then we have, first, a lower bound for speed and second, a smallest possible increment; speed must then be an integer multiple of slowest possible speed (1 atomic unit of length per 1 atomic unit of time)