Recently, I spoke with a professor of mine - an experimentalist. I asked him this: "If a massless particle travels one planck length in one planck time, then does this imply that a massive particle is 'stuck' in a planck volume as long as necessary to give an average velocity (as measured by humans) that is less than the speed of light?"

He said that this question is not one that can be answered by experimentation as we can't probe anywhere near this level (and I suppose the uncertainty principle is an issue).

But, I'm still intensely curious about this. Am I missing something, or is there just no definitive (or otherwise) answer?

Thanks all,
M74

If space is quantized, does imply that each volume, that a massive particle enters, acts like a spherical potential well?

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Yes, his answer is certainly correct, you are asking about what is happening at a scale that we cannot observe. Having a Planck scale doesn't mean that space is really broken up into discrete pieces of that size, it just means that we cannot give even theoretical meaning to our concept of space on scales smaller than that. But we cannot give practical, observable meaning to our concept of space on much larger scales than that. We don't know that something observable does not happen on a scale in between what we can now observe, and the Planck scale. Put differently, our concept of space is not discrete, it is continuous-- and we know it has to stop being a useful concept somewhere between the scales we can now probe, and the Planck scale. That's a lot different from saying that we have a model of space that comprises of discrete bits of the Planck size, as that is not our model of space.
There's no definitive answer. It sounds like you are worrying about something along the lines of the Zeno paradoxes, where if space is infinitely subdividable, then a particle has to take an "infinite number of steps" to get anywhere, but the fact is that space is not a real thing in physics, it is a purely mathematical entity to which we apply continuous mathematics (calculus), and we cannot speak of "what space is made of."
It doesn't imply that, it would be more correct to say we have no model for what space is comprised of, it's just a mathematical conceptualization that is continuous and infinitely subdividable, but ceases to have meaning on some scale. In other words, a longstanding question about matter is whether it was continuous or made of indivisible parts called "atoms". We still use both atoms and fields to talk about matter, but the atom picture is of dominant importance. The same statement cannot be said about space, instead if we asked if space was continuous or made of "atoms of space", we'd probably conclude that neither one is a particularly reliable way to talk about space on the smallest scales, but that the continuous picture works fine on the scales we can now probe.