finite point of smallness

[bozo the clown]

Is there a point at which you cannot go any smaller ?
if there is, than to move from X to Y (the distance between X and Y being 1 unit of that finite smallness) would be instantaneous right as if it wasnt you would have to move acroos that point indicating smaller units so therefore if there is a point of finite smallness than faster than speed of light would be passed if faster than light is not possible than there must be infinite smallness
understand ?

[Chen]

This pretty much explains it all:
http://www.physlink.com/Education/AskExperts/ae281.cfm
You can't do anything instantaneously because that has no physical meaning. As that page says, even a photon travelling at the speed of light would take some time (planck time) to cover this smallest space (planck length).

[Bob3141592]

Is there a point at which you cannot go any smaller ?
if there is, than to move from X to Y (the distance between X and Y being 1 unit of that finite smallness) would be instantaneous right as if it wasnt you would have to move acroos that point indicating smaller units so therefore if there is a point of finite smallness than faster than speed of light would be passed if faster than light is not possible than there must be infinite smallness
understand ?

If there is a smallest possible distance, then wouldn't there be a smallest possible duration as well? These could balance out so that faster than light travel wouldn't happen.

Keep in mind that the energy levels required to explore these domains gets drastically big, and then you've got relativistic effects to account for. I'm not an expert, but it's possible that looking too closely at these domains would create a black hole that you miht fall into, so be careful!

[jcsd]

This pretty much explains it all:
http://www.physlink.com/Education/AskExperts/ae281.cfm
You can't do anything instantaneously because that has no physical meaning. As that page says, even a photon travelling at the speed of light would take some time (planck time) to cover this smallest space (planck length).

The answer in the link isn't authoritve, it's inaccurate to call the Planck lenght the quanta of length as we simply don't know. It's the length at which quantum gravity is expected to manifest itself.

So the answer to the original question is that nobody knows if there is a 'quanta of length'. All experiments so far have shown no evidnece of that there is one, but it may well be the case that it will arise out of a theory of quantum gravity.