Can Grid Theory Define the Smallest Possible Movement?

[JoesKepler]

I was just curious, has there been any theories on how small of a movement is possible?
For example, moving an atom a certain length, then moving it half that length, then again half, is there a point when you would get to the smallest movement possible (looking at it as the smallest unit of a 'grid' type system), or could it go on continuously?
I understand this is most likely metaphysics, but would anyone know of any published theories or thoughts with this issue?

 

[Crosson]

There is no established theory that predicts discrete space, but the current crop of grand unified theories (string theory etc...) is exploring this idea in the context of quantum gravity.

Someone will probably mention the Planck length, which is the length at which...well we expect something different to happen in the neighborhood of the Planck length.

 

[DyslexicHobo]

I asked this question once on Anandtech's HT forum. I got a lot of answers talking about the Planck length.

I'm not sure if my comprehension of this unit is correct, but I don't think it has anything to do with the theory being mentioned (well, at least it does not answer the question).

The Planck length something like 1.0x10^-35 cm. Say this much is the Planck length (just for demonstration purposes)

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The Planck length is that much, but we can measure a Planck length in intervals less than that length, such as:

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Is this correct? It's not really a "grid" with a scale of 1.0x10^-35 cm, it's just the smallest unit which fits our current, complete grasp of physics.

 

[lpfr]

We are far, very far (I mean very, very far) to measure something $$10^{10}$$ bigger than the Plank length.
The smaller distance we can measure is about 1/10 of an atom, that is $$10^{-11}$$ meters.