Can objects move towards each other in less than one Planck length?

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Can two objects move towards each other as a consequence of their gravity a distance smaller than one Planck unit of length?
 
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It's not clear that the idea of position, and hence of "moving toward" has any meaning at the Planck scale. Spacetime may be foamy, uncertain, and/or topologically complex at that scale.
 
No one really knows what "distance smaller than one Planck unit of length" means. So the question probably doesn't make sense. We'll have to wait for a better theory to know for sure.
 

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