I quote from the Wikipedia article on Planck length:
According to the generalized uncertainty principle, the Planck length is in principle, within a factor of order unity, the shortest measurable length – and no improvements in measurement instruments could change that.
I also link to an answer provided to this Phys.SE question:
The reason there is only a finite number of ways is that we assume separations smaller than the Planck length can't be distinguished.
I have hear this claimed every once in a while, but I never learned this formally at university. Can it be proven using quantum mechanics/uncertainty principle that the Planck length is the smallest measurable quantity, or is this still an area of debate and opinion in modern physics?
If you have a simple proof, could you please provide.
