Length contraction on quantum scale?

[jbrussell93]

How can relativistic length contraction be measured at the quantum scale? Since a Planck length by definition cannot be divided, how can something that is 1 Planck length, traveling near the speed of light, contract with respect to an observer? In other words, how can an observer possibly measure the length of contraction?

 

[Fredrik]

The Planck length is many orders of magnitude smaller than anything that can be measured, so there are no practical issues with length contraction. There is probably a theoretical issue, but it's only an issue in quantum gravity theories, where the Planck scale has a special significance. The current theories of elementary particles are just quantum theories of matter in Minkowski spacetime (i.e. the spacetime of special relativity), and the Planck length doesn't have any significance in Minkowski spacetime, so these theories don't predict that anything will be different at those scales. They are expected to fail at those scales (or sooner), but that's another story. The precise way in which they will fail is unknown. Only a quantum theory of gravity can explain that.