Complex sentence: These can detect a change in the 4 km mirror spacing of less than a ten-thousandth the charge diameter of a proton, equivalent to measuring the distance to Proxima Centauri with an accuracy smaller than the width of a human hair.
Split into simpler sentences: These can detect a change in the 4 km mirror spacing of less than a ten-thousandth the charge diameter of a proton. It's equivalent to measuring the distance to the nearest star Alpha Proxima to an accuracy less than the width of a human hair.