Experimental Test of Time Dilation by Laser Spectroscopy on Fast Ion Beams

Abstract

The Ives-Stilwell experiment – measuring the time dilation relation γSR = (1 – β ₂)–½ – is one of the three classic experiments to test Special Relativity. Together with the interferometric tests of the velocity-independence as well as the isotropy of the speed of light, governed by the Michelson-Morley and the Kennedy-Thorndike experiment, respectively, the Ives-Stilwell experiment entirely establishes Special Relativity on an experimental basis and replaces Einsteins postulates [1]. While the interferometric experiments are ‘nullexperiments’ looking for deviations of the constancy of the speed of light, the time dilation test provides a positive measurement based on a Lorentz boost. It was Einstein who proposed already in 1907 to look for the time dilation effect by observing the Doppler-shifted wavelength of light emitted by excited fast atoms perpendicularly to the motion. In this direction, the classical Doppler effect vanishes leaving pure time dilation. However, it turned out that this scheme is difficult to implement as already small deviations of the observation angle from 90 degree would cause frequency shifts due to the classical Doppler effect which varies linearly around π/2. It took another 31 years until Ives and Stilwell performed the first measurement. Contrary to Einsteins idea they observed the Doppler shifts not perpendicularly but in forward and in backward direction of the atomic motion. This scheme provides different advantages. First, the classical Doppler shift vanishes in this scheme because it is of equal magnitude but opposite in sign in both directions of observation. Secondly, the measurement is less sensitive to small misalignments as the classical Doppler shift varies only quadratically around 0 and π. And finally, as two frequencies are measured, both the time dilation factor as well as the atoms’ velocity can be extracted to an accuracy given by the frequency uncertainty. When observing perpendicularly, the velocity has to be determined separately to provide a test of the time dilation relation. In the next section the principle of the Ives-Stilwell experiment