The primary use of measurements of is that they directly give a very accurate value of . However, due to their precision, these measurements also provide good tests of CPT and Lorentz invariance. In the mSME, the only framework that has been applied to Penning trap experiments, the factor for electrons and positrons receive no corrections at lowest order. However, the frequencies and both receive corrections . At lowest order in the Lorentz violating coefficients these corrections are (with the trap’s magnetic field in the z-direction)
The functional form of Equation (50) immediately makes clear that there are two ways to test for Lorentz violation. The first is to look for instantaneous CPT violation between electrons and positrons which occurs if the parameter is non-zero. The observational bound on the difference between for electrons and positrons is . This leads to a bound on of order . The second approach is to track over time, looking for sidereal variations as the orientation of the experimental apparatus changes with respect to the background Lorentz violating tensors. This approach has been used in  to place a bound on the diurnal variation of the anomaly frequency of , which limits a particular combination of components of , , and at this level. Finally, we note that similar techniques have been used to measure CPT violations for proton/anti-proton and hydrogen ion systems . By measuring the cyclotron frequency over time, bounds on the cyclotron frequency variation (50) for the anti-proton have established a limit at the level of on components of .
© Max Planck Society and the author(s)