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 [60]. 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
[97]. 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 [217] 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 [118]. 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
.
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