about how Lorentz violations might have been hidden in past experiments, or might be revealed in future ones. Lorentz violation tests with Penning Traps A Penning trap is a research apparatus capable of trapping individual charged particles and their antimatter counterparts. The trapping mechanism is a strong magnetic field that keeps the particles near a central axis, and an electric field that turns the particles around when they stray too far along the axis. The motional frequencies of the trapped particle can be monitored and measured with astonishing precision. One of these frequencies is the anomaly frequency, which has played an important role in the measurement of the gyromagnetic ratio of the electron (see ). The first calculations of SME effects in Penning traps were published in 1997 and 1998. They showed that, in identical Penning traps, if the anomaly frequency of an electron was increased, then the anomaly frequency of a positron would be decreased. The size of the increase or decrease in the frequency would be a measure of the strength of one of the SME background fields. More specifically, it is a measure of the component of the background field along the direction of the axial magnetic field. In tests of Lorentz symmetry, the noninertial nature of the laboratory due to the rotational and orbital motion of the Earth has to be taken into account. Each Penning-trap measurement is the projection of the background SME fields along the axis of the experimental magnetic field at the time of the experiment. This is further complicated if the experiment takes hours, days, or longer to perform. One approach is to seek instantaneous differences, by comparing anomaly frequencies for a particle and an antiparticle measured at the same time on different days. Another approach is to seek sidereal variations, by continuously monitoring the anomaly frequency for just one species of particle over an extended time. Each offers different challenges. For example, instantaneous comparisons require the electric field in the trap to be precisely reversed, while sidereal tests are limited by the stability of the magnetic field. An experiment conducted by the physicist Gerald Gabrielse of Harvard University involved two particles confined in a Penning trap. The idea was to compare a proton and an antiproton, but to overcome the technicalities of having opposite charges, a negatively charged hydrogen ion was used in place of the proton. The ion, two electrons