Terrestrial experiments will continue to improve. Cold anti-hydrogen can now be produced in enough quantities [117, 27] for hydrogen/anti-hydrogen spectroscopy to be performed. The frequency of various atomic transitions (1S-2S, 2S-nd, etc.) can be observationally determined with enough precision to improve bounds on various mSME parameters [61, 256]. Spectroscopy of hydrogen-deuterium molecules might lead to limits on electron mSME parameters an order of magnitude better than current cavity experiments .
There are proposals for space based experiments (cf. [59, 194]) that will extend current constraints from terrestrial experiments. Space based experiments are ideal for testing Lorentz violation. They can be better isolated from contaminating effects like seismic noise. In a microgravity environment interferometers can run for much longer periods of time as the cooled atoms in the system will not fall out of the interferometer. As well, the rate of rotation can be controlled. Sidereal variation experiments look for time dependent effects due to rotations. In space, the rate of rotation can be better controlled, which allows the frequency of any possible time dependent signal to be tuned to achieve the best signal-to-noise ratio. Furthermore, space based experiments allow for cavity and atomic clock comparison measurements to be combined with time dilation experiments (as proposed in OPTIS ), thereby testing all the fundamental assumptions of special relativity. The estimated level of improvement from a space based mission such as OPTIS over the corresponding terrestrial experiments is a few orders of magnitude.
Another possibility for seeing a novel signal of Lorentz violation is in GLAST . GLAST is a gamma ray telescope that is very sensitive to extremely high energy GRBs. As we have mentioned, DSR evades almost all known high energy tests of Lorentz invariance. If the theoretical issues are straightened out and DSR does eventually predict a time of flight effect then GLAST may be able to see it for some burst events. An unambiguous frequency to time-of-arrival correlation linearly suppressed in the Planck energy, coupled with the observed lack of birefringence at the same order, will be a smoking gun for DSR, as other constraints forbid such a construction in effective field theory .
The question that must be asked at this juncture in regards to Lorentz invariance is: When have we tested enough? We currently have bounds on Lorentz violation strong enough that there is no easy way to put Lorentz violating operators of dimension coming solely from Planck scale physics into our field theories. It therefore seems hard to believe that Lorentz invariance could be violated in a simple way. If we are fortunate, the strong constraints we currently have will force us to restrict the classes of quantum gravity theories/spacetime models we should consider. Without a positive signal of Lorentz violation, this is all that can reasonably be hoped for.
© Max Planck Society and the author(s)