An essential ingredient of Einstein's special theory of relativity is the notion that the laws of physics do not depend on the orientation or velocity of the laboratory in which they are viewed. This property is known as "Lorentz invariance" and it is the reason the trajectory of a ball thrown while on a moving train is the same as that of one thrown while standing on the ground. Indeed, experiments have shown with exceptionally high precision that Lorentz invariance holds for a wide variety of physical processes occurring at an equally wide range of energies. Today the special theory of relativity and subsequently Lorentz invariance stand as fundamental pillars of modern quantum field theories, including the highly successful standard model of particle physics. Accordingly, evidence for departures from Lorentz invariance (so-called Lorentz invariance violation) would have dramatic implications for our understanding of the physical world.
At the same time it is thought that quantum mechanical descriptions of gravity, the only force not included in the standard model, may allow for or even imply Lorentz invariance violation. Since the effects of quantum gravity are expected to become significant at energies near 1019 GeV, a positive signal for the existence of such phenomena would provide insight into the physics of the early universe, the last place such energies were seen. For this reason searching for evidence of Lorentz invariance violation is a topic of considerable importance to elementary particle physics and cosmology.
It is interesting to note that the tiny mass of the neutrinos and the interferometric nature of their oscillations make them a very sensitive probe of these phenomena. Though standard neutrino oscillations convert neutrinos of one type into another with a frequency determined by the ratio of their travel length, L, to their energy, E, the existence of Lorentz invariance violation would produce oscillations that are a function of L only or additionally the product of L and E.
Since atmospheric neutrinos have travel lengths ranging from 10 to 10,000 km and energies that span 10-1 to 105 GeV, they are a useful tool to search for these effects. Using 4,438 days of atmospheric neutrino data Super-Kamiokande has performed a search for Lorentz invariance violating neutrino oscillations. This is the first study that makes no assumptions about the size of a potential signal and has resulted in one of the most sensitive tests of this phenomenon. Though no evidence of a positive signal was found, Super-Kamiokande has improved limits on the existence of certain Lorentz invariance violating oscillations by between three and seven orders of magnitude and has additionally placed the first limits on some hitherto unexplored types of these oscillations.
These results have recently been published in Physical Review D, and were highlighted in a Synopsis by the American Physical Society