On a possible evidence for Cantorian space–time in cosmic ray astrophysics

It is known that invariance under Lorentz transformations is a fundamental principle underlying both relativity and quantum field theory. It has been recently suggested that global Lorentz invariance is only an approximate symmetry of nature that may be broken for subnuclear particles participating in high-energy interactions. In particular, several research groups have argued that violation of Lorentz invariance may provide a satisfactory answer to anomalies reported in the detection of ultrahigh energy cosmic rays (UHECR) and TeV-photon spectra. Since breaking of Lorentz invariance amounts to a manifest violation of relativity, it is highly desirable to search for alternative explanations of these anomalies. Our work suggests a possible solution that complies with relativity and is consistent with the Cantorian geometry of space–time at high-energy scales.