Effect of Cherenkov Radiation on Superluminal Free Spin-half Particles Motion in Spacetime

Abstract

Conservation laws, consisting of the existence of quantities which do not change in time, independent of the dynamical evolution of a system, are crucial and vital for the construction of any dynamical system theory. The basic properties such as conservation of energy, momentum, angular momentum, charge, isospin, or generalization thereof are fundamental and must be guaranteed by a physical system, if it is to give a valid description of nature. One persistent objection against the concept of superluminal entities is based on the anticipation of fast energy loss which could be incurred under Vavilov-Cherenkov radiation, with the consequent prediction that no such particles could be detected. Yet presently, no theoretical or experimental explication exists which justifies this claim. Here we show, in the limit of a kinematically permissible and non-dispersive medium, that energy conservation is feasible. Corresponding to radiation intensities from large energy-momentum transfer, when the parameter of the generalized linear velocity of the superluminal free spin-half field is made sufficiently large, Cherenkov cone becomes flattened at 90 with direction of motion, bringing the radiated energy to merge with the circulating energy flow in the wave field of the particle.