The rest momentum as an additional property of a massive particle in Finsler space-time

It is shown that a flat relativistically-invariant Finslerian space-time with partially broken 3D isotropy, i.e. an axially-symmetric space of events is a natural generalization of the Minkowski space of special relativity. The respective Finsler metric depends on two constant parameters, one of which determines the magnitude of spatial anisotropy or, in other words, the degree of deviation of the Finsler metric from the Minkowski metric, while the second parameter represents the physically preferred direction in 3D space. The replacement of the Minkowski line element in the action integral for a free massive particle by the Finsler line element leads to the Lagrange function which describes the relativistic particle in partially anisotropic 3D space. The respective function allows us to conclude that, like the situation in Minkowski space, if particle's velocity tends to zero, energy of the particle tends to its absolute minimum, i.e. to ordinary rest energy. As for momentum of the particle, unlike the situation in Minkowski space, it does not tend to zero, if particle's velocity tends to zero. Thus, in the anisotropic space, in addition to the rest energy, any massive particle obtains one more observable parameter - the rest momentum directed along the locally preferred direction in 3D space. Due to the directly proportional dependence of the rest momentum on the magnitude of local space-time anisotropy and also on mass of a particle and speed of light, the fact that in our time the magnitude of the local space-time anisotropy is extremely small does not at all mean the impossibility of detecting anisotropy in astrophysical processes with a giant energy release and, accordingly, with a giant mass defect. Obviously, in the processes with giant mass defects, one can also expect noticeable momentum defects. With allowance for the law of conservation of momentum, this implies a possible self-acceleration of matter and local isotropization of the Universe.