Group property of space-time and the upper bounds to velocity and accerelation

Assuming the group property of the transformation between two systems of ti me-position-velocity coordinate where the origins of the two systems of pos ition coordinate are relatively translating, not rotating, we obtain two an d only two transformations. One is the Lorentz transformation and the other is such that the two systems of position coordinate are relatively transla ting with a constant acceleration, where the upper bound to acceleration is required. From the particle motion which is invariant under the second tra nsformation, where the Lorentz correction is taken into account, it is sugg ested that the rest mass of an (elementary) particle with mass m should be approximately given by m + O (root 2nmg); where g represents the upper boun d to acceleration. This implies that the excited particle may be observed f or energy more than about root 2mg (for g >> m). Thus, the excited particle may be first observed for an electron neutrino (considered to be the light est massive particle, with m similar to 10 eV) with energy around 500 TeV, if g is estimated as the Planck mass (similar to 10(28) eV).