The system with discrete interactions II: Behavior of the relativistic particle in space and in time

Abstract

The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently covariant equation of motion of the particle (Klein-Gordon) is defined. Based on the assumption that the form of the equation has to be invariant in inertial reference frames, the principle of constancy of the speed of light can be deduced. Consequently the basic statements of special relativity can be established in relation to the principles of discrete interaction. The condition that Klein-Gordon equation was established without explicit use of the principle of correspondence gives a way to specify the area of applicability of the statement about the speed of light as the maximal speed of propagation of information. This would permit interpretation of superluminal phenomena with no contradictions to special relativity. The conventional interpretation of time as a category which specifies succession and coexistence of events leads to interpreting of the Klein-Gordon and related equations (such as Maxwell or Dirac) as equations of the fields. This would justify the procedure of second quantization, so that the states of the field are identified with the sets of particles.