The energy-momentum relationship is obtained in para-Lorentzian dynamics. It is shown that the well-known correspondence rule for the operators energy and momentum holds in any inertial system if it is assumed to hold in the preferred reference frame. The new Dirac equation is obtained. Some qualitative features of the new theory are given; one of then is the spontaneous appearance of conserved-vector and nonconserved-axial weak currents. Finally one evaluates the convenience of further developments of the present theory in view of (...) the excellent agreement of QED with experiment. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one (...) free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

The revised Robertson's test theory of special relativity (SR) has been constructed upon a family of sets of passive coordinate transformations in flat space-time [J. G. Vargas and D. G. Torr,Found. Phys., 16, 1089 (1986)]. In the same paper, it has also been shown that the boosts depend in general on the velocities of the two frames involved and not only on their relative velocity. The only exception to this is SR, if one has previously used an appropriate constraint to (...) remove the other relativities—like Galilean relativity—from the family.In this paper we look at these coordinate transformations in the only way there is to do so, namely as transformations in a seven-dimensional “Cartan Space” (Cartan first considered this in his dealings with Newtonian kinematics). In this space, the boosts only depend on the relative velocity of the frames. The passive coordinate transformations in each set are shown to have a nonlinear group structure isomorphic to that of the Poincaré group.The existence of a preferred frame, except in SR, makes the active transformations inequivalent to the passive ones. It is shown that the composite active-passive transformations act on a ten-dimensional space and that each member set of the family also has a group structure. As a result, one ends up with a family of mutually isomorphic 9-parameter (homogeneous) supergroups and a family of mutually isomorphic (9 + 4)-parameter (inhomogeneous) supergroups. The presence of extra parameters could be looked upon as “internal” degrees of freedom, which are, however, an offshoot of the Robertson space-time. (shrink)