The role of the light postulate in special relativity is reexamined. The existing theory of relativity without light shows that one can deduce Lorentz-like transformations with an undetermined invariant speed based on homogeneity of space and time, isotropy of space and the principle of relativity. However, since the transformations can be Lorentzian or Galilean, depending on the finiteness of the invariant speed, a further postulate is needed to determine the speed in order to establish a real connection between the theory (...) and special relativity. In this paper, I argue that a certain discreteness of space-time, whose existence is strongly suggested by the combination of quantum theory and general relativity, may result in the existence of a maximum and invariant speed when combing with the principle of relativity, and thus it can determine the finiteness of the speed in the theory of relativity without light. According to this analysis, the speed constant c in special relativity is not the actual speed of light, but the ratio between the minimum length and the shortest time of discrete space-time. This suggests a more complete theory of relativity, the theory of relativity in discrete space-time, which is based on the principle of relativity and the constancy of the minimum size of discrete space-time. (shrink)

ABSTRACT In Einstein’s physical geometry, the geometry of space and the uniformity of time are taken to be non-conventional. However, due to the stipulation of the isotropy of the one-way speed of light in the synchronization of clocks, as it stands, Einstein’s views do not seem to apply to the whole of the Minkowski space-time. In this work we will see how Einstein’s views can be applied to the Minkowski space-time. In this way, when adopting Einstein’s views, chronogeometry is a (...) physical chronogeometry. (shrink)

The existence of a definite tangent space structure (metric with Lorentzian signature) in the general theory of relativity is the consequence of a fundamental assumption concerning the local validity of special relativity. There is then at the heart of Einstein's theory of gravity an absolute element which depends essentially on a common feature of all the non-gravitational interactions in the world, and which has nothing to do with space-time curvature. Tentative implications of this point for the significance of the vacuum (...) solutions in general relativity, and for the issue of quantising gravity, are briefly examined. (shrink)

We give a description of the effect of the gravitational field by using the geodesic equation of motion with respect to a first order Finslerian approximation of the Minkowski metric. This motivates linking the physical force of gravity to the non flat nature of space in the Finslerian setting and leads to an anisotropic version of the red shift formula. We solve the linearized Finslerian field equations proposed by S.F. Rutz (Gen. Relativ. Gravit. 25(11):1139–1158, 1993).