Gao, Shan
(2017)
Relativity without Light: A Further Suggestion.
[Preprint]
Abstract
The role of the light postulate in special relativity is reexamined. The existing theory of relativity without light shows that one can deduce Lorentzlike 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 spacetime, 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 spacetime. This suggests a more complete theory of relativity, the theory of relativity in discrete spacetime, which is based on the principle of relativity and the constancy of the minimum size of discrete spacetime.
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