Abstract

In effort to investigate how quantum physics might modify Einstein's Theory of Relativity at speeds v→c, the relationship between space-time coordinates of different reference frames is revisited by introducing only one new parameter xo, a fundamental constant for the quantization of space. The starting point is three criteria: (a) real space-time data are conditioned by standard quantum effects on measurements; (b) since currently used apparatus are only capable of probing the aggregate behavior of these quanta the relevant model is one which maximizes the Entropy subject to certain defining constraints; and (c) the constraints simply involve fixed ensemble averages in the case of an inertial frame, or boundary conditions on running averages in the case of an accelerated frame. In this context it is found that both the Lorentz transformation and a simple scheme for the quantization of space-time which resembles identically Planck's photon picture of radiation are a direct consequence of the Principle of Relativity. Non-inertial behavior corresponds to local Entropy maxima, obtainable by solution of a diffusion equation which gives gradually varying ensemble averages across space-time, as demonstrated by the example of a profile which connects a central region of highly agitated quanta with an asymptotic ambient environment—the outcome is the Schwarzschild metric of General Relativity. Apart from the above, a new feature emerges from the theory: the space-time data of an observer, when referred to the frame of his moving partner, are subject to extra quantum fluctuations which increase indefinitely in severity as v→c, with the Lorentz transformation providing only the mean data values. Thus for fast moving bodies like cosmic rays or matter at the horizon of a black hole, physical processes which affect them may not always be perceived by us to occur at the expected length or time scales