In effort to investigate how quantum physics might modify Einstein's Theory
of Relativity tit speeds v --> c, the relationship between space-time coor
dinates of different reference frames is revisited by introducing only one
new parameter x(o), a fundamental constant for the quantization of space. T
he starting point is three criteria: (a) real space-time data are condition
ed by standard quantum effects on measurements, (b) since currently used ap
paratus are only capable of probing the aggregate behavior of these quanta
the relevant model is one which maximizes the Entropy subject to certain de
fining constraints; and (c) the constraints simply involve fixed ensemble a
verages 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 quantizati
on of space-time which resembles identically, Planck's photon picture of ra
diation are a direct consequence of the Principle of Relativity. Non-inerti
al 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 c
entral region of highly agitated quanta with an asymptotic ambient environm
ent-the outcome is the Schwarzschild metric of General Relativity. Apart fr
om 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 percei
ved by its to occur at the expected length or time scales.