  Can a simple microscopic model of space and time demonstrate Special
Relativity as the macroscopic (aggregate) behavior of an ensemble ? The
question will be investigated in three parts. First, it is shown that the
Lorentz transformation formally stems from the First Relativity Postulate (FRP)
{\it alone} if space-time quantization is a fundamental law of physics which
must be included as part of the Postulate. An important corollary, however, is
that when measuring devices which carry the basic units of lengths and time
(e.g. a clock ticking every time quantum) are `moving' uniformly, they appear
to be measuring with larger units. Secondly, such an apparent increase in the
sizes of the quanta can be attributed to extra fluctuations associated with
motion, which are precisely described in terms of a thermally agitated harmonic
oscillator by using a temperature parameter. This provides a stringent
constraint on the microscopic properties of flat space-time: it is an array of
quantized oscillators. Thirdly, since the foregoing development would suggest
that the space-time array of an accelerated frame cannot be in thermal
equilibrium, (i.e. it will have a distribution of temperatures), the approach
is applied to the case of acceleration by the field of {\it any} point object,
which corresponds to a temperature `spike' in the array. It is shown that the
outward transport of energy by phonon conduction implies an inverse-square law
of force at low speeds, and the full Schwarzschild metric at high speeds. A
prediction of the new theory is that when two inertial observers move too fast
relative to each other, or when fields are too strong, anharmonic corrections
will modify effects like time dilation, and will lead to asymmetries which
implies that the FRP may not be sustainable in this extreme limit.
