A microscopic derivation of Special Relativity: simple harmonic oscillations of a moving space-time lattice

The starting point of the theory of Special Relativity is the Lorentz transformation, which in essence describes the lack of absolute measurements of space and time. These effects came about when one applies the Second Relativity Postulate (which states that the speed of light is a universal constant) to inertial observers. Here I demonstrate that there is a very elegant way of explaining how exactly nature enforces Special Relativity, which compels us to conclude that Einstein’s theory necessitated quantization of space and time. The model proposes that microscopically the structure of space-time is analogous to a crystal which consists of lattice points or ‘tickmarks’ (for measurements) connected by identical ‘elastic springs’. When at rest the ‘springs’ are at their natural states. When set in motion, however, the lattice vibrates in a manner described by Einstein’s theory of the heat capacity of solids, with consequent widening of the ‘tickmarks’ because the root-mean-square separation now increases. I associate a vibration temperature T with the speed of motion v via the fundamental postulate of this theory, viz. the relation v 2 c 2 = e − ǫ kT where ǫ is a quantum of energy of the lattice harmonic oscillator. A moving observer who measures distances and time intervals with such a vibrating lattice obtains results which are precisely those given by the Lorentz transformation. Apart from its obvious beauty, this approach provides many new prospects in understanding space and time. For example, an important consequence of the model is the equation ǫ = κx o , where xo is the basic ‘quantum of space’ and κ is the spring constant which holds together the lattice. Thus space-time, like mass, has an equivalence with energy.