We deduce that the speed of light is constant in all inertial frames of reference because both time and space are discretized. To provide a theoretical basis for this discreteness, we postulate our space to be an ocean of the “Gamma elements” having extremely small size and energy (or mass) density. The relativistic relationship between time and space with respect to the constant speed of light is then determined by the process of light propagation in this medium. The theory finds light energy propagating as “elemental waves” with the phase velocity, c. Here a photon is no longer a particle traveling with the velocity, c, but a Gamma element transforming into a Planck element, an energized state carrying an angular momentum, h, with a frequency, v, substantially behaving like a particle with the energy, Eph = hν, traveling with the velocity, c. The lifetime of each Planck element is on the order of the elemental time, tp. A possible mechanism for this transformation is proposed by the use of the quantum field process involving a vector boson transforming between a massive state (Planck element) and a massless, charged state (Gamma element.) We note that the vacuum state in the quantum field theory is approximately equivalent to the Gamma element state. A visualized space-time and photon models are presented and the Compton experiment and the double slit experiment are re-validated by the theory. Owing to the relativistic effect, in particular, the Compton scattering variables, the wavelength change of the incident Gamma rays and the velocity acquired by the electron by the scaterring, are shown to be the same whether the scattering is by the single photon particle or by the series of Planck elements. The difference is the rate at which the energy of the incident Gamma ray is assumed to be delivered, which will then manifest the difference in the acceleration of the electron. This difference may be explored to verify the theory by experiments.