Space is discrete for a moving mass and continuous for an electromagnetic wave. Using this differentiation and by bringing in infinity, we provide a simple explanation for the constancy of the speed of light. We introduce velocity addition and distance-time equations that are consistent with both postulates of special relativity. Thus, widely accepted derivations, showing that the two postulates necessarily lead to the Lorentz transformations, cannot be correct. Our theory leads to different time measurements by observers and to special relativity’s momentum-energy formulas. However, in our theory length of an object remains invariant, and we do not have a time dilation formula that applies between inertial frames. In our theory clock mechanism would play a role; thus, while many clocks would match the special relativity formula, not all clocks will give that exact same time shift. We note that quasars and gamma-ray bursts, which are not showing the needed exact time dilation of special relativity, might be examples of such clock mechanisms. We suggest other Lorentz violation time dilation experiments where special relativity and our theory give different predictions. In particular, we suggest an experiment using atomic clocks and sophisticated quartz clocks — OCXO — together in a high speed vehicle; such space vehicle launches are numerous nowadays. We predict these two clocks will go out of sync, thus providing a controlled and easily replicable violation of special relativity's time dilation.