The theory presented here is the third part of the quantum gravitational formulation of Einstein's special theory of relativity. I shall derive two new relativistic formulas. Firstly, based on 'quantum length to classical length transformations', I shall derive the quantum gravitational length contraction equation introduced without proof in Part I. Secondly, based on 'quantum time interval to classical time interval transformations', I shall derive the quantum gravitational time dilation equation. I have shown, in Part I, that the Fitzgerald-Lorentz length contraction formulation violates the space quantization postulate, and consequently, a new quantum gravitational equation was introduced. If the second postulate I put forward in Part I turns out to be correct, then the new length contraction formula should be preferred over the Fitzgerald-Lorentz length contraction counterpart. On the other hand, Einstein's time dilation formula does not violate the time quantization postulate. This means that when we apply the same technique to time we obtain a new time dilation formula that differs from that of Einstein. But then the question arises: which of the two time dilation formulas is the correct one? I found that I do not have solid arguments in favour of either of them, except for a feeling in favour of Einstein's equation. It seems that only the experiment can answer this question beyond reasonable doubt.