Past time is based on a certainty, while future time is based on uncertainty. The past has already happened, therefore it has been recorded in some way or another, such as in our memory. There is no mystery, within the limits of our understanding and all the odds are in, etc. One could say the past is determined. The future is not definitive, since it is still unfolding and the dice have not settled yet. The present is where certainty and uncertainty meet. This where the definitive relationships of the past are compared to similar things in the future that have yet to settle. One would need two sets of equations, one to reflect past determinism and the other for the future uncertainty. Where they meet, we have the present.
Something that I have thought about, concerning SR, that may be unique, is how does SR deal with randomness and uncertainty as it occurs between references? SR appears to work, just fine for cause and effect, like clocks ticking. However, randomness, although also occurring in time and space, it not sequenced in cause and effect. I would guess that one could apply SR to the average of random events but unique events may not be predictable in time and space since these are not based on cause and effect?
As an example of two references looking at an average of random events, say we have two factories built on earth, that are identical, right down to both factories averaging 10 defects per day. One factory is placed on a huge space ship and given a relativistic velocity such its time slows to half relative to the earth factory.
In a side by side comparison, the stationary factory will still have 10 defects per day, while the moving factory will appear to only have 5 defects per day from the stationary reference due to time slowing to half. What this also says is, in a side-by-side comparison, the stationary or the expanded space-time reference has a higher rate of entropy. Or the expansion of space-time, in the universe, is consistent with the 2nd law; cousin of random. The second law in light of SR would imply an expanding universe as a way to increase entropy.