Everything past is definite, everything future is probabilistic.
No, there is no difference between the past and the future. Causality is not probabilistic, neither in the past nor in the future.
Einstein:
"I do not believe in free will. Schopenhauer's words: 'Man can do what he wants, but he cannot will what he wants,[Der Mensch kann wohl tun, was er will, aber er kann nicht wollen, was er will]' accompany me in all situations throughout my life and reconcile me with the actions of others, even if they are rather painful to me. This awareness of the lack of free will keeps me from taking myself and my fellow men too seriously as acting and deciding individuals, and from losing my temper." Schopenhauer's clearer, actual words were: "You can do what you will, but in any given moment of your life you can will only one definite thing and absolutely nothing other than that one thing." [Du kannst tun was du willst: aber du kannst in jedem gegebenen Augenblick deines Lebens nur ein Bestimmtes wollen und schlechterdings nichts anderes als dieses eine.]
I dunno why you brought causality into it. I'm 100% with nagarjan on that one, its his most fundamental thought...
Neither from itself nor from another,
Nor from both,
Nor without a cause,
Does anything whatever, anywhere arise.
If my words misled you (highly probable! i get excited and just spraff sometimes) into thinking that, then I apologise that wasn't my intention.
My original hypothesis still stands the future is probable outcomes, the past is memory of what happened. I think that makes the different (in fact I believe they are opposites hence the term anti-future).
You can make them semi-equivalent by suggesting that what happened becomes probabilistic based on the observer. (You said X, no I said Y. both remembering different) but I have since discarded this, as it felt the 'future/anti-future' concept sat better with everything else. Yin yang etc.
Maybe anti-future is just another way of viewing observation, it cancels out future (possibility) leaving us with a concrete instant in 'time'. (I kept calling it 'T' but I guess planck time would be better) 1 unit later fresh observation, fresh new reality! Probably not much different from the last one, but possibly is
The reason we find it so hard to see is because its all happening so fast, and our observational capacity is just so woefully underpowered on the quantum scale. We can see a tiny fraction of electromagnetic radiation, we careen through ~10^42 outcomes in the blink of an eye. Its bound to look complicated to us