Can more than one past state lead to the current state of the universe?

Question

I am seeking to assess the philosophical consistency between modern physics and the Damascene theologian Ibn Taymiyya's theory of natural causation. Ibn Taymiyya seems to have endorsed the view that the current state of the universe is open to multiple potential subsequent states, with only one becoming actual. Moreover, he maintained that natural causes are not superfluous by definition, which, in my reading, suggests that he believed that each state of the universe could only have arisen from a unique, immediately preceding state. (See this lecture, discussion, and article for more on the Taymiyyan theory of causation: https://www.youtube.com/watch?v=5_s5kOPXclc , https://www.youtube.com/watch?v=a1CIzBI8rqA , https://www.youtube.com/watch?v=WX5y3mLZ68I )

Do physicists generally believe that the current state of the universe could only have arisen from the immediately preceding state, making it physically impossible for any other preceding state to have theoretically given rise to the current state? Are there interpretations of quantum mechanics that maintain indeterminism towards the future while preserving determinism towards the past? Please provide a comprehensive answer if possible.

Answer 1

1. This answer originally addressed the question in the title before it was edited: "Is it possible for the current state of the universe to have arisen from an immediately preceding state other than the one that actually preceded?"
   The only theories of physics that we have are all using time evolution by (partial) differential equations, so by definition they describe "the current state of the universe to have arisen from a different immediately preceding state", as you phrase it in the title of your question.
   So in a sense we could say that it is not just theoretically possible (as you ask), but it's even the only possibility our theories give us! NB: of course none of this proves whether the idea is correct, which it may or may not be. We're just discussing the theoretical possibility here, and by merely looking at what the existing theories are, the answer is clearly yes.

2. As to the question whether there is only one unique state in the past that could have evolved to the present state: As the last paragraph asks, is it possible for "any other preceding state to have theoretically given rise to the current state?"
   If we look at QM, that would not be the case if the time-evolution in QM is unitary. You could instead look at non-unitary versions of QM (like the ones with objective wave function collapse) but it is disputable whether those are "interpretations" of QM (as you ask) or downright alterations of QM. Nevertheless it seems obvious that with randomness added you could get what you ask, but note that we do not have any widely accepted "altered QM" theory of that kind! So within QM we simply do not know the answer to your question.
   If we look at classical physics, there is a clear example, ["Norton's dome"], which has non-deterministic time-evolution. If you time-reverse its description in Wikipedia, you have what you ask for: indeterminism into the past!
   To be precise: the situation with the particle at the top of the dome may have arisen at any point of time in the past from the particle rolling upwards and coming to rest at the top, you can't derive at which time it was, even if you fully know the present, with infinite accuracy.

3. The question at the very end of the last paragraph: "Are there interpretations of quantum mechanics that maintain indeterminism towards the future while preserving determinism towards the past?"
   Asking for "determinism towards the past" would mean there is only one unique past that could have led to the present, so in that sense it's the same question as 2), formulated in the opposite way. But if you simultaneously ask for indeterminism towards the future it becomes more restrictive. The framework of classical physics where you can have Norton's dome is no longer an example of such a theory (because it has indeterminism both into the past and into the future). Neither is QM with unitary time evolution (it has determinism in both time directions). An example could perhaps be found in some altered theory of QM with randomness included in a non-time-reversable way, see e.g. Objective collapse models (But as noted before, no widely accepted theory of that kind exists.)