[deleted]
I am the editor of the "Markov Chain Universe" website and would like to comment on the above discussion from the context of Markov Chain Universe theory. (If you are curious what it is, please google the term).
The flow of time represents the transitions of the universe from one state to another state. The future of potential states is determined completely by the current existing state of the universe (and there is no secret hidden markings somewhere outside of the current state dictating its future trajectory). Hence, the universe is a Markov Chain.
It unfolds through a time history where the past is distinguishable from the future by a set of distinctly available states. The states of the future are not the same available states as the past. This is the primary distinguishing feature of the passage of time- movement into a new state space.
Quantum theory does indeed prescribe a specific deterministic movement through time to the future- excluding the "decoherence" which is physically observed that places the outcome of the future into only one of the possible sets of that deterministic evolution of the probability function of quantum theory.
The exciting aspect of Markov Chain Universe theory is that some states are lower probability than others. It appears that living organisms themselves are lower probability structures propagating themselves through time.
In any event, whether or not you accept that you do have to accept the universe behaves as a markov chain, providing you describe the set of states of the system coherently with regards to what is observed by physical law.