Configuration-Space, Transition Probabilities, and Time

NB: I am no physicist, so take nothing that follows as at all authoritative, valid or meaningful. I've been thinking about Julian Barbour's ideas about time recently. Essentially, the universe can be represented by a configuration space (or state- or phase-space, not sure which is most appropriate) each point of which represents one possible state of the universe. This space is essentially a state-vector for the entire universe. Each point in it has an amplitude, which can for our purposes be considered as a probability. Julian Barbour argues in The End of Time that time has no actual existence. What appears to us to be the flow of time is a path thru the state-space connecting high-probability points (I've probably got this somewhat wrong, but am on the right track). I've been wondering if there is some way we could legitimately consider amplitudes for transitions between points in the space instead of amplitudes for points in the space itself. An immediate risk of tautology emerges: we may be implying time by referring to motion, change or transition of any kind. Assuming we can essentialy square our original space and produce a space each point of which is the probability of transition between two points in the original space, the question then arises: is the probability of transition from state B to state A always the same as the probability of transition from state A to state B? Classical physics should tell us it is, that time has no arrow and all transitions are fully reversible. However, there is some experimental evidence which casts doubt in this, tho' it is by no means disproved. (Search 'time symmetry'). What if we need to cube our original space, and have separate probabilities for transitions A->B and B->A? Any inequality between these probabilities would imply a local preferred direction in time, if by time we mean just transitions from one state to another. A path thru this space connecting points that had similar assymetries would create a high-probability sequence in one direction (imagine a dropped egg breaking) and a low-probability sequence in another (a dropped egg reassembling). Assuming we are not simply committing a tautology by basing an idea of time on ideas of transition, we could start with a source in the state-space (the Big Bang Singularity) and find high-probability transitions from that singularity leading to other high-probability transitions and in this way delineate probable world-lines, with a clear preferred direction, ending if you like in a state-space sink such as a possible Big Crunch. This seems consistent with a Many-Worlds interpretation. It might be legitimate to prune the space a bit by eliminating transitions that violate we take to be impossible, such as all the mass in the universe moving instantaneously to a small South Pacific island, and other things involving faster-than-light travel or violating conservation laws. Then again, it might not. If we can prune the space, we go from a universe-cubed space to a much sparser path-space. Normally in a state-space, each point can be traversed by only one path. If that is true in our universal space, then each path is a world-line forever separate from all others, and the underlying structure is that of a directed graph originating in the Big-Bang source. Conceivably the graph, the transitions, are more fundamental than the original state-space. I'm quite certain these ideas are either generally-accepted commonplaces or viewed as elementary misconceptions among actual physicists. I'm just sort of musing out loud because they interested me enough to comment on them, and I don't personally know anyone who thinks much about this sort of thing.