I am working with a setting in a block universe that is deterministic. Starting from an initial garden of Eden configuration at time
t = 0 every configuration of the universe at a future point in time can be calculated by a function applied to the configuration of the previous point in time. This means I can calculate the whole block universe from start to finish based on the garden of Eden configuration - basically Laplace's Demon creating a block universe.
Now I consider whether bi-directional time travel is possible. Jumping forward in time doesn't pose a problem, because the algorithm to calculate a configuration only takes past events into account.
I don't see a way how traveling back in time would work though, because to calculate e.g. the configuration at
t = 1000, I would need to take the configuration of
t = 999 as well as
t = 2000 into account, assuming someone or something travels back in time from
t = 2000 to
t = 1000. This is not possible, because I cannot calculate the configuration at
t = 2000 without knowing the configuration at
t = 1000. This seems to be an unsolvable circular relationship.
It doesn't matter whether I allow arbitrary traveling back in time or only at certain intervals, the circular relationship always arises.
I could of course rework the algorithm that builds the universe to start at the end of the universe and calculates all the configurations backwards until I reach the garden of Eden configuration, meaning the configuration of the universe at
t = n-1 can be calculated based on the configuration
t = n. This only switches the problem, because traveling backwards in time suddenly becomes feasible while traveling forward in time no longer works for the same reason as before.
Did I miss something, or is bi-directional time travel in a deterministic block universe never possible? Are there changes I can introduce that would allow bi-directional time travel in this setting?