In your strictly deterministic universe, if Alice travels through time to today, it was always inevitable that she was going to do it. From the moment of the big bang it was already decided that she would arrive today, and that would be equally true if she was travelling towards or backwards.
As you have noticed, it would be impossible for a human to perform ...
If someone travels from t=2000 intending to go to t=1000, they actually go to a t=2001 state, which is calculated by the algorithm using what it already knows about t=1000, and internally looks just like t=1000 did except with the addition of the time traveller. You basically recycle t=1000 except with something changed by the state at t=2000, which is ...
Who says time is one-dimensional?
If time has more than one dimension, you can allow bi-directional time travel along some of the axes, as long as one only allows one-directional travel. Consider a universe with two time dimensions - one which allows bidirectional travel ("time") and one which doesn't ("meta-time").
As long as time travel ...
Similar to Robyn's answer, but with some different reasons.
Alice travels back in time. In your deterministic universe, the fact that she does so is determinable from the laws of physics and the initial state of the universe. Not only that, but everything she does when she goes back in time is determinable from the initial state of the universe.
That means ...
Your function is impossible:
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.
The reason is that "previous" is an infinitely long time away once you introduce a ...
I don't see why it cannot be calculated, as long as the machine/human/god doing the calculation has infinite time and resources.
If backward time travel is possible, you have a feedback loop. It makes the math more complicated, but not impossible.
Until the first time travel, the process go sequentially: first t=999, then t=1000... then t=2000. Once Alice ...
In my thinking about this problem, there is no reason that you cannot have time travel in a block universe. It would be a poor kind of time travel but it would be time travel.
For example, X in year 2000 devises a means to travel back in time to year 1000. In your model, everything in year 1000 is determined absolutely by the year 999. In my block universe, ...
Reverse engineer the seed.
What you describe is the same problem faced by people who want to determine the seed used to generate a Minecraft world. In Minecraft a seed number is used to generate the entire world. Minecraft will pick one at random or you can give it one. A given seed will generate the same world each time.
It's simply an extra consistency constraint on the system
A system of equations (and/or constraints) can have any number of solutions, be it zero, one, five, a billion, or infinite. "Time travel consistency" is simply an extra equation or constraint.
A deterministic universe needs a set of constraints with exactly one solution. Adding a time-travel ...
The problem here is that you need to use an iterative calculation. Once you figure out that Alice will go back 100 years you need to back up your calculation 100 years, add Alice and recalculate those 100 years. Note that this will get exceedingly complex if there is any substantial amount of time travel. That doesn't mean it can't be calculated, though.
Assume f(t) generates (t+1).
t1 = f(t0)
t2 =f(t1) = f(f(t0))
traveller x travels from 7 to 5. Traveller is based on t7, so denote it x(t7)
We need to insert this into the calculation for T6. Thus:
T6 = f(t5, x(t7))
T7= f(f(t5, t7))
This will presumably require some kind of time-based calculus to compute, which may or may not be easily solved, ...