Without getting into the math too much there are a couple of reasons I believe time travel is nothing but a pipe dream.
My point being is I dont think traveling through time is a easy problem to crack given the computational resources required to establish where you are and where you would like to go.
As Peppa Pig would say "it's impossible."
Nothing is impossible, Mr. Dabs. What you want is simply expensive.
Both Loops are Open, either Past or Future. However, for this world to tap into that there is not enough time or compassion

If it were in fact possible by some yet to be invented technology, do we really believe then, that our current point in time is SO utterly boring that no future time travelers have been interested enough to travel back to this point in history? I mean certainly we'd recognize some indicators that our distant progeny has come to visit! Right?