If time travel is possible and time travel enabled one to change the past, then no time travel machine will ever be invented.
Here's the proof:
Assume that time travel is possible and one can change the past. Then, as people travel back in time, "reality" is in constant flux as the past changes again and again. This will continue until the past in changed in such a way that no time travel machine is ever invented, anywhere, at anytime. Once that happens, reality is fixed with no time machines ever being invented.
Assume Hallett puts a collection of free neutrons into a trap, he will measure decay products at a predictable rate.
Hallett now turns on his light circulator, he puts the neutrons into closed timelike spacetime trajectories.
What does he now observe, zero decay products (because decay now occurs in the past? Does he measure decays products before he turns on the circulator?