The Terminator as 100% possible, logically and physics wise
Time displacement is possible, although it doesn't affect that future. So there in lies the single conundrum of the film, logic. Why would Skynet create another reality that has no effect on this one, it's illogical. NOT SO, Skynet may not have sent a Terminator, that would require energy on the Planck length...perhaps what it did was recreate the big bang and the cosmos as we know it, a computerized universe simulation of the cosmos about 60 years in the past, and placed a Terminator and a human there, to gather intell on the resistance and how they operate, to learn more about human nature to better combat these humans whom they underestimated.
The affected past would be simulated war games, for Skynet to work out. It is an operable past that it can alter and base strategies off of.