If time travel movies existed in the same universe, where would they overlap?

From World Science Festival:

In movies, time travel methods are mostly explained along the lines of “something something plutonium something wormhole.” But physicists do have some idea of methods that might allow for actual time travel—though they might not necessarily prevent you from killing your own grandfather.

One trope in time travel science fiction is slightly plausible, if physically impossible—traveling faster than the speed of light. The crew of the U.S.S. Enterprise did this in Star Trek IV: The Voyage Home, by using the sun’s gravitational pull to accelerate their spaceship to super-light speed. If it were possible to travel faster than light (Einstein calculated it would take an infinite amount of power), it is theoretically possible for signals to be sent back in time; it’s questionable if the same method could work with people.

Wormholes are another possible route for traveling backwards and forwards through time. In the 1960s, New Zealand mathematician Roy Kerr calculated under the right conditions, a spinning star can collapse not into a point, but into a ring; if something passed through this ring, it might travel through a tunnel in spacetime called an Einstein-Rosen bridge, or wormhole. The two ends of the wormhole might connect to different universes, or to different points in the same universe (separated by time as well as space). Scientists have yet to actually find evidence for wormholes, but they do square with Einstein’s theory of gravity. Caltech physicist Kip Thorne took the theory of wormholes to another level later, showing that if you can move the openings around, the entrances and exits can exist at different moments in time.

Assuming you make it back to the past, what happens if you kill an ancestor of yours? Do you cease to exist? Does you ceasing to exist then mean you don’t go back in time in the first place to kill your grandfather? Russian physicist Igor Novikov developed a theory called the Self-Consistency Principle, under which the odds of any action that you might take creating a time paradox are zero.

“There is no global division of events on closed timelike curves into future and past,” Novikov wrote in the book Black Hole Physics. “Not only the future is a result of evolution of the past, but the past is a result of the future also… all events on closed timelike curves influence each other around the closed timelike line in a self-adjusted way.”

So it’s impossible to change the past because you’ve already been there in the past, taking actions that resulted in your future-present. Not all physicists (or philosophers, given the implications of Novikov’s principle on free will) agree; some think that actions during time travel may create new timelines (as seen in Back to the Future II; for more on theories of alternate universes, check out the World Science Festival program “Multiverse: One Universe or Many?”). Whichever theory of timelines you subscribe to, it’s probably best to play it safe and not kill anyone.