Would-be time travellers have long wrestled with the grandfather paradox: if you change things in the past and prevent yourself ever existing, how did you time travel in the first place? In other words, if Alice goes back in time and kills her grandfather Bob, she won’t have been born and can’t carry out her murderous plot.
One way to avoid such paradoxes is the idea of branching universes, in which the universe we are in splits with each instance of time travel, creating two different universes going forward, leading to an infinite number. Another suggestion is infinite copies of parallel universes that evolve differently over time.
But physicists would prefer to avoid the infinite if possible. Now Barak Shoshany and Jacob Hauser at the Perimeter Institute in Canada have come up with a model of time travel that merely requires a very large, rather than infinite, number of parallel histories in order to avoid paradoxes.
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The pair suggest that to travel between these timelines, a person could step through a wormhole with no length – essentially, a hole in space-time – in a way that they say is mathematically possible.
One way to think of the universe is as a set of points in space and time, and a timeline or a history of events is a mathematical function ordering these points, says Shoshany. In the branching universe and parallel universe solutions, you expand the number of points in space-time to create multiple sets of points and thus mathematically distinct universes. But Shoshany and Hauser modelled a third possibility called parallel histories.
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“The parallel universes approach that we suggest says there are different parallel universes where things are roughly the same, and each one is mathematically on a separate space-time manifold. You can go between those manifolds when you travel back in time,” says Shoshany.
Held within one universe, meaning just one set of points, are multiple timelines represented by mathematical functions rearranging those points. Simply by building a wormhole and emerging from it, the function is altered and the timeline has a different arrangement.
This means Alice 1 can travel from timeline 1 to timeline 2, where she attempts to kill Bob 2 by releasing a crocodile. If the crocodile doesn’t kill him, he can go on to have grandchildren and Alice 2 can try again. She travels to timeline 3 and attempts to drop a piano on Bob 3.
The key here is that the Alices have the ability to change their actions and aren’t locked into Alice 1’s failing plan of releasing a crocodile. If she were to travel within a single timeline, she would be bound to repeat that act because that is the only way to keep history consistent and eliminate the possibility of a paradox.
It may seem a bit of a cheat to expand the playing field with multiple timelines, but Shoshany and Hauser calculated that this paradox-free time travel can be achieved with a finite number of histories in one universe. Alice is ultimately made of a finite number of particles that can only be in a finite – but incredibly large – number of arrangements, he says.
There is one big flaw in the pair’s model as it stands: it only works with one dimension of space, rather than our usual three, says Geraint Lewis at the University of Sydney. Shoshany says he has plans to translate the model to three dimensions to better represent the real world.
Still, it’s not as satisfying as Lewis would like. “What time travel means here is stepping between those histories – that’s even freakier,” he says. “At some level it doesn’t even feel like time travel anymore, because what’s the point of going back and killing Hitler if the second world war still plays out in the universe you’re from?”
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