Since I watched Stargate Continuum </em last week, I've been thinking more about the Grandfather Paradox, a puzzle that sooner or later crops up in all good time travel-related science fiction. The Grandfather Paradox revolves around this question: "What would happen if someone went back in time and killed their own grandfather before the grandfather had a chance to have any children?" By killing their grandfather, the time-traveler erases themselves from existence. But if the time traveler is erased from existence, they couldn't have travelled back in time to kill their grandfather, so therefore they should exist. Does the time-traveler exist or not? This is the paradox. 1985's Back to the Future went with the logic that the time-traveler would cease to exist. In the movie, after the protagonist Marty McFly accidentally prevents his parents from dating, he begins to literally disappear until he can get their romance back on track. In the Stargate franchise, time-travelers originating from a future that no longer occurs because of what they do in the past continue to exist in whatever time period of the past they wind up in. This makes manipulating time for personal advantage an attractive proposition for some: a similar time travel logic seems to hold sway in the Eureka and Terminator and Doctor Who universes as well. So which logic is right? Because my head started to hurt after trying to work it out on my own, I turned to my trusty computer. Using Processing, a free computer language and development system developed by MIT that makes it ridiculously easy for even someone with my limited programming skills to whip up an application, I created a virtual time machine. My time machine lives in an equally virtual universe. This universe is pretty tiny, with only room for 2,500 particles total, and only has two dimensions. It also doesn't live very long, just 64 ticks of its cosmic clock. The laws of physics in the universe are also pretty simple. Particles can only move north, south, east or west. Whenever a particle meets another particle, they annihilate each other, except in the case of a west-moving particle meeting a east-moving particle. Then the west-moving particle destroys the east-moving particle and carries on. The time machine is simple too -- a particle that collides with the time machine will be sent back in time to 11 ticks after the universe begins, but with its direction reversed, so a east-moving particle becomes a west-moving particle. To be able to see how the universe evolves in time, I displayed the universe at each tick of its clock, arranged in a grid, as someone might look at a sequences of frames from a movie. To allow for changes wrought by time travel, I reran the entire history of the universe in an endless loop.
I set things up so that a east-moving particle (the green circle in the first image above) starts moving towards the time machine (yellow circle) at tick zero. At tick 37, the particle enters the time machine and vanishes from the universe, having been transported back in time. To make sure the universe continued to operate normally during these temporal shenanigans, I threw in a North-moving particle (white circle) at tick 15. Even after the green particle interacts with the time machine, you can see the white particle happily moving north. The point of all this was to create the simplest possible version of the Grandfather Paradox -- a particle enters the time machine and gets sent back in time in such a way that is is guaranteed to annihilate itself before it has a chance to enter the time machine. So what happens? After the green particle enters the time machine, the universe evolves normally until the end of time at tick 64. The universe runs through its history again and the result is shown in the lower image. At tick 11, the particle emerges from the time machine and starts moving west (now colored blue to distinguish it from the earlier version of itself). At tick 23, the collision completes (because of the order in which I drew the circles, the green particle completely overlaps the blue particle). By tick 24 the blue particle has finished annihilating the green particle, which now never reaches the time machine. The blue particle then continues merrily on its way, before hitting the 'wall' of the universe at tick 47, at which time it vanishes from view only because my model universe is so small. So it seems as if the Stargate, Eurkea, Doctor Who and Terminator logic is correct -- you can kill your grandfather without disappearing from existence. However what's really interesting is that that isn't the end of the story. My little universe simulator is endlessly rerunning history. It turns out that on the next run through, the original state of affairs, as shown in the upper image, is restored! Because the green particle never made it to the time machine to kill itself, on the next run through there's no killer blue particle at time 11. So the green particle continues to the time machine. The next run through after that is identical to the lower image, blue particle and all. So from this simulation, the ultimate resolution to the Grandfather Paradox is that the universe would naturally oscillate between two time-lines, one in which your Grandfather lives out his life unmolested by homicidal grandchildren, and the other in which you kill your Grandfather, but continue on with your life. Because the oscillation occurs outside of the time experienced by objects in the universe, no-one would be aware of it, unless, perhaps, they had access to some sort of cool-looking time machine.
