It’s northern summer time, and thoughts drift occasionally from the purely scientific. Take for example the idea of time travel. As far as we know, on macroscopic physical scales the only kind of time travel that works is moving into the future. You can sit around and wait, or you can scoot off at very high velocities and exploit relativistic time dilation to alter the passage of time you experience compared to the universe around you. The famous Twin Paradox (which is not really a paradox, since it makes perfect sense) offers one example of how to accomplish getting to the future while experiencing less passage of time (the key is in the changing of inertial reference frames).

But travel to the past, or to instantaneously travel to any chosen moment in time is for now in the realm of fantasy. And there’s some pretty good fantasy about this. From H.G. Wells to Back to the Future, and a gazillion other stories and movies spanning Dr Who to Star Trek to Bruce Willis.

Despite gallant efforts to root some of these stories in known physics there’s an aspect of all fictionalized time travel that has, to my knowledge, been consistently overlooked. I call this the ‘spatial problem’ of time travel.

Let’s do a quick thought experiment. Imagine you have a nifty time machine and decide to pop one month into the past. Maybe you need to avoid a parking ticket or a particularly debilitating curry, the reason is not important. In a typical story you’ll appear at precisely the same location, just a month earlier. But how on earth does your time machine (or whatever device/spell/weird alien entity you’re using) get you to that unique physical place?

On Earth’s surface we’re in constant motion. The planet’s spin has us racing around at about 1,600 kilometers an hour at the equator. The Earth is orbiting the Sun at an average of 110,000 kilometers an hour. The Sun is currently moving relative to the center of the Milky Way galaxy at about 828,000 kilometers an hour, and our Local Group of galaxies is plunging through the cosmos at a velocity of about 2.4 million kilometers an hour relative to the cosmic microwave background. That radiation field offers a way to establish a universally agreed-upon measure of rest or motion. But space is of course expanding, so on very large scales no physical object can be said to be truly at rest with respect to others – it may just be equally not at rest in all directions.

That’s gets us back to our time travel experiment. To go back 1 month, and to appear at the same place – your favorite coffee shop, your dining room, your DeLorean trundling down a main street – you must also move a significant amount of physical distance. And you must do this extremely accurately. This is the spatial problem.

Let’s take the Earth’s motion around the Sun. A month of orbit corresponds to moving in an arc of approximately 78 million kilometers. During that same period the entire solar system will have also moved approximately 600 million kilometers around our galaxy, and our entire Local Group of galaxies will have swept through about 1.7 billion kilometers of space relative to the cosmic microwave background. Not only do you need to traverse those kinds of distances, you need to get it correct to within a part in a trillion.

In other words: your time travel device has to be exceedingly good at figuring out where in the universe to place you, not just when. 

Now I know that it’s silly to pick a fight with fiction. After all, who cares? We know this is all for entertainment and a little intellectual provocation. But in this instance there are some genuinely intriguing things to consider, even if entirely hypothetical.

On the one hand it’s scientifically interesting to think about how to actually deal with coordinates in a real, and very dynamic universe. Where you are at this instant is not a fixed point in any cosmic sense. Indeed, you follow a quite complex trajectory through the universe, and thanks to complicated gravitational and mechanical interactions and behaviors this trajectory is probably not fully predictable. Earth’s spin varies, its orbit varies subtly over very long timescales, and even our intergalactic motion will evolve as other galaxies and mass concentrations get closer or further away over time. 

It’s also fun to consider that this could provide an answer to the question of why, if time travel is ever invented, we haven’t been visited by beings from the future (you know, right before certain presidential elections, or other key moments). Perhaps the reason is that no one has (ever) solved the spatial problem, and the cosmos is littered with time travelers adrift between the stars and galaxies.