We, as humans, just love time travel. Just imagine the possibilities! You could wander in the woods of times long gone amidst the dinosaurs, experience ancient civilizations for yourself or perhaps sit in on one of Shakespeare’s original performances. Or, on the other hand and equally fascinating, travel to the future and partake in the wonder of what you’ll see there: flying cars? A world ruled by cyborgs? Actually stable, affordable wireless internet?
Storytellers, too, love a sprinkling of time travel every once in a while, simply because of the wonderful way that no matter how much things change, they inevitably also, in some way, stay very much the same. But beyond our dreams of being taken away by a madman with a box, is there any fact to the fiction? What is the reality behind our dreams of time travel?
Anyone order a TARDIS?
Surprisingly enough, physics has quite a lot to say about this. Our good friend Albert Einstein was one of the first to make some major contributions to our understanding of what time actually is, most importantly by formulating his theories of relativity: Special Relativity (SR) and General Relativity (GR). Both allow time travel in their own specific way and I’ll be going over both in the remainder of this article. This is going to get a bit hairy, so hold on tight and stay sharp!
To be able to understand Special Relativity at all, it’s important to establish the fact that the speed of light is absolute1. As weird as it might be, everyone sees a ray of light moving at the same speed, no matter the speed at which you’re moving relative to that light. To explain why this is strange, let’s draw upon the famous example of a ray of light being shot off inside a speeding train made entirely of glass (thankfully, we don’t have to deal with sensible building constraints in thought experiments). If I’m the one beaming out the light, I see it moving away from me at the speed of light, which I’ll call c. However, someone who’s on solid ground next to train, it turns out, also sees it moving at this same speed c. This is weird, isn’t it? If I threw a baseball, for example, the observer outside the train would see the baseball moving at the speed of the train (the speed at which I and the baseball were already moving, and which I’ll be calling v from here on out), with the speed of my throwing (the speed I’m giving to the baseball in addition to the speed we already had) added to it. As it turns out, light always travels at the same speed, no matter how much we try to speed it up.
The above might imply that the reality of two observers who move relative to each other is simply not the same. As it would seem to be the case that we are part of the same reality, we’d really like to patch this up somehow. It turns out there is really only one practical solution to this problem: distances and times2 are not necessarily the same for different frames of reference! For observers moving relative to us, time runs faster and distances are shorter – once you start going very fast the people around you start appearing very slow and very thin.
As such, we can travel through time by going very fast, in a sense: everything else would seem to age much faster, and you’d be traveling to the future! “But surely, mister president, you can’t be serious?” Actually, this really works! You could travel away from the earth with something like three-quarters the speed of light, and turn around a light-year or so away, and when you’d get back the earth would have aged much more than you would have! The only problem with this is that you need to accelerate yourself to such speeds first: the greatest speed any object sent out from Earth has ever achieved relative to the sun, for example, is 250.000 km/h. This is still a factor 4000 or so smaller than the speed of light – and still much, much too small for us to notice any relevant effects from Special Relativity beyond the milli-, or even microsecond range. So what about that other theory, then: General Relativity?
Whereas SR deals with how observers are influenced by going at speeds close to the speed of light, General Relativity (GR) instead deals with the very nature of gravity. Imagine being inside a closed box in outer space. If the box is moving at a constant speed, we don’t notice a thing: the very foundation of SR is the fact that the laws of physics are the same for all observers moving at a constant speed. If we’re moving at a constant speed, we might as well not be moving at all3. However, once we start to accelerate, the rules start to change on us. Imagine accelerating upwards, still inside our closed box: the box would start to go upwards faster, and faster, and we would lag behind because of our inertia: we’d be pushed to the floor. “Well gee, that sounds an awful lot like gravity!” Aha! This was what Einstein himself called his ‘happiest thought’ (which in turn tells us a lot about ol’ Albert): the fact that the downward force of gravity and upward acceleration are in essence indistinguishable.
This has all sorts of very, very weird effects4, but for our purposes only one is really relevant: clocks that are being pulled on harder by gravity run slower. As the force of gravity a heavy object exerts on you scales inverse to your distance to the heavy object (that is, gravity gets weaker as you get further away), this means that being closer to heavy things makes your clock go slower. This effect is quite beautifully observed by astronauts living on a space station: every day, their clocks desynchronize with our earth-bound clocks by a second or so!
“But wait, does that mean that I’m ‘traveling through time’ right now?”
Well… not really. While, technically, you ‘gain’ a few seconds every day on a satellite zooming around the earth, that’s a negligible effect: to have the satellite gain an extra year on you, you’d have to wait for about a hundred thousand years. In the end, while it does provide us with a way to ‘travel through time’, it’s hardly a TARDIS. And so, sadly, we come to the conclusion that our dreams of traveling to the future are, at least currently, condemned to the future itself.
But what about the ultimate brain-crunching mother of paradoxes? What about traveling to the past? Amusingly enough, that one does not work because of exactly the reason you’d think it doesn’t: it breaks the laws of causality, which is more of a physical reality than you might realize. You see, as you start going faster and faster SR dictates that your clock starts running slower, and slower, and slower… until you hit the speed of light, at which your clock stops and freezes irreversibly. Your clock speed becomes zero – or, in other words: time ceases to pass for you at all5. But what happens when we go to the forbidden realms that lie beyond Einstein’s paradigm? What if we start traveling faster than light? With our newfound knowledge of SR in hand, we know that the question then becomes: what happens when we slow our clocks down even further? Precisely: and we start traveling backwards in time. You would see events play out in reverse order: people dropping dead before the gun is fired, goals being scored before the player shoots, etc. However, your own clock still moves the ‘normal’ way, which means you would be able to influence things in reverse order – complete bogus by the laws of causality! This is exactly why the presumed discovery of neutrino’s moving at speeds greater than light speed was such a big deal. We (or rather, the media hype train) thought we’d discovered particles that are traveling back in time.
But why can’t you do this? Why can’t you accelerate beyond the speed of light? Simply put: because the universe is a bitch. In Special Relativity, we have to work with the fact that there exists such a thing as a finite speed limit: the speed of light. This implies that increasing speeds must eventually converge to the speed of light, c, and so the adding of speeds becomes a problem – the faster we go, the more energy we need to increase our speed, up to that coveted c, which would cost infinite energy to accelerate up to, even if we started at 99.9999999% of c! If you thought that sounded ridiculous, imagine then what it would require to accelerate to beyond the speed of light: it would take more than infinite energy. Talk about impossible.6
I hope that, today, you’ve gained some insights into the do’s and don’t of time travel: while actual ‘time machines’ are an impossibility, who knows, we might just be able to build something that launches us into the future at some point not too far from now. Though the past might be a forever-closed book to us (and a good thing too, if we are to believe many science-fiction writers) the future might be reachable at some point in, well, the future. Until that time comes, though, I’ll just sit here, traveling through time at the mundane speed of one second per second, content with my stories.
Footnotes
1. I already explored that train of thought in this post, in case you’re interested. For further reading on Special Relativity and the nature of light and it’s strange, ultimate speed, I’d direct you to Wikipedia’s fine article on the subject as a first step.
2. Which are, as can be concluded from this very theory, different aspects of the same thing: space-time!
3. Evidenced by the fact that our little planet is blazing through the void of space with a speed of roughly 100.000 km/hr – and yet we don’t notice a thing!
4. Such as light being bent by gravity despite having no mass, for example.
5. At least, that’s what we imagine happens at c; we have no actual way to determine what would actually happen at that boundary.
6. This is precisely why physicists typically define three regimes of speed: sub-light speed, light speed, and post-light speed. You can’t transition between them, because this involves dealing in infinite amounts of energy: it takes an infinite amount of energy to accelerate to c, no matter how close you are to it, which means that to decelerate downwards from c into sub-light speed, you’d have to lose an infinite amount of energy, which is impossible. The same reasoning goes for post-light speed – accelerating beyond c takes more than infinite energy, so decelerating down to it requires you losing more than infinite energy.
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