I actually intended "Time Travel in Fiction" to be a single blog post, but I wrote way more than I intended so I decided to split it up. Now, writing the second part, I remembered more interesting stuff that I had to talk about. It's funny. Sometimes I find it really hard to make myself write, but once I get some momentum it's just as hard to stop. I guess Newton's First Law of motion applies to more than just physical objects.

Timey-Wimey Stuff - Time Travel in Fiction, Part II

We usually think of time travel as purely fictional. Mostly, it is. Travel into the past is still considered impossible by most physicists, although there are exceptions (more on that later). However, travelling into the future is, with some help from Albert Einstein, perfectly plausible, as long as you have access to either a powerful gravitational field or a craft that can travel near the speed of light.

Einstein's Theories of Relativity (don't get me started on this 'just a theory' nonsense - both of them have stood up to test after test of their validity) link space and time intrinsically together. These theories are fundamental to our current scientific understanding of the universe and its history, and we use them every day. Special Relativity deals with very specific circumstances (hence the 'special'): objects that are either not moving or travelling at a constant velocity. It turns out that, in this universe full of circular motion and errant forces, that doesn't actually happen very often. So General Relativity is needed to cover the rest.

General Relativity acts as a wholesale explanation for the obscure phenomenon of gravity (perhaps you've heard of it?) while also revealing the fundamental nature of space and time. As a result it's a great deal more complicated than Special Relativity, for the same reason that coming up with a general solution to a mathematical problem is usually tougher than finding a specific solution: it has to encompass every single possible circumstance, while a specific solution has only to address a single set of conditions. Or, it's easier to plan your finances for the year ahead, knowing your current situation, than to conceive a general plan that attends to everything that could possibly happen in the next decade.

Anyway, back to time travel. Special Relativity forbids any object moving faster than c, which is shorthand for the speed of light in a vacuum (about three hundred thousand kilometres per second). But you're still free to try. As you get closer to the magic number c, a whole mess of reality-bending consequences take hold. From a stationary vantage point, your mass is seen to grow (which is the actual mechanism preventing you from reaching the speed of light - imagine trying to push a shopping trolley that gets heavier and heavier the faster you go), your length along the axis of travel contracts, and any clocks you have with you slow down. It's nothing to do with their battery life: it's because time itself, relative to a stationary observer, has slowed down. Your time literally (the proper definition of literally, as in "it really, actually does") runs slower than their time. Of course, you can't notice this. Time seems to click away as normal from your perspective. Actually, the mind-bending part of all this is that from your point of view, the observer is the one moving, so their time seems to be moving more slowly than yours, and their mass is increased. However, if you come back together with the observer and compare clocks, one of you will definitely have had a slower time of it. The one who accelerated so that you could meet again, and was hence no longer moving at a constant speed, is the one who concedes to time dilation in the end.

So you take off from Earth in a spacecraft that can travel at nine-tenths of the speed of light, zip around for a year from your perspective, then come back. 22.94 years will have passed while you were gone on this extrasolar gap year (See Calculation 1 below for full working). You've travelled two decades into the future. If you travel at 99% of lightspeed for a year instead, it'll be 71 years (Calculation 2). You can keep pushing up the decimal places on that 99%, provided you can find the energy and you don't mind gaining some weight (incidentally, assuming you weigh around 80kg and your ship is massless, that energy is 4.384×10^19 Joules (Calculation 3), three times the USA's annual energy consumption). So there's nothing preventing you from travelling as far into the future as you want (if you can hijack the United States' power stations for three years).

I don't feel entirely qualified to talk about the ways you can use General Relativity to travel into the future, since I haven't been taught about it in any formal setting, but I can talk about the general principles (pun intended). General Relativity states that your position in a gravitational field determines the rate at which time passes for you. If you're close to a massive object, time is slower in the same way as if you're moving fast. So if you travel near a neutron star or a black hole (don't go past the event horizon - that'll get you in a mess) you'll be catapulted into the future. That exact thing happened in Interstellar: they landed on a planet that was orbiting a black hole, stayed there for an hour, and it was twenty years later when they left.

You don't actually have to travel to such exotic locales to experience this. The difference in gravity between the Earth's surface and high orbit is enough to affect satellite communications. GPS satellites have to take time dilation into account when they're calculating your position because they rely on ultraprecise clocks that talk to each other and the surface. They use trigonometric calculations involving the time-of-flight of their radio signals between satellites and your phone to triangulate your position. Any difference in the clocks makes a big difference to these calculations, because radio signals travel at the speed of light, which is very high. So in order to tell you where you are, your phone has to speak to a computer thirty-five thousand kilometres above you, which uses its knowledge of time travel to give you the answer.

So travelling forwards in time is fine. Happens all the time. It doesn't violate causality, it just makes you lonely. So what about going back? It's no good getting to see the future if you can't go back to your own time to brag about it. Also, maybe you want to go back and see some dinosaurs. How could one do that?

Well, there are actually solutions to General Relativity that allow that kind of past tourism. Theoretical physicists talk about "closed time-like curves", which essentially means that, in some interpretations of Relativity, two locations in spacetime can be linked by the curvature of reality. You could have a wormhole which leads not just to another place, but another time.

A wormhole is yet another hypothetical concept that has yet to be seen in the real world. Relativity is all about the curvature of spacetime (in very, very short, the presence of mass bends spacetime, altering geometry in such a way that objects tend to move towards other objects - i.e. gravity) and wormholes are what would happen if you bend that spacetime far enough. You bend space so that there's a shortcut between two locations (see Interstellar for a succinct demonstration involving a piece of paper and a pencil). Anyway, in theory, if you could produce a wormhole (which is still hotly debated) there's nothing to stop you from accelerating one end of that wormhole, which I'll call a portal for simplicity's sake, to high speeds. Speeds, perhaps, approaching the speed of light. As I explained earlier, that'll take the accelerated portal out of sync with the stationary portal, so when you bring it back it has experienced a great deal less time than the static one. It will connect to the other portal's location, but also to a time corresponding to the accelerated portal's experience.

Let's say the accelerated portal experiences ten days in its reference frame, but a year has passed on Earth (It's doubtful whether a wormhole has ever found its way into a backpacker's souvenirs when returning from a gap year, but you could end up with all sorts of exotic contraband on a holiday to interstellar space). The portal will now lead to the other portal, but at time in which ten days has passed from its perspective. Which is three hundred and fifty days in the accelerated portal's past. Boom. You've created a time machine that leads a year into the past. Of course, you can't travel any further back than when the wormhole was first built. And you can't just pick an arbitrary date, either. The two wormholes have a fixed relationship, with a fixed temporal distance between them. You can extend that distance if you want to take your portal on another trip at high speeds or near a black hole, but you can't shrink it.

So, that all seems pretty fantastical. But it's not that far-fetched in our current understanding of physics. However, you still get all of the violations of causality and weird paradoxes that come with it. Many scientists, the great Stephen Hawking included, feel that once we've worked out how General Relativity and quantum mechanics fit together, there will be some mechanism preventing the wormhole scenario from occurring. At the moment, these two areas of physics don't fit together in the slightest. Both are demonstrably correct in their own contexts - the very large and the very small, respectively - but the idea of them working together, a theory of quantum gravity, still eludes our finest minds. Quanum electrodynamics are used in computer circuits, and General Relativity is necessary to calculate your place on the Earth, but damned if we can work out how to connect them. It's one of the largest ongoing fields of enquiry in physics. Maybe it won't even be possible to create a wormhole in the first place! Then again, maybe.

Anyway, these are the methods you, dear reader, might use to explore the future or the past. Not so much fiction in this entry, except for the fictional space all of us, physicists included, use when we develop our ideas.

See you next week!

On to Part III: Come With Me If You Want to Live

Back to Part I: Where we're going, we don't need roads

Appendix

Forgive me if I've made some mistake with these calculations. It's been known to happen. I'm also not sure if the formulae are 100% correct. They're the formulae used to calculate time dilation in special relativity, but since you would have to accelerate at some point to return to Earth, General Relativity is required for a complete description of your activities, and that dark and complex world has yet to open for me.

Calculation 1:

\( t = \dfrac{t_0}{\sqrt{(1−(\frac{v}{c})^2) }} \)

\( = \dfrac{60 \times 60 \times 24 \times 365.25\ \mathrm{s}}{\sqrt{1-(\frac{0.9×3×10^8\ \mathrm{ms^{-1}}}{3×10^8\ \mathrm{ms^{-1}}})^2}} \)

\( = \dfrac{31557600s}{\sqrt{(1-0.9^2)}} \)

\(= 7.24×10^7\ \mathrm{seconds} \)
\( = 22.94 \ \mathrm{years} \)

Calculation 2:

Using step 3 from Calculation 1:

\( t = \dfrac{31557600s}{\sqrt{(1-0.9^2)}} \)

\( = 2.24×10^8\ \mathrm{seconds} \)
\( = 70.98\ \mathrm{years} \)

Calculation 3:

K = γmc^2 - mc^2

= mc^2/√(1-(v/c)^2) - mc^2

= 80×(3×10^8)^2/√(1-0.99^2) - 80×(3×10^8)^2)

= 4.384×10^19 Joules