In other issues we discussed the possibility (or impossibility) of travelling faster than the speed of light. We saw that hyperdrive transport, by any method, was the equivalent of time travel: if two people move relative to each other it is always possible to define a point in space-time that is in the past for one of them and in the future for the other; a place inaccessible to both of them, unless hyperdrive travel is possible. This would make way for time paradoxes, the prospect of a universe that would contradict itself, would not be consistent. And we concluded that this was a very solid proof of the impossibility of hyperdrive travel … unless there was a way to avoid such paradoxes.
In fact, time travel does not necessarily imply paradoxes as these only occur when travelling into the past. We can travel into the future without problem, in fact, relativity itself provides several means to do so (for example, travelling at near-light speed, time itself slows down, and the traveller can spend a few minutes while years go by on the Earth). However, travelling into the past is inherently paradoxical.
One of the most famous paradoxes, and one which demonstrates more clearly that travelling into the past can produce a self-contradictory universe, is the grandfather paradox (reflected in the first instalment of Back to the Future): I take a time machine, I travel back fifty years and kill my paternal grandfather before he engenders my father. This way my father cannot be born, and cannot have me. In this case, as I do not get to be born, I cannot travel into the past, nobody will kill my grandfather, my father and I will be born, so I can travel back in time and kill my grandfather … ad nauseam (well, if we are to be rigorous, for the paradox to work I should actually kill my grandmother…).
Not all paradoxes produce contradictions; some are perfectly self-consistent, but despite this they are amazing, like the paradox of the statue, according to science-fiction writer Samuel Mines: I get into my time machine in 2050 and travel into the future, the year 2092. Upon arrival, I find a statue of myself there, with an engraving which reads: «Erected in 2051 in honour of the first time traveller». I put the statue in my time machine and I take back it as proof that I have travelled into the future, and I go back to 2050. I unload the statue to everyone’s astonishment, and in 2051 the statue is erected in my honour; a fully coherent story without contradictions of any kind. But who built the statue?
Another similar paradox is the creation of knowledge, a version of which can be found in Asimov’s novel The End of Eternity. I will tell another version here: I get in a time machine and travel to the year 3000. Once there, I find and read a famous article that solves the problem of aging, entitled «Immortality». It was published in 2050 in Nature by Luis López. I learn the theory, get back into my time machine and travel back in time, to 2050. I search for and find Luis López, I tell him about the theory and convince him to write the article? A few months later, it comes out in Nature. Again, the question remains: where did the knowledge come from
Is there any way to allow travel into the past without having paradoxes? Actually there is. But as some remedies, their side effects may be stranger than the «disease» they are intended to cure.
Films have often used ideas related to time travel and the paradoxes this entails.
One way is that every time I travel back into the past, the universe splits into two parallel universes, from that point they follow different paths. When I travel back in time and kill my grandfather, two universes are created: one in which nobody killed my grandfather (and that is the one I come from) and another where I will never be born, and never will exist, except as a traveller from another universe to kill my grandfather (and it is in this second universe where I was trapped, unable to return to my original universe). It is easy to see how the same trick can also solve the paradox of the statue..
But this creates a multiplicity (intolerable for many) of parallel universes, which can also generate curious situations. Let’s suppose that one Tuesday I decided to travel a day back in time to have a coffee with myself on Monday. Here the universe splits into two, one in which I will stop there on a Tuesday, and another where there will be two Fernandos from that Monday on. Now, in the universe with two Fernandos, on Tuesday we decide to travel to Monday and … now there are four of us!
For this reason, other proponents of the journey back in time decided to solve the paradoxes by imposing a kind of «natural law», Novikov and Lewis’ consistency (or self-consistency) principle, which basically amounts to saying that no matter how hard you try, it will be impossible –any which way– for the paradox to arise. For example, if I decide to travel back in time to kill my grandfather, something will happen that will prevent me from killing him: my gun will explode, or I will have an accident and I will be unable to commit «grannycide», or anything else. Of course, this solution is almost magical as it assumes that I am not as capable as anyone else of killing my grandfather, or alternatively that there is no free will, chaos, chance … and that the fate of the whole history of the universe is already written and sealed, from beginning to end. Something that new physics (quantum mechanics, chaos theory, and others) shows us is false.
Besides paradoxes, time travel has other problems: can a time machine travelling to the future collide with another journeying into the past? What if I put a time machine into operation inside another time machine? If I travel one day back in time, since the Earth is moving, will I end up in space? And most importantly, the Hawking paradox: if time travel is possible, where are the time tourists?
Actually, mathematics, physics and logic firmly point in one direction: it is not possible to travel back in time, nor is hyperdrive travel possible. So why are we bent on these ideas?
Because these ideas are fascinating, exciting and captivating. But that has never been a guarantee of reality…
Fernando Ballesteros. Astronomical Observatory of the University of Valencia.