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Currently, time travel research is performed only by theoretical physicists. We therefore cannot honestly expect a real functional time machine any time soon – after all, these are theoretical physicists. Even if they had the ability to invent a time machine, they would have probably crashed it while trying to get it out of its parking space.
 

Time travel using a wormhole

That being the case, in this column I will talk about paradoxes of time travel. In other words, had a time machine been possible and available here and now, what problems and strange paradoxes would arise.

What is a paradox? A paradox is a contradiction. In a paradox, we start with a basic postulation and by following a series of logical steps we end up with a conclusion that contradicts our basic postulation.

Achilles and a tortoise (Credit: Weber State University)

This paradox is solved with the use of a mathematical tool called "Limit,” which basically puts a finite value on how far the tortoise can go in a given time. This solution merely gives a mathematical description of some facts of life that we already know are true. But time travel paradoxes are different: we do not have any experience with time travel; hence we can not easily solve its paradoxes.

The idea of time travel is especially enticing for science fiction writers. Time travel allows the writer to begin the story from a familiar starting point that the reader can identify with – for example, a bored high-tech worker that spends his days in front of a computer monitor – and then transfer the reader to another, much more exciting reality, thousands of years into the future or millions of years backwards to the dinosaur era. Time travel also allows the writer to speculate about possible future technological advances and other topics that science fiction likes to deal with.

But good ideas do not come free of charge. Time travel trails many paradoxes and logical problems that the writer or screenwriter must deal with and solve, or hope that the special effects department does an exceptionally good job and then no one would notice the problem.

One famous time travel paradox is the “grandfather paradox.” The name “grandfather paradox” was given to this problem because the general idea is as follows: the time traveler goes back to the past and shoots his young grandfather. Since the grandfather is dead, the father of the time traveler was never born, meaning that the time traveler himself doesn’t exist. But the traveler exists, otherwise who shot the grandfather? That is the paradox. Interestingly, almost all the examples of time travel paradoxes include killing a family member. Sometimes you travel to the past to stab your grandmother, sometimes you run over mom; some people will even take the trouble to kill their young selves. When reading about time travel paradoxes, it seems like no one goes back to the past to enjoy a good meal in a restaurant that already closed – everybody tries to settle a debt with their grandfather for not giving them enough Christmas money.

McFly and Doc (Credit:Amblin Entertainment)

The screenwriters of “Back to the Future” decided to gracefully ignore the chaos theory, but scientists did try to deal with this paradox. One possible solution is the “many-worlds interpretation.” According to this theory, when a time traveler goes back to the past and changes something – be it a dramatic or a tiny change – the universe splits at that moment into two parallel universes.

One universe is the original one, where nothing has changed and everything remained the same. If we continue the previous example, this would be the universe where Marty couldn’t save his father from the car accident. The critical point for understanding this solution is that the time traveler always remains in the second universe, the universe where the change happens. In this universe, he really was never born, but there is no paradox since Marty comes from a parallel universe, where the accident did take place, the parents fell in love, and everything continued as normal.

Some people think that this solution, splitting into two parallel universes, voids the meaning of time travel because the traveler cannot really affect “his” universe, the universe from which he came. If, for example, the time traveler went back in time in order to kill Hitler and prevent the Second World War, he cannot truly prevent the war. There will be two parallel universes, one in which the war, holocaust, and suffering remain exactly as they were – and a parallel universe where none of it happens.

Another paradox that might arise from time travel is the “causality paradox.” Common sense tells us that everything has a reason. If every night I open the refrigerator and devour an entire box of ice cream and later at work people tell me I’ve gained weight, obviously there is a reason. I have big bones. Genetics.

Skynet in a time loop? (Credit: Hemdale Film)

There is another paradox that is derived from the causality paradox. Let’s suppose I went back to the past, searched for young Ran Levi, gave him an ice cream spoon and told him “Here, at least eat the ice cream like a decent human being and not with your hands.” Ran keeps the ice cream spoon all these years, then goes back to the past to give the spoon to young Ran. Beyond the question of “Where did the spoon originally come from?” we must ask ourselves, “What will happen to the spoon in the future?” In each of these cycles, the spoon becomes older and damaged. Another cycle goes by and another one, and the spoon rusts, becomes crooked – and eventually I have to go back to eating the ice cream with my hands. If this is the case then this loop cannot last forever, even though it seems there was never a starting point and it always existed.

Roger Penrose and the cosmic censorship hypothesis (Credit: Brookhaven Lab/ Jerry Bauer)

Let’s return to “Back to the Future” and Marty McFly. In one of the scenes from the first movie Marty goes up on stage and plays the song “Johnny B. Goode” by Chuck Berry. In the second movie we see Marty, the one who went back to the past at the end of the first movie, climbing the scaffolds above the stage looking at Marty from the first movie playing the song. Therefore, at the same time, in the same universe, there are two identical copies of Marty. This is strange; it might even raise the production cost of the movie, but it is still not the paradox.

The real problem begins when we realize that in principal, we can create an infinite number of Marty McFlys by this method. For example, if every time future Marty goes back to the past a few seconds earlier than the previous Marty, theoretically, the universe could be filled with identical clones of Marty McFly until there is no space for anything else.

By the way, the screenwriters managed to squeeze into this single scene, in which Marty plays on stage, two other paradoxes simultaneously. At the same time Marty plays “Johnny B. Goode,” one of the band members phones his uncle, Chuck Berry, and tells him about the cool song – a song that Chuck Berry ends up singing himself. We have here the causality paradox since it seems that nobody wrote the song “Johnny B. Goode” and it always looped between Marty and Chuck. Later in the scene Marty’s future mom asks Marty for his name, and when he answers she falls in love with the name and decides to call her future son by that name. The paradox here is clear, I think.

Twelve Monkeys having a causality paradox (Credit: Atlas Entertainment)

Dr. Igor Novikov (Credit: University of Copenhagen)

The discussion about time travel paradoxes is long and complex and in this column I only covered a small portion of it. For example, some scientists claim that if time travel is possible, it will only be possible to go back in time up to the point when the time machine was invented and that’s why we don’t see tourists from the future around us. Some science fiction writers predict that if a time travel paradox occurs, the universe will decide it’s had enough and commit suicide. We probably won’t get an answer to our questions... at least not in the near future. If time travel were possible, what would you change in your own past?...

Special thanks to Pazit Polak for translating the column from the original Hebrew version.