You, Grandpa, and Time Travel Paradoxes

The idea of time travel is possibly one of the most intriguing topics in modern science. If it becomes a reality it could have a fundamental effect on our world- but nothing comes without its price. Time travelers will have their fair share of troubles and paradoxes – not to mention one very angry grandparent.

A little over a hundred years ago, no one would have taken seriously the idea of exploring the possibility to travel back and forth through time. Only after Albert Einstein published his theory of relativity did scientists begin to pay attention to this field. According to the theory of relativity time is “fluid,” or flexible: time can slow down or accelerate, as well as condense or extend like a spring. And if time is so flexible, perhaps it can also be bent, or reversed? Of course, intuitively, time travel seems to most of us like an unrealistic and impossible idea, belonging only in science fiction books, but anyone who ever studied quantum theory knows how bizarre the behavior of small particles such as electrons are. Let’s take, for example, the phenomenon called “tunneling”: according to the quantum theory, if we close an electron in a sealed container it might suddenly appear outside the container, just like that; pass through the walls of the container as if they didn’t exist. Tunneling is also an absurd idea, but computer chip designers must take it into consideration daily as chip dimensions get smaller and smaller.

Physicist Niels Bohr once said that if a person doesn’t find the quantum theory weird, surely he doesn’t understand it. Of course, no physicists study time travel; they all research “closed timelike curves,” which are (of course…) something completely different. If you declare that you are trying to build a time machine, you will find that there is only one substance in the universe that can travel faster than light, and that is the letter from the administration of your university informing you that your research funding has been discontinued.

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.

Throughout the years several ideas have been raised concerning time travel. Some scientists believe flying at a high velocity in the vicinity of a black hole might send the astronauts into the past. Other physicists, who probably find the above idea ridiculous and impossible, suggested creating a worm hole in space and passing through it to the other side. Surely there are further similar ideas. In this column I will not focus on the theoretical ideas for time travel, for several reasons. First – the validity of these ideas is controversial, since there is a chance that some of the basic laws of the quantum theory might prevent them from being possible. There is still no perfect theory that can unify the force of gravity with quantum theory, and until such a theory emerges any idea based on objects with strong gravity (such as black holes or worm holes) are considered to be unfounded hypotheses. Second – even if one of these ideas might be valid, it would be extremely difficult to accomplish and would probably not be relevant to our period in time.

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)
Achilles and a tortoise
(Credit: Weber State University)

A classic example for a paradox that is not related to time travel is widely known as “Achilles and the tortoise,” or “Zeno’s Paradox.” In this example, Achilles and the tortoise are racing against each other. Achilles should be the winner, naturally- so he gracefully lets the tortoise have a head start. After some time, Achilles starts running after the tortoise- but is unable to catch up with him. At each period of time, Achilles crosses a certain distance, but the tortoises moved ahead by some small (but not zero) distance. If so, Achilles can never out run the tortoise! It will always be some small distance ahead of him.

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.

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