What is the Bootstrap Paradox?

If you were watching Doctor Who last weekend, you’d have seen a little about paradoxes. In the opening to ‘Before the Flood’, Peter Capaldi’s Doctor gives us a quick run-through the Bootstrap Paradox, one of the most famous paradoxes in time travel. Trying to picture the problems this paradox causes is a challenge that forces us to reason out the intricacies of time travel. So what exactly is this paradox, and what is the science behind it?

In the episode, the Doctor proposes a brain teaser. Imagine a time traveller who loves Beethoven, and so travels back in time to meet his hero. When he’s there, he discovers that the composer has written and will never write any of the music attributed to him. In desperation, the time traveller decides to copy out all of his favourite tunes for Beethoven. The plan is successful, and Beethoven’s place in history is secure. Then, several centuries later, the time traveller listens to Beethoven and decides to meet him. The question the Doctor offers is this one: who really wrote Beethoven’s Fifth Symphony?

This paradox causes several ontological problems, as it shatters our very concept of being. We can imagine time broadly as a straight line, denoting a series of events which come one after the other. Imagine throwing a ball at a window, charted as a timeline. I pick up the ball, I throw the ball, the ball hits the window – it’s a logical sequence of cause and effect events, in which each event is contingent on the prior ones. I cannot throw the ball before I’ve picked the ball up, for example. If we gave every event a letter, we’d have A, then B, then C. It’s simple to picture.

Now, imagine trying to picture the Beethoven story in the same way. Instead of a straight line, what is being described is a circle, in which event A leads to event B, which then leads back to event A. We cannot choose a start point because there is no clear start point – every stage of the journey requires something coming before it. The issue is that such a system bypasses the question entirely. This is a ‘causal loop’, which simply is and requires no further explanation. Using this set-up is a way of saying the concept of a beginning doesn’t matter.

The distortion of space-time necessary for travelling to the past pretty much renders it impossible

One approach is to say that Beethoven wrote the music, and then we wind up in an alternate timeline in which something derailed history. The time traveller is then forced to step in and repair the damage – so, Beethoven didn’t write the music in this particular timeline, and that’s why we have ambiguity. But there’s another problem here. No matter how many timelines we create, there still needs to be one in which Beethoven wrote his music, and that’s what we’re trying to prove in the first place.

The science that essentially shuts down time travel helps deal with this paradox. Einstein’s theory of general relativity tells us that we’ve got almost complete freedom of movement into the future, but the distortion of space-time necessary for travelling to the past pretty much renders it impossible. Such breeches include a disruption of the Law of Causality, as described above, and the Law of Entropy – systems always flow from a state of order to one of disorder, and information trapped in the system would necessarily decay or vanish.

In Back to the Future, Marty McFly plays ‘Johnny B. Goode’ and helps inspire Chuck Berry to write it, thus creating another Bootstrap Paradox. But, fun though the sequence is, the science means it can’t have happened – time travel and logic don’t mix, and attempting to reason out these paradoxes will only hurt your head.