What does mathematics say about time travel?

On September 21st, an article on time travel by Germain Tobar and Fabio Costa was published in the scientific magazine Classical and Quantum Gravity. This article has been given considerable coverage by the mass media. The article argues that time travel would be possible if certain mathematical restrictions were fulfilled that would eliminate the paradoxes. In a previous post in this blog I explain those paradoxes and their different types.

In relation to this we must distinguish two different things:

1. What the article actually says: it only mentions the grandfather paradox (the time traveler who returns to the past to kill his grandfather as a child, which would make his own existence impossible), and specifies a mathematical equation that supposedly prevents it, without making the traveler's freedom of action totally impossible. The equation is this:

According to the authors, this equation establishes the condition for paradoxes not to happen, and intuitively amounts to forbidding the agent (the time traveler) from interacting with his own past. Let’s point out that this solution had been considered long ago by scientists and science fiction writers, as I mentioned in this other post (see what it says about the principle of consistency) although they did not propose a mathematical equation to represent that condition.

The problem is that this solution solves the grandfather paradox at the cost of making time travel impossible beyond a few generations, because over longer periods of time, practically anything travelers try to do will interact with their own past: remember that the number of ancestors of a person increases exponentially going back in time, so that, beyond twenty generations, every inhabitant of our country who left offspring is most likely to be our ancestor.

2. What the authors of the article have said in their interviews with the media, which seems to have been this (at least, that is what the media say):

To explain it, the researchers turn to another example, different from that of the grandfather: the time traveler tries to stop the current pandemic by preventing patient zero from being infected. The mathematical model assumes that the time traveler finally achieves it, but this does not change the situation: there will be another zero patient that will become contagious and cause the pandemic. Even the time traveler himself can end up infected. The conclusion of this research is that the paradox is no longer a problem to assume time travel: there are always alternatives that neutralize the possible temporal contradiction. Both Tobar and Costa emphasize that the numbers add up so that time travel time is no longer incompatible with a specific time dynamic: if we could go to the past, we shouldn’t worry about our grandfather or the coronavirus.

This explanation cheats. First, it sneaks the grandfather paradox away and replaces it by a version of the completely different predestination paradox. Second, it describes a special case of the predestination paradox where it’s easy to show that things would have happened in the same way despite the action of the traveler. But consider the case of the train crash mentioned in my previous post cited above, or the man who traveled in time to save Jesus Christ from the cross: the considerations attributed to Tobar and Costa are not applicable there. Much less would they be applicable to the grandfather paradox. Imagine the equivalent reasoning: if the traveler managed to kill his grandfather, someone else would have been his grandfather. Oh yeah? And with different genes, would that have been the same traveler?

Welcome for time travellers

The authors strongly emphasize that their formula would not affect the free will of the traveler, except in those things forbidden by their mathematical formula, equivalent to the principle of consistency. But they have forgotten the paradox I proposed in a post in this blog and in this article, signed by me and by Francisco José Soler Gil, which shows that free will and time travel are incompatible. For those who believe that free will is real, this implies that time travel is impossible.

In short: the article in question does not mathematically prove that time travel is possible; it simply offers a mathematical formulation of the principle of consistency, which has been known for a long time. This formulation is also incomplete, because it would not solve all the paradoxes, just a few.

Thematic Thread on Time: Previous Next

The same post in Spanish

Manuel Alfonseca