Paradoxes of Time Travel

In several previous posts, I have discussed various paradoxes that time travel could cause if it were possible. Travels to the future controlled from the past do not cause paradoxes. That they are possible is obvious, since we all travel to the future at a rate of twenty-four hours each day.

It is also possible to travel to the future if one is in a coma and later awakens; or through hibernation, if it were possible, which it is not at the moment, but it may become so someday; or by traveling through space at relativistic speeds, which would result in a time dilation that, upon returning to the starting point, translates into a journey to the future. This last procedure is not possible right now, but it could become so someday, apart from the technical difficulties of achieving it.

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: