On Valentine’s Day, University of California at Berkeley math professor Edward Frenkel wrote an essay in The New York Times entitled, “Is the Universe a Simulation?” It became the most forwarded essay on Facebook for the Times.
The classic science series Cosmos recently relaunched, so it seems appropriate to describe how math can help explain another aspect of our universe. Since this is “Pi Day,” such an essay couldn’t be more timely:
In the summer of 2005, students at the Massachusetts Institute of Technology hosted a conference for time travelers. Their idea was that, if time travel ever became possible, these travelers would know about the MIT meeting and attend. There were many strange and funny-looking people at the conference, but no one from the past or future came─at least, as far as we know.
The immediate question is, “Why not?” The first and most obvious answer is because time travel is impossible, as the philosopher Norman Swartz has argued. Wheelchair-bound physics phenom Stephen Hawking has said, “The best evidence that time travel never will be possible is that we have not been invaded by hordes of tourists from the future.”
But that is not the only possible answer. For instance the great logician Kurt Goedel showed that time travel into the past is consistent with accepted physics, and director Spike Lee is making a movie about a real physicist who intends to show just that, at least at the subatomic level.
A second possible answer, inspired by the Doomsday Argument that Oxford University’s Nick Bostrom has popularized, is that time travel is theoretically possible, but some cataclysmic event will overwhelm the earth─or humanity─in the near future, before anyone has a chance to invent a time travel device. Note: this is not a paid advertisement for Travelers’ Insurance.
A third possible answer to the Time Travelers’ Conference Conundrum is as follows:
Let us assume that time travel involves passage between many possible worlds, differing from one another in ways large or small: for instance, an electron near the center of Alpha Centauri in one universe is spin up instead of spin down; in another universe Napoleon wins the battle of Waterloo; etc. This is consistent with the “Many Worlds” interpretation of quantum mechanics.
One can argue that the number of possible universes is finite: There may be a googolplex particles, for instance, and so a finite number of configurations of those. We can suppose there is some “distribution” of universes where time travel is developed, and some distribution of universes where the MIT conference takes place. There is no reason to suppose that these sets of universes overlap; but, even assuming that time travel is possible, that it occurs in a universe like ours, and that every time traveler arrives at a universe where the MIT conference takes place, there is still a significant probability that, in our universe, no time traveler arrives.
The probability that time travel is possible, but no traveler arrives in our universe, is the probability that a random function from the set of universes with time travel “misses” our universe. The theory of “derangements” from algebraic combinatorics tells us that this probability tends to 1/e, approximately 0.37. So, because we really do live in a mad, mad, mad, mad world, the probability is greater than 1/3 that time travel is possible in a universe like ours, yet no traveler ever comes to our universe─at least, not to MIT.
In conclusion, the absence of time travelers at the MIT conference is not prima facie evidence that time travel is impossible.
It’s just evidence that time travelers have better things to do with their time.
Professor Jonathan David Farley is the co-founder of Hollywood Math and Science Film Consulting.