The probability of time travel

Time travel isn’t merely of interest to Dr. Who fans; philosophers and physicists alike worry about whether or not it’s possible. You probably know the sort of story that causes concern: if time travel were possible you could kill your maternal grandmother long before your mother’s conception, but if you did then how would you be born in order to go back in time and commit the dreadful act of murder in the first place?

This ‘Grandfather Paradox’ seems to tell against time travel’s possibility.Within philosophy the most famous contribution to this debate is David Lewis’s ‘The Paradoxes of Time Travel’. We could travel in time, says Lewis, but don’t think you can thereby do the impossible – that (unsurprisingly!) is something you will definitely fail to do. If you go back in time and try and bring about a paradox, then something will get in your way. Perhaps you slip on a banana peel and miss, perhaps the gun jams, perhaps you bump into the man/woman of your dreams and decide an evening of romance is better than an evening of blood-soaked ancestor murder, perhaps… well, lots of things might stop you. Lewis nonetheless assures us that one of those possibilities will definitely come about if you go back in time and try.

These questions about the possibility of time travel are still live questions, and are still discussed in the philosophical literature. What have received less attention are issues concerning the probability of time travel. The ‘Probability and Time Travel’ project headed by myself and Alastair Wilson investigates just these questions. For instance, if it’s definitely the case that something will stop you when you go back in time to kill your grandmother, and one of those things is having a stroke, does that mean that the chanceof having a stroke when travelling in time is higher than it would be if you stayed at home? Is time travel hazardous to your health? If so, how hazardous is it?

Nor are these the only questions. Time travel gives rise to all sorts of strange situations called bootstrapping paradoxes. The famous example is Robert Heinlein’s story ‘–All You Zombies–’ wherein the protagonist, who undergoes a sex change and travels through time, is both their own mother and father (the just-released Australian film Predestination is directly based on it). The person ‘comes from nowhere’; they ‘bootstrap’ themselves into existence. Or perhaps (spoiler alert!) you've seen the recent blockbuster Interstellar: there mankind is set on a course for extinction but humans from the future interact with the past to save mankind – they ‘bootstrap’ the survival of the entire human race. Similarly there are ‘information paradoxes’ where information appears only through the use of time travel e.g. a time traveler coming back from the future and telling themselves how to build a time machine.

These situations are all very interesting, and the philosophical consensus is that they are, in fact, logically possible (at least, they are if you buy into the possibility of time travel in the first place!). But how likely are they? If time machines were commonplace, should we expect lots of people to be bootstrapped people, or virtually no-one to be bootstrapped? And why focus on humans? Couldn’t a Tyrannosaur Rex bootstrap itself into existence? And why stop with actually existing things? If time travel were possible you could meet a Wookie that only exists because he’s his own mother and father. Is a Wookie as likely to bootstrap itself into existence as a human? Similarly, if mankind is about to die (and we’re certain time travel is possible) should we expect our time travelling future selves to save us? With the information paradoxes we have the same questions. Is Stephen Hawking as likely as Joey Essex to find his future self telling him how to build a time machine? Am I as likely to meet myself coming from the future telling myself how to build a time machine as I am to meet myself coming from the future telling me how to answer a tricky crossword puzzle?

Answers to these questions are difficult to figure out. They also appear to be relevant. For instance, these issues feature in various attempts to reconcile quantum physics with relativity. Such theories talk about ‘closed timelike curves’ – effectively tunnels through space and time that go back to the past – and so what one says about probability and time travel will have bearing on these difficult questions in physics. So musing about Wookies appearing from nowhere and the likelihood of slipping on banana peels is more than mere navel gazing.

The Probability and Time Travel Project is headed by Nikk Effingham and Al Wilson. It is funded by the ‘New Agendas for the Study of Time: Connecting the Disciplines’ project based at the University of Sydney. As part of the project a two day workshop took place in Sydney, 19/20 November 2014.  A second workshop is scheduled to take place in Birmingham, UK, during 2015.