The possibility of travelling in time continues to capture our imaginations. A sizeable proportion of science fiction – in film, TV and novels – involves the idea in some form or other. The threat of paradox resulting from loops in time is well-known and endlessly puzzling. But our familiar conception of time travel is actually remarkably recent - it emerged only in the 1880s and 1890s in fiction such as H.G. Wells’ The Chronic Argonauts and Mark Twain’s A Connecticut Yankee in King Arthur's Court.
The root cause of this sudden emergence is often traced to what John Bigelow has called the ‘radical spatialisation of time’: the new view of time as a parameter associated with a co-existing set of ordered instants, or time-line. This picture of time as an extended, ‘spatialised’, dimension came out of mathematical physics, in which it is indispensable to more abstract forms of theorising about the state of the universe. What is perhaps more unexpected is that thinking creatively about time travel also has potential to feed back into physics.
In 1949, the ‘Gödel solutions’ to the equations of general relativity were discovered. The possible universes described by these solutions contain closed time-like curves ¬– paths through time which circle around to bring you back to the very same time at which you started out. Thinking about such cases helps to bring into sharp focus the relation between two of our most fundamental physical theories – general relativity and quantum mechanics. The tension between these two theories is probably the biggest conceptual problem in fundamental physics. These theories are incredibly successful in their own domains, but continue to resist unification.
One important aspect of the tension between general relativity and quantum mechanics involves what happens when a quantum system travels around a closed time-like curve.
Quantum mechanics seems to predict that the system cannot, in principle, end up in exactly the same state in which it started out. A quantum system embedded in a Gödel universe would give rise to the same kind of paradox as your travelling back in time and successfully killing your own grandfather. In such cases the usual rules for ascribing quantum probabilities break down: they seem to ascribe some positive probability to reality’s being inconsistent with itself, and this seems impossible. Any acceptable solution to the problem needs to provide a non-paradoxical way of ascribing probabilities to histories of quantum systems. And here, we come full circle (like a time traveller on a closed time-like curve) to questions that regularly arise in science-fiction literature.
In a spontaneous causal loop case, your older self might arrive from the future and hand you the blueprints to a time-machine, with strict instructions to use them to later travel back and deliver a copy of the blueprints and thereby complete the loop. What, if anything, caused the loop to occur? From where, if anywhere, did the information on the blue-print come? What was the probability of such a loop occurring? Answering these questions could help us to make sense of quantum mechanics on closed time-like curves. And of course, if we knew how to manipulate the probability of causal loops occurring, we could bring about time travel directly. Sadly, the signs from cosmology are that our universe is of a kind which will always keep this beyond our grasp. Nonetheless, thinking through these issues has the potential to improve our best philosophical theories of the nature of time and probability, and to cast some light on deep questions in physics.
The project ‘Time Travel and Probability’, led by myself and Nikk Effingham and supported by a grant from the New Agendas in the Study of Time project at the University of Sydney, is helping to improve our understanding of these puzzles. A forthcoming workshop at Birmingham in May will bring together some of the world's leading researchers to discuss them. Nikk is currently working on a book about time travel that focuses on the probability (or otherwise) of various different kinds of spontaneous causal loops, and on whether it makes sense to ascribe non-zero probability to impossible outcomes. (See his blog post for a taste of the exotic variety of possible cases!)
I am working on the explanatory and metaphysical issues that arise from the puzzle of quantum mechanics on closed time-like curves; I'm especially interested in the potential consequences for constraints on the initial quantum state of the universe. Time travel, surprisingly enough, is not just a subject of idle speculation.
Dr. Alastair Wilson is a Birmingham Fellow in the Department of Philosophy