Closed Causal Loops and the Bilking Argument

The most potentially powerful objection to the possibility of time travel stems from the fact that it can, under the right conditions, give rise to closed causal loops, and closed causal loops can be turned into self-defeating causal chains; folks killing their infant selves, setting out to destroy the world before they were born, and the like. It used to be thought that such chains present paradoxes; the received wisdom nowadays is that they give rise to physical anomalies in the form of inexplicably correlated events. I argue against the received wisdom. I can find nothing in them that argues against the possibility (even, the probability) of time travel. The most popular examples of self-defeating causal loops are cases involving time travelers going back to kill their infant selves, or the grandfathers whose industrial success made possible the construction of their time machines, but simpler cases can be found that involve nobody doing anything, just inanimate systems behaving in familiar ways in accordance with known laws. Such cases are cleaner because they don’t introduce intuitions about freedom and agency. The following set-up – due to John Earman, and which I’ll refer to heretofore as an ‘Earman rocket’ – is an especially elegant example: Consider a rocket ship which at some space-time point x can fire a probe which will travel into the past lobe of the null cone at x. Suppose that the rocket is programmed to fire the probe unless a safety switch is on and that the safety switch is turned on if and only if the ‘return’ of the probe is detected by a sensing device with which the rocket is equipped. (Earman, p. 231) If the rocket fires, then the probe travels into the past, is detected by the sensing device, the safety switch is activated, and it doesn’t fire. If it doesn’t fire, on the other hand, no probe is detected, the safety switch remains off and the rocket fires as programmed. So, the probe is fired, it appears, if and only if it is not fired.1 It used to be thought that we could stop there, i.e., that the mere supposition of the existence of Earman rockets was by itself a conceptual absurdity and we could rule out any physical hypothesis that allowed for their construction on purely logical grounds. Nowadays it is acknowledged that that isn’t so; the argument contains a loophole. The resolution of the Synthese 136: 305–320, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.