Loops and the geometry of chance

Abstract

Suppose your evil sibling travels back in time, intending to lethally poison your grandfather during his infancy. Determined to save grandpa, you grab two antidotes and follow your sibling through the wormhole. Under normal circumstances, each antidote has a 50% chance of curing a poisoning. Upon finding young grandpa, poisoned, you administer the first antidote. Alas, it has no effect. The second antidote is your last hope. You administer it—and success: the paleness vanishes from grandpa's face, he is healed. As you administered the first antidote, what was the chance that it would be effective? This essay offers a systematic account of this case, and others like it. The central question is this: Given a certain time travel structure, what are the chances? In particular, I'll develop a theory about the connection between these chances and the chances in ordinary, time‐travel‐free contexts. Central to the account is a Markov condition involving the boundaries of spacetime regions.