QUANTUM IMMORTALITY AND NON-CLASSICAL LOGIC

The Everett Box is a device in which an observer and a lethal quantum apparatus are isolated from the rest of the universe. On a regular basis, successive trials occur, in each of which an automatic measurement of a quantum superposition inside the apparatus either causes instant death or does nothing to the observer. From the observer's perspective, the chances of surviving m trials monotonically decreases with increasing m. As a result, if the observer is still alive for sufficiently large m she rejects any interpretation of quantum mechanics which is not the many-worlds interpretation (MWI), since surviving m trials becomes vanishingly unlikely in a single world, whereas a version of her will necessarily survive in the branching MWI universe. That is, the MWI is testable, at least privately. Here we ask whether this conclusion still holds if rather than a classical understanding of limits built on classical logic we instead require our physics to satisfy a computability requirement by investigating the Everett Box in a model of a computational universe using a variety of constructive logic, Recursive Constructive Mathematics. We show that although the standard argument sketched above is no longer valid, we nevertheless can argue that the MWI remains privately testable in a computable universe.