Quantum Immortality and Non-Classical Logic

Abstract

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 must reject 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 the observer will necessarily survive in the branching MWI universe. 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 We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we nevertheless can argue that Everett's conclusion still holds within a computable universe. Thus we claim that since Everett's argument holds not only in classical logic (with embedded notions of continuity and infinity) but also in a computable logic, any counter-argument claiming to refute it must be strengthened.