Quantum Immortality and Non-Classical Logic

TL;DR

This paper examines the implications of quantum immortality within a computable universe modeled by constructive logic, showing that Everett's argument favoring the many-worlds interpretation remains valid under computability constraints.

Contribution

It extends the Everett Box thought experiment to a computational universe using constructive logic, demonstrating the robustness of Everett's argument against non-MWI interpretations.

Findings

Everett's conclusion holds in a computable universe.

Standard arguments against non-MWI are strengthened under constructive logic.

The analysis bridges quantum interpretation debates with computability theory.

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 We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett's conclusion still holds within a computable universe.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