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 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 We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett’s conclusion still holds within a computable universe.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.

💡 Research Summary

The paper revisits the “Everett Box” thought experiment, a variant of the quantum suicide scenario, to examine whether the many‑worlds interpretation (MWI) of quantum mechanics can be empirically distinguished from single‑world interpretations. In the standard formulation, an observer is placed in an isolated box containing a lethal quantum device that measures a qubit at regular intervals. If the qubit is found in one state the device fires, killing the observer; if it is in the other state nothing happens. Each trial is independent, so the classical survival probability after m trials is (½)ⁿ (or more generally ∏ₖ pₖ). Consequently, if an observer survives a large number of trials, the probability of doing so in a single‑world universe becomes astronomically small, and the observer can, in principle, reject non‑MWI interpretations. This is the conventional Quantum Immortality Argument (QIA) and underlies the claim that MWI is “privately testable”.

The authors argue that this argument relies on classical notions of limits, continuity, and the existence of infinite sets—concepts that are not available in constructive or computable frameworks. They adopt Recursive Constructive Mathematics (RUSS), a form of constructive logic in which every mathematical object must be computable. In RUSS, pathological probability distributions can exist, and the usual limit argument that survival probability tends to zero as m→∞ cannot be formulated. Therefore the standard QIA collapses: one cannot claim that surviving many trials forces the observer to conclude that MWI is true.

Nevertheless, the paper introduces a new “Computable Quantum Immortality Argument”. The authors prove a “Pathological Mortality Theorem” showing that even within RUSS, there must exist at least one branch of the multiverse in which the observer survives indefinitely. The proof hinges on two facts: (1) every possible sequence of trial outcomes can be enumerated by a computable algorithm, and (2) for each sequence there is a computable predicate that determines whether the observer lives or dies at each step. By constructing a computable selection function that picks a surviving branch whenever one exists, they demonstrate that the existence of an eternally surviving world is guaranteed, independent of classical limit reasoning. Hence, MWI remains testable (albeit privately) even when the underlying logical framework is restricted to computable mathematics.

The paper also discusses why computability should be a desideratum for physical theories. It cites digital physics, cellular automata, loop quantum gravity, and other finite‑discrete models as motivations for rejecting reliance on actual infinities. By embedding physics in a computable logic, experimental design and interpretation become algorithmically verifiable, aligning with a broader philosophical stance that the universe should be ultimately knowable through finite procedures.

In summary, the authors (i) expose the dependence of the traditional quantum immortality argument on classical limit concepts, (ii) show that this dependence invalidates the argument in a constructive, computable setting, and (iii) provide a new constructive proof that the many‑worlds picture still yields an eternally surviving branch, preserving the private testability of MWI. This work therefore adds a novel dimension to the debate over quantum interpretations, demonstrating that the claim “MWI is testable” survives even under stringent computability constraints.