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Quantum Immortality and Non-Classical Logic
- Source :
- Journal of Applied Logics - IfCoLog Journal of Logics and their Applications 9(2):635-650 01 Apr 2022
- Publication Year :
- 2020
-
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 We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett's conclusion still holds within a computable universe.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.<br />Comment: 14 pages
Details
- Database :
- arXiv
- Journal :
- Journal of Applied Logics - IfCoLog Journal of Logics and their Applications 9(2):635-650 01 Apr 2022
- Publication Type :
- Report
- Accession number :
- edsarx.2007.09847
- Document Type :
- Working Paper