Landsman, Klaas (2020) Indeterminism and Undecidability. [Preprint]

Preview

Text FQXiEssay2020Landsmanv2.pdf Download (448kB) | Preview

Abstract

The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e. almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Landsman, Klaas
Keywords:	quantum mechanics, determinism, randomness, hidden variables
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics
Depositing User:	Nicolaas P. Landsman
Date Deposited:	24 Nov 2020 23:57
Last Modified:	24 Nov 2020 23:57
Item ID:	18441
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics
Date:	24 November 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/18441

Available Versions of this Item

• Indeterminism and Undecidability. (deposited 24 Nov 2020 23:57) [Currently Displayed]

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item