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A Proof of Specker's Principle

Bacciagaluppi, Guido (2023) A Proof of Specker's Principle. [Preprint]

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Specker's principle, the condition that pairwise orthogonal propositions must be jointly orthogonal, has been much investigated recently within the programme of finding physical principles to characterise quantum mechanics. It largely appears, however, to lack a transparent justification. In this paper, I provide a derivation of Specker's principle from three assumptions (made suitably precise): the existence of maximal entanglement, the existence of non-maximal measurements, and no-signalling. I discuss these three assumptions and describe canonical examples of non-Specker sets of propositions satisfying any two of them. These examples display analogies with various approaches in the interpretation of quantum mechanics, notably ones based on retrocausation. I also discuss connections with the work of Popescu and Rohrlich. The core of the proof (and the main example violating no-signalling) is illustrated by a variant of Specker's tale of the seer of Nineveh, with which I open the paper.

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Item Type: Preprint
Keywords: Specker's principle, reconstructions of quantum mechanics, retrocausation, Popescu-Rohrlich boxes
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Guido Bacciagaluppi
Date Deposited: 15 May 2023 12:58
Last Modified: 15 May 2023 12:58
Item ID: 22101
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 4 March 2023

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