Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics II: Concepts and Axioms

Abstract

Having analyzed the formal aspects of Wallace's proof of the Born rule, we now discuss the concepts and axioms upon which it is built. Justification for most axioms is shown to be problematic, and at times contradictory. Some of the problems are caused by ambiguities in the concepts used. We conclude the axioms are not reasonable enough to be taken as mandates of rationality in Everettian Quantum Mechanics. This invalidates the interpretation of Wallace's result as meaning it would be rational for Everettian agents to decide using the Born rule.

References in corpus (11)

• Classical Equations for Quantum Systems
• Quantum Theory of Probability and Decisions
• On the Consistent Histories Approach to Quantum Mechanics
• Probabilities from Entanglement, Born's Rule from Envariance
• Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics
• Quantum Probability from Decision Theory?
• Discreteness and the origin of probability in quantum mechanics
• When Worlds Collide: Quantum Probability From Observer Selection?
• Position eigenstates and the Statistical Axiom of Quantum Mechanics
• Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects
• On the Nature of $a_k^{\ast }{a}_k$ and the Emergence of the Born's Rule

Cited by in corpus (5)

• Understanding quantum mechanics: a review and synthesis in precise language
• Quantum fractionalism: the Born rule as a consequence of the complex Pythagorean theorem
• Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects
• The Born rule
• Derive the Born's rule from environment-induced stochastic dynamics of wave-functions in an open system