[Paper Review] Guildenstern and Rosencrantz in Quantumland -- A Reply to Adrian Kent

Vincent Duhamel, Paul Raymond-Robichaud|arXiv (Cornell University)|Nov 10, 2011

Quantum Mechanics and Applications1 references3 citations

TL;DR

This paper challenges Adrian Kent's critique of the many-worlds interpretation (MWI) of quantum mechanics by arguing that Kent's objections to probability in multiverse frameworks also apply to single-world models, exposing conceptual flaws in his proposed single-world alternative. Using thought experiments, the authors demonstrate that the problems Kent identifies in MWI—regarding probability and scientific confirmation—stem not from the multiverse structure itself but from deeper foundational issues in probability theory, which remain unresolved in single-world interpretations as well.

ABSTRACT

This paper is an answer to the first part of Adrian Kent's One World versus Many : the Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation [arXiv:0905.0624]. We take issue with Kent's arguments against many-world interpretations of quantum mechanics. We argue that his reasons for preferring single-world interpretations are logically flawed and that his proposed singleworld alternative to probability theory suffers from conceptual problems. We use a few thought-experiments which show that the problems he raises for probabilities in multiverses also apply in a single universe.

Motivation & Objective

• To counter Adrian Kent's argument that many-world interpretations fail to account for probability and scientific confirmation in quantum mechanics.
• To demonstrate that Kent's proposed single-world alternative to MWI suffers from the same conceptual problems as multiverse approaches.
• To show that the issues Kent raises about probability in the multiverse are not unique to MWI but stem from deeper foundational flaws in probability theory.
• To use thought experiments to illustrate that problems with probability and self-location uncertainty arise equally in single-world and many-world frameworks.
• To defend the coherence and scientific viability of the many-worlds interpretation against Kent's criticisms.

Proposed method

• The authors employ thought experiments inspired by the namesake characters from Shakespeare’s Hamlet—Guildenstern and Rosencrantz—to model decision-making under uncertainty in quantum contexts.
• They analyze Kent's argument that probabilities in the multiverse are incoherent by showing that similar incoherences arise even in single-world quantum mechanics.
• The paper uses a framework of self-location uncertainty to examine how agents assign credences in branching or non-branching worlds.
• It compares the behavior of probability assignments in both single-world and many-world models under identical experimental conditions.
• The authors apply principles of Bayesian reasoning and decision theory to assess the consistency of probability assignments in both interpretations.
• They argue that if Kent's objections invalidate MWI, they must also invalidate single-world models, undermining his preferred alternative.

Experimental results

Research questions

• RQ1 Can the problems Kent identifies with probability in the many-worlds interpretation be shown to also affect single-world quantum theories?
• RQ2 Is Kent's proposed single-world alternative to the many-worlds interpretation logically coherent in the face of self-location uncertainty?
• RQ3 Do thought experiments involving quantum observers reveal that probability problems are inherent to quantum mechanics regardless of the number of worlds?
• RQ4 Can a consistent probability calculus be maintained in a single-world quantum framework without appealing to branching or multiple outcomes?
• RQ5 Does the incoherence of probability in multiverses stem from the multiverse structure or from deeper issues in the interpretation of probability?

Key findings

• The problems Kent raises against probability in the multiverse also apply to single-world quantum mechanics, indicating that the issue is not the existence of multiple worlds but the interpretation of probability.
• Kent's single-world alternative fails to resolve the conceptual problems he claims to solve, as the same incoherences in probability assignments persist.
• Thought experiments with observers like Guildenstern and Rosencrantz show that self-location uncertainty leads to inconsistent credence assignments in both single-world and many-world models.
• The authors conclude that the incoherence in probability is not specific to MWI but stems from foundational issues in how probability is applied in quantum theory.
• The paper demonstrates that Kent's critique undermines not only MWI but also the viability of single-world interpretations, suggesting a deeper problem in quantum probability.
• The analysis reveals that the core issue lies not in the number of worlds but in the consistency of probability assignments under quantum uncertainty.