[Paper Review] Bell's Theory of Beables and the Concept of `Universe'

Ian T. Durham|arXiv (Cornell University)|May 6, 2018

Quantum Mechanics and Applications4 citations

TL;DR

This paper investigates whether a universe can be a nonlocal beable within John Bell's ontological framework, arguing that if a universe is treated as a beable in a physical theory, it cannot be fundamental because it depends on underlying structures. The analysis concludes that universes modeled via the Wheeler-DeWitt equation as functionals of field configurations are beables but not fundamental, as they are defined relative to deeper entities.

ABSTRACT

From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many. Not the least of its problems is that it is a theory about the results of measurements. As John Bell once said in introducing the concept of `beables', it should be possible to say what is rather than merely what is observed. In this essay I consider the question of whether a universe can be a (nonlocal) beable and what that implies about the fundamental nature of that universe. I conclude that a universe that is a beable within the framework of certain theories, cannot also be fundamental.

Motivation & Objective

• To examine whether a universe can be considered a beable in the sense defined by John Bell’s ontological program in physics.
• To investigate the implications of treating the universe as a beable within a theory, particularly in the context of quantum gravity and the Wheeler-DeWitt equation.
• To clarify the distinction between beables and fundamentality, especially in theories where the universe is defined as a solution to a timeless equation.
• To assess whether the concept of a universe as a beable is consistent with Bell’s vision of a theory that describes reality as it is, not just what is observed.

Proposed method

• Analyzes Bell’s evolving definition of 'beables' as objective physical properties that exist independently of observation, including classical quantities like field configurations and later, more abstract entities such as fermion number density and the state vector.
• Applies Bell’s criterion—'not that such and such may be observed to be so, but that such and such be so'—to the concept of a universe as a solution to the Wheeler-DeWitt equation.
• Examines the Wheeler-DeWitt equation as a timeless, non-dynamical equation whose solutions are functionals of field configurations, suggesting such solutions could be candidates for beables.
• Uses reductio-deductivist reasoning to argue that if a universe is defined via a functional of fields, it depends on those fields, implying it is not fundamental.
• Contrasts the role of beables in standard physical theories (e.g., E and H fields in electromagnetism) with their role in quantum gravity, where the wavefunction is timeless and does not evolve.
• Evaluates the philosophical implications of treating the universe as a beable, particularly the tension between being a complete ontology and not being fundamental.

Experimental results

Research questions

• RQ1 Can a universe be considered a beable in the sense defined by John Bell’s ontological program in physics?
• RQ2 What are the implications for fundamentality if a universe is treated as a beable within a physical theory?
• RQ3 How does the timeless nature of the Wheeler-DeWitt equation affect the status of the universe as a beable?
• RQ4 Is it logically coherent to define a universe as a beable if it depends on underlying field configurations or other structures?
• RQ5 Does the concept of a universe as a beable contradict the idea of ultimate fundamentality in physical theories?

Key findings

• A universe modeled as a solution to the Wheeler-DeWitt equation, defined as a functional of field configurations, can be considered a beable within that theory’s ontology.
• Such a universe cannot be fundamental because it is defined in terms of other entities—specifically, the field configurations it depends on—making it derivative rather than ultimate.
• Bell’s notion of beables, which aims to describe reality as it is rather than what is observed, leads to the conclusion that universes as beables are not fundamental, despite their apparent totality.
• The timeless nature of the Wheeler-DeWitt equation supports the idea that the universe’s existence is independent of observation, aligning with Bell’s vision of objective reality.
• The paper acknowledges that Bell’s concept of beables evolved over time, and alternative interpretations may lead to different conclusions about the fundamentality of the universe.
• Despite being a beable, the universe is not a fundamental entity because its definition relies on a substrate (e.g., field configurations), implying a deeper level of reality.