Systematizing the Interpretation of Quantum Theory via Reconstruction

TL;DR

This paper proposes a reconstruction-based approach to interpreting quantum theory, anchored by an interpretation-free zone and a stratified, operational framework that encompasses formalism, experimental practice, and modelling heuristics. It argues that traditional schematic and no-go based interpretations neglect large swathes of content and biases, and shows how reconstruction can distill interpretationally relevant facts into clear postulates. By deriving quantum postulates from physically motivated principles and linking them to operational procedures, the method promises new physical principles and a more coherent metaphysical picture of quantum reality. The work also outlines practical steps for applying reconstruction to interpretation, emphasizing case studies and the integration of reconstruction results into interpretive practice.

Abstract

For a century, quantum theory has posed a fundamental challenge to philosophical thinking. On its face, it repudiates many of the key features of the mechanical conception of physical reality. However, the challenge of developing a precise, coherent alternative to that conception has yet to be met. Here, I argue that a major hindrance to the project of quantum interpretation is its existing interpretative methodologies, which suffer from a lack of systematicity in their judgements about what aspects of the theory are interpretational relevant. In particular, I argue that current interpretations tend to marginalize the informal part of the theory in favour of its formal part, and place inappropriate emphasis on the natural language component of the formalism over its detailed mathematical structure. To counterbalance these biases, I propose that an interpretation-free zone be constructed around the theory, wherein an interpreter initially adopt a descriptive stance which considers all parts of the theory, and that the results of this deliberation~(and the judgements about what facts are interpretationally relevant) are reported as part of their interpretation. I argue that the interpretation of quantum theory poses special challenges and difficulties which necessitate this interpretation-free zone, and that existing interpretative methodologies are insufficient to address them. Further, I argue that a reconstructive interpretative methodology, which harnesses the recent results of the quantum reconstruction program, provides a powerful means to identify almost all facts that could be interpretationally relevant, and naturally meets these challenges and difficulties. Moreover, I argue that the quantum reconstruction program offers a powerful way to discover new physical principles, and offers a systematic pathway to build a rich, coherent conception of quantum reality.

Figures (8)

• Figure 1: (a) Components of a physical theory (for interpretational purposes), illustrated using classical point mechanics. (b) Types of interpretational bias, with examples drawn from text.
• Figure 2: Interpretation of Conservation of Momentum.
• Figure 3: Interpretation of Maxwell's equations.
• Figure 4: Schematic overview of classical physics.. A depiction of the classical conception of physical reality prior to Maxwellian electrodynamics, based on Goyal2022c. This hierarchical conception is divided into several levels: 1. Overarching desiderata, which shape the entire conception. 2. Categories (space, time, matter, laws, mind); 3. Metaphysical and physical axioms; and 4. Physical principles which underpin Newtonian particle mechanics.
• Figure 5: Stratification in derivation of conservation of momentum. Diagram depicting the stratification achieved by derivation of conservation of momentum (based on Goyal2020 and Schutz1897). A solid line from $A$ to $B$ indicates logical dependency of $B$ on $A$. A dashed line from $A$ to $B$ indicates that $A$ rationalizes $B$; a dotted line that $B$ is a precisification of $A$.