Publications

Previous work on relational physics by the PI:

The paper explores how self-subsisting structures in Pure Shape Dynamics support a materialist metaphysics of time. Temporal notions such as ordering and flow are presented as reducible to changes in relational configurations, without positing time as fundamental. A relational three-body model illustrates how the experience of time emerges solely from the dynamics of self-subsisting structures..

  • A. Vassallo, P. Naranjo. On the prospects of a de Broglie-Bohm-Barbour-Bertotti theory. In A. Oldofredi (Ed.), Guiding Waves in Quantum Mechanics: One Hundred Years of de Broglie-Bohm Pilot-Wave Theory, pp. 297-314, Oxford University Press, 2025.

The paper examines how Pure Shape Dynamics can accommodate a de Broglie-Bohm description of an N-body system within a relational framework. A relational implementation of the de Broglie-Bohm theory is constructed, eliminating reference to external space or time while preserving the guiding role of the wave function. The analysis highlights how this approach offers conceptual clarity regarding the nature of the wave function and supports a relationalist interpretation of quantum mechanics.

The paper extends the metaphysics of self-subsisting structures to non-relativistic quantum physics within the framework of Pure Shape Dynamics. A relational de Broglie-Bohm N-body model is presented, interpreting quantum behavior through the dynamics of self-subsisting structures without relying on external space or time. Special attention is given to the role of the wave function, arguing that its influence can be understood relationally without assigning it ontological primacy.

The paper formulates a de Broglie–Bohm model of an N-body system within the framework of Pure Shape Dynamics. The dynamics are governed by a wave function guiding the evolution of relational configurations, with no reference to external space or time. Numerical analysis of the three-body case reveals attractor-driven behavior of complexity, supporting the idea that the growth of relational complexity underlies the observed arrow of time.

The paper provides an overview of the foundations and metaphysical implications of Pure Shape Dynamics. It traces the development of modern relational mechanics from Barbour and Bertotti’s original ideas to present-day formulations, emphasizing the relational description of physical systems in shape space. The discussion highlights how Pure Shape Dynamics supports a nuanced relationalist metaphysics, offering a parsimonious framework applicable to both classical and quantum contexts.

The paper develops a metaphysical framework based on self-subsisting structures to describe classical physics within Pure Shape Dynamics. Physical systems are characterized entirely by relational configurations, dispensing with any background space or time. The approach emphasizes ontological parsimony, proposing that all physical properties and dynamics emerge from the intrinsic relations among fundamental elements.

The paper develops a general framework for describing relational physical theories under the name Pure Shape Dynamics. The dynamics are formulated in terms of the intrinsic geometry of curves in shape space, with the evolution governed by an equation of state relating geometric degrees of freedom. This relational formalism eliminates external structures, offering a fully background-independent description of physical systems.

The paper develops a relationalist account of classical mechanics based on a minimalist ontology consisting solely of matter points individuated by distance relations. Two strategies are assessed: a Humean approach that interprets standard mechanics as a descriptive tool for relational facts, and an alternative attempt to construct a fully relationalist physical theory. It is concluded that, under current formulations, the minimalist relationalist ontology is best supported by the Humean strategy without committing to additional ontological structures.

The paper examines how Leibnizian relationalism can be applied to general relativistic physics while maintaining a minimalist ontology of matter points individuated solely by distance relations. Using a Humean strategy, general relativity is interpreted as a descriptive tool for tracking changes in these relations without positing spacetime as a fundamental entity. The duality between general relativity and shape dynamics is leveraged to show how a relationalist ontology can underlie standard gravitational physics.

The paper addresses conceptual challenges in formulating a relational version of Bohmian mechanics that eliminates fundamental references to space and time. It examines the application of Barbour’s best-matching framework to construct a relational Bohmian theory with a parsimonious ontology of point-like particles and their relations. The analysis shows that such a formulation maintains the core motivations of primitive ontology approaches while offering a clearer understanding of the timelessness inherent in relational quantum dynamics.

The paper examines the compatibility of Bohmian mechanics with background independence, focusing on its formulation as a theory of point-like particles guided by a wave function. Using Barbour’s best-matching framework, the analysis shows how Bohmian dynamics can be reformulated to eliminate dependence on absolute space and time. It is argued that Bohmian mechanics can achieve background independence while preserving its core features, including non-locality and a primitive ontology of particles.