arXiv subjects

Antonio Vassallo

Publications and source records attributed to Antonio Vassallo.

At least 19 recordsLinked to original sources

arXiv2026

General Relativity and Background Independence

General Relativity (GR) is widely regarded as a paradigmatic example of a background independent theory, a feature often taken to mark a decisive conceptual advance over its Newtonian and special relativistic predecessors. Yet the notion of background independence admits multiple formalizations, and its precise physical and philosophical significance remains contested. This chapter offers a systematic analysis of the strategies that have been proposed to capture background independence in classical spacetime physics. The discussion then turns to a central open question: whether, and in what sense, a successor theory of GR -- such as a theory of quantum gravity -- should be expected to inherit GR's background independence. Drawing on contemporary debates and a range of case studies, the chapter argues that background independence is best understood as a diagnostic and comparative tool rather than as a necessary physical requirement. The resulting perspective highlights both the conceptual virtues and the interpretive costs of eliminating background structures, and helps to explain why background independence remains an open problem in contemporary foundational research.

gr-qc↗

arXiv2025

Shape space as a conceptual space

The notion of shape space was introduced in the second half of the 20th Century as a useful analytical tool for tackling problems related to the intrinsic spatial configuration of material systems. In recent years, the geometrical properties of shape spaces have been investigated and exploited to construct a totally relational description of physics (classical, relativistic, and quantum). The main aim of this relational framework - originally championed by Julian Barbour and Bruno Bertotti - is to cast the dynamical description of material systems in dimensionless and scale-invariant terms only. As such, the Barbour-Bertotti approach to dynamics represents the technical implementation of the famous Leibnizian arguments against the reality of space and time as genuine substances. The question then arises about the status of shape space itself in this picture: Is it an actual physical space in which the fundamental relational dynamics unfolds, or is it just a useful mathematical construction? The present paper argues for the latter answer and, in doing so, explores the possibility that shape space is a peculiar case of a conceptual space.

physics.hist-ph↗

arXiv2024

A proposal for a metaphysics of self-subsisting structures. II. Quantum physics

The paper presents an extension of the metaphysics of self-subsisting structures set out in a companion paper to the realm of non-relativistic quantum physics. The discussion is centered around a Pure Shape Dynamics model representing a relational implementation of a de Broglie-Bohm $N$-body system. An interpretation of this model in terms of self-subsisting structures is proposed and assessed against the background of the debate on the metaphysics of quantum physics, with a particular emphasis on the nature of the wave function. The analysis shows that elaborating an appropriate Leibnizian/Machian metaphysics of the quantum world requires a substantial revision of the notion of world-building relation.

quant-ph↗

arXiv2024

Pure shape dynamics, self-subsisting structures, and the nature of time

The paper discusses the possible implications of the relational framework of Pure Shape Dynamics for the metaphysics of time. The starting point of the analysis is an interpretation of shapes in ontic structural realist terms, which gives rise to the notion of self-subsisting structure. The relational version of a Newtonian-particle toy model is introduced and discussed as a concrete example.

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arXiv2023

A de Broglie-Bohm Model of Pure Shape Dynamics: $N$-body system

We provide the construction of a de Broglie-Bohm model of the $N$-body system within the framework of Pure Shape Dynamics. The equation of state of the curve in shape space is worked out, with the instantaneous shape being guided by a wave function. In order to get a better understanding of the dynamical system, we also give some numerical analysis of the 3-body case. Remarkably enough, our simulations typically show the attractor-driven behaviour of complexity, well known in the classical case, thereby providing further evidence for the claim that the arrow of complexity is the ultimate cause of the experienced arrow of time.

gr-qc↗

arXiv2023

On the Prospects of a de Broglie-Bohm-Barbour-Bertotti Theory

Pure shape dynamics (PSD) is a novel implementation of the relational framework originally proposed by Julian Barbour and Bruno Bertotti. PSD represents a Leibnizian/Machian approach to physics in that it completely describes the dynamical evolution of a physical system without resorting to any structure external to the system itself. The chapter discusses how PSD effectively describes a de Broglie-Bohm N-body system and the conceptual benefits of such a relational description. The analysis will highlight the new directions in the quest for an understanding of the nature of the wave function that are opened up by a modern relationalist elaboration on de Broglie's and Bohm's original insights.

quant-ph↗

arXiv2022

Pure shape dynamics: General framework

We put forward a general framework for describing relational physical theories, which we call Pure Shape Dynamics (PSD). Elaborating on the original insights brought about by the Shape Dynamics program, PSD's novel take on relationalism is its insistence on describing any dynamical system by means of the intrinsic geometry of its associated curve in the suitable relational configuration space of the theory, namely shape space, whereby the corresponding equation of state of the curve expresses the ratio of change of one of its geometric degrees of freedom with respect to another one. The mathematical structure underlying the equation of state is a local section over a natural generalization of the unit tangent bundle, which we call shape phase space.

gr-qc↗

arXiv2022

A Proposal for a Metaphysics of Self-Subsisting Structures. I. Classical Physics

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered -- and is thus susceptible to scientific progress -- , the empirically successful structural features of the framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space.

physics.hist-ph↗

arXiv2022

The Physics and Metaphysics of Pure Shape Dynamics

The goal of this essay is twofold. First, it provides a quick look at the foundations of modern relational mechanics by tracing its development from Julian Barbour and Bruno Bertotti's original ideas until present-day's pure shape dynamics. Secondly, it discusses the most appropriate metaphysics for pure shape dynamics, showing that relationalism is more of a nuanced thesis rather than an elusive one. The chapter ends with a brief assessment of the prospects of pure shape dynamics in light of quantum physics.

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arXiv2021

The metaphysics of decoherence

The paper investigates the type of realism that best suits the framework of decoherence taken at face value without postulating a plurality of worlds, or additional hidden variables, or non-unitary dynamical mechanisms. It is argued that this reading of decoherence leads to an extremely radical type of perspectival realism, especially when cosmological decoherence is considered.

quant-ph↗

arXiv2021

Does General Relativity Highlight Necessary Connections in Nature?

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities -- qua part of a physical law -- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

gr-qc↗

arXiv2020

How Humean is Bohumianism?

An important part of the influential Humean doctrine in philosophy is the supervenience principle (sometimes referred to as the principle of separability). This principle asserts that the complete state of the world supervenes on the intrinsic properties of its most fundamental components and their spatiotemporal relations (the so-called Humean mosaic). There are well-known arguments in the literature purporting to show that in quantum mechanics the Humean supervenience principle is violated, due to the existence of entangled states. Recently, however, arguments have been presented to the effect that the supervenience principle can be defended in Bohmian mechanics. The key element of this strategy lies in the observation that according to Bohmian mechanics the fundamental facts about particles are facts about their spatial locations, and moreover, for any proper subsystem of the world its state may non-trivially depend on the spatial configuration of the rest of the universe. Thus quantum-mechanical states of subsystems do not represent their intrinsic properties but rather characterize their relations with the environment. In this paper we point out the worry that this Bohmian strategy --known as Bohumianism-- saves the letter but not the spirit of the Humean doctrine of supervenience, since it prima facie violates another seemingly important Humean principle, which we call Strong Supervenience and whose denial implies the existence of necessary connections among distinct individuals. We argue that the best defense for Bohumians is to question the fundamental existence of complex physical systems and their states by treating any reference to them as a convenient description of the underlying collection of Bohmian particles. We consider several pros and cons of this strategy.

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arXiv2019

Dependence Relations in General Relativity

The paper discusses from a metaphysical standpoint the nature of the dependence relation underpinning the talk of mutual action between material and spatiotemporal structures in general relativity. It is shown that the standard analyses of dependence in terms of causation or grounding are ill-suited for the general relativistic context. Instead, a non-standard analytical framework in terms of structural equation modeling is exploited, which leads to the conclusion that the kind of dependence encoded in the Einstein field equations is a novel one.

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arXiv2019

The Metaphysics of Machian Frame-Dragging

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding.

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arXiv2016

Relationalism about mechanics based on a minimalist ontology of matter

This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as example: the Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations instead of committing us to additional elements of the ontology. The alternative theory strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology.

physics.hist-ph↗

arXiv2016

Leibnizian relationalism for general relativistic physics

An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple and being informative.

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arXiv2016

A Metaphysical Reflection on the Notion of Background in Modern Spacetime Physics

The paper presents a metaphysical characterization of spatiotemporal backgrounds from a realist perspective. The conceptual analysis is based on a heuristic sketch that encompasses the common formal traits of the major spacetime theories, such as Newtonian mechanics and general relativity. It is shown how this framework can be interpreted in a fully realist fashion, and what is the role of background structures in such a picture. In the end it is argued that, although backgrounds are a source of metaphysical discomfort, still they make a spacetime theory easy to interpret. It is also suggested that this conclusion partially explains why the notion of background independence carries a lot of conceptual difficulties.

physics.hist-ph↗

arXiv2016

On the Conceptual Issues Surrounding the Notion of Relational Bohmian Dynamics

The paper presents a program to construct a non-relativistic relational Bohmian theory, that is, a theory of $N$ moving point-like particles that dispenses with space and time as fundamental background structures. The relational program proposed is based on the best-matching framework originally developed by Julian Barbour. In particular, the paper focuses on the conceptual problems that arise when trying to implement such a program. It is argued that pursuing a relational strategy in the Bohmian context leads to a more parsimonious ontology than that of standard Bohmian mechanics without betraying the original motivations for adopting a primitive ontology approach to quantum physics. It is also shown how a relational Bohmian approach might clarify the issue of the timelessness of the dynamics resulting from the quantization of a classical relational system of particles.

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