Owino, Benjamin (2025) Against Spacetime Substance: A Relational Interpretation of General Relativity. [Preprint]
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Abstract
General relativity is often interpreted as describing a four-dimensional spacetime ``substance'' whose metric curvature constitutes the gravitational field. This substantivalist reading underlies familiar conceptual pictures: spacetime as a container for matter, curvature as deformation of a medium, gravitational waves as ripples propagating through a fabric, and the cosmological constant as energy stored in empty space. Yet these interpretations conflict with the mathematical structure of the theory itself. Diffeomorphism invariance, background independence, the absence of local gravitational energy, the nature of singularities, the behavior of radiation in vacuum, the alignment of inertial and gravitational mass, the origin of temporal asymmetry, and the persistent failure to quantize the metric all suggest a different ontology. In this paper I articulate a coherent relational interpretation of general relativity. On this view, the manifold is a representational scaffold, the metric encodes relational structure rather than properties of a substance, curvature expresses relational dynamics, and the Einstein equation is a global consistency condition on that structure. I argue that many of general relativity's celebrated ``paradoxes'' arise only under a substantivalist ontology, and that a relational reading dissolves them without altering the mathematics. The resulting framework presents spacetime not as a thing but as an evolving order of relations---a perspective that clarifies the conceptual foundations of gravitation and opens a path toward a relational understanding of quantum gravity.
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Against Spacetime Substance:
A Relational Interpretation of General Relativity. (deposited 20 Nov 2025 12:32)
- Against Spacetime Substance: A Relational Interpretation of General Relativity. (deposited 22 Nov 2025 14:37) [Currently Displayed]
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