What Grounds Dimension? Dynamical Accessibility and Ontological Commitment in Physics
Abstract
Abstract Dimension is indispensable to modern physics, but formal indispensability does not establish ontological fundamentality. This paper asks what warrants the passage from representing physical phenomena within a dimensional structure to treating dimension as an independent and explanatorily prior feature of reality. It distinguishes mathematical description, physical realisation, and ontological fundamentality, arguing that evidence for dimension is invariably obtained through motion, propagation, scaling, interaction, and the number of dynamically accessible directions. A thought experiment involving a four-dimensional space of dynamical rank three shows that geometric independence and dynamical independence need not coincide. The argument is then developed through the inverse-square law, classical mechanics, general relativity, quantum field theory, string theory, effective low-dimensional systems, spectral dimension, and the Navier–Stokes equations. These cases reveal that dimensional labels acquire physical content through the organisation of processes rather than through an independent observation of dimension itself. The paper therefore proposes a positive criterion: dimensional attribution gains ontological weight only when its physical realisation is grounded in dynamically accessible structure and cannot be exhausted by representational usefulness. Dimension is not an established ontological ground of physics, but a presupposition whose justification remains…
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