Observer equivariance as a Constraint Architecture for Physical Theory

Gustaf Ullman

Published May 11, 2026• 0 citations

Abstract

This paper argues that observer equivariance is best understood not merely as an interpretive motif attached to particular physical theories, but as a higher-order constraint on the admissible form of physical theory. If physical law is to count as genuinely public, it must be transportable across admissible changes of perspective without loss of objective content. On this view, observer equivariance constrains not only the covariance of equations, but also the admissibility of representational frameworks, the structure of weighting schemes, the role of compatibility conditions, and the interpretation of residual freedom in theory construction. The argument is synthetic, drawing together earlier work on shared physical law, translational and spectral form, path-integral measure selection, Born-type weighting, and Machian boundary constraints. Three levels of claim are kept distinct throughout: conceptual claims about the public form of physics, partial formal results (such as orbitwise rigidity of weighting schemes and conditional uniqueness of quadratic weighting under additional structural assumptions), and conjectural extensions (most notably to renormalization-related residual freedom). The main philosophical consequence is a strengthened, prospective motivation for epistemic structural realism: the structural content of physics is not merely what happens to survive theory change, but what must already be stably coordinable across admissible perspectives if public physical knowledge is to be possible at all. This route is contrasted with Worrall's retrospective appeal to theory change, with Ladyman and French's ontic structural realism, and with Rovelli's relational quantum mechanics. Keywords: observer equivariance, epistemic structural realism, philosophy of physics, symmetry and invariance, intersubjectivity, path-integral measure, Born rule, Machian inertia, renormalization.

DOI: 10.5281/zenodo.19125980

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