Respecting Boundaries: Theoretical Equivalence and Structure Beyond Dynamics

Abstract

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Knox (2011) that general relativity is equivalent to teleparallel gravity, and by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity.

Updated to match published version

References in corpus (3)

• Extended corner symmetry, charge bracket and Einstein's equations
• Noether charge and black hole entropy in teleparallel gravity
• Role of spacetime boundaries in Einstein's other gravity

Cited by in corpus (7)

• The Non-Relativistic Geometric Trinity of Gravity
• Underdetermination in Classic and Modern Tests of General Relativity
• Constraint characterization and degree of freedom counting in Lagrangian field theory
• Is spacetime curved? Assessing the underdetermination of general relativity and teleparallel gravity
• Conventionalism, cosmology and teleparallel gravity
• Gravitational redshift revisited: inertia, geometry, and charge
• Equivalent Gravities and Equivalence Principle: Foundations and experimental implications