  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.
