  A previous paper~\cite{Bern:2022kto} identified a puzzle stemming from the
amplitudes-based approach to spinning bodies in general relativity: additional
Wilson coefficients appear compared to current worldline approaches to
conservative dynamics of generic astrophysical objects, including neutron
stars. In this paper we clarify the nature of analogous Wilson coefficients in
the simpler theory of electrodynamics. We analyze the original field-theory
construction, identifying definite-spin states some of which have negative
norms, and relating the additional Wilson coefficients in the classical theory
to transitions between different quantum spin states. We produce a new version
of the theory which also has additional Wilson coefficients, but no
negative-norm states. We match, through $\mathcal O(\alpha^2)$ and $\mathcal
O(S^2)$, the Compton amplitudes of these field theories with those of a
modified worldline theory with extra degrees of freedom introduced by releasing
the spin supplementary condition. We build an effective two-body Hamiltonian
that matches the impulse and spin kick of the modified field theory and of the
worldline theory, displaying additional Wilson coefficients compared to
standard worldline approaches. The results are then compactly expressed in
terms of an eikonal formula. Our key conclusion is that, contrary to standard
approaches, while the magnitude of the spin tensor is still conserved, the
magnitude of the spin vector can change under conserved Hamiltonian dynamics
and this change is governed by the additional Wilson coefficients. For specific
values of Wilson coefficients the results are equivalent to those from a
definite spin obeying the spin supplementary condition, but for generic values
they are physically inequivalent. These results warrant detailed studies of the
corresponding issues in general relativity.
