  The problem of observables and their supposed lack of change has been
significant in Hamiltonian quantum gravity since the 1950s. This paper
considers the unrecognized variety of ideas about observables in the thought of
Peter Bergmann, who invented observables. Whereas initially he required a
constrained Hamiltonian formalism to be mathematically equivalent to the
Lagrangian, in 1953 Bergmann and Schiller introduced a novel postulate,
motivated by facilitating quantum gravity: observables were _invariant_ under
transformations generated by _each individual_ first-class constraint. While
modern works rely on Bergmann's authority and sometimes speak of "Bergmann
observables," he had much to say about observables, plausible but not all
consistent or remembered.
  At times he required observables to be locally defined (not changeless and
global); at times he wanted them independent of the Hamiltonian formalism (not
essentially involving separate first-class constraints). But typically he took
observables to have vanishing Poisson bracket with each first-class constraint,
purportedly justified by electrodynamics. He expected observables to be
analogous to the transverse true degrees of freedom of electromagnetism. Hence
there is no coherent concept of observables which he reliably endorsed.
  A revised definition of observables that satisfies the requirement that
equivalent theories should have equivalent observables using the
Rosenfeld-Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum of
first-class constraints that changes the canonical action $\int dt(p\dot{q}-H)$
by a boundary term. Bootstrapping from theory formulations with no first-class
constraints, the "external" coordinate symmetry of GR calls for covariance
($4$-dimensional Lie derivative), not invariance ($0$ Poisson bracket), under
$G$ (not each first-class constraint).
