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The problem of observables and their supposed lack of change has beensignificant in Hamiltonian quantum gravity since the 1950s. This paperconsiders the unrecognized variety of ideas about observables in the thought ofPeter Bergmann, who invented observables. Whereas initially he required aconstrained Hamiltonian formalism to be mathematically equivalent to theLagrangian, in 1953 Bergmann and Schiller introduced a novel postulate,motivated by facilitating quantum gravity: observables were _invariant_ undertransformations generated by _each individual_ first-class constraint. Whilemodern works rely on Bergmann's authority and sometimes speak of "Bergmannobservables," he had much to say about observables, plausible but not allconsistent or remembered.  At times he required observables to be locally defined (not changeless andglobal); at times he wanted them independent of the Hamiltonian formalism (notessentially involving separate first-class constraints). But typically he tookobservables to have vanishing Poisson bracket with each first-class constraint,purportedly justified by electrodynamics. He expected observables to beanalogous to the transverse true degrees of freedom of electromagnetism. Hencethere is no coherent concept of observables which he reliably endorsed.  A revised definition of observables that satisfies the requirement thatequivalent theories should have equivalent observables using theRosenfeld-Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum offirst-class constraints that changes the canonical action $\int dt(p\dot{q}-H)$by a boundary term. Bootstrapping from theory formulations with no first-classconstraints, 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).

Peter Bergmann on Observables in Hamiltonian General Relativity: A Historical-Critical Investigation