The problem of observables and their supposed lack of change has been significant in Hamiltonian quantum gravity from the 1950s till now.  This talk considers the unrecognized variety of ideas about observables in the thought of constrained Hamiltonian dynamics co-founder Peter G. Bergmann, who also trained many students at Syracuse.  Whereas initially Bergmann required a constrained Hamiltonian formalism to be mathematically equivalent to the Lagrangian formalism, in 1953 Bergmann and Schiller introduced a novel postulate, motivated by facilitating quantum gravity.  This postulate held that observables were invariant under transformations generated by each individual first-class constraint.  While modern works rely on Bergmann’s authority, he had much to say about observables (e.g., 1953, 1956, 1956, 1957, 1961, 1962, 1962), not all mutually consistent and much of it rarely read.

On occasion he required observables to be locally defined (contrary to the inference that Bergmann observables are changeless and global); at times he wanted observables to be independent of the Hamiltonian formalism (contrary to the definition involving separate first-class constraints).  Hence there is no concept of “Bergmann observables” (pace the physics literature) which he reliably endorsed.  A revised definition of observables that is coherent, is physically reasonable, and satisfies the requirement that equivalent theories should have equivalent formalisms can be devised with help from Bergmann (assisted by insights from others).  It implies that observables vary locally and are independent of the Hamiltonian formalism, as Bergmann sometimes wanted.