Scholars Award: Observables in Hamiltonian Dynamics

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This award supports a technical project in the philosophy of physics. The PI, who has a PhD in both Physics and History and Philosophy of Science, will address an issue in the philosophical foundations of the General Theory of Relativity concerning the equivalence of two formulations of the theory. One tends to be preferred because it is much closer to how quantum mechanics is standardly formulated, which is better for the purposes of finding a viable theory of quantum gravity. However, that formulation seems to imply that change is an illusion; observables (what the formulation designates as real physical quantities) do not change with time. The other formulation of the theory is more in line with common sense; observables (within that formulation) do change with time. Nevertheless, this difference between the two formulations of the theory borders on the paradoxical; it is not clear what it means to say that they are equivalent. The PI proposes to resolve this tension by giving a novel and compelling argument for a new definition of observables that vary locally resolving the problem of time while maintaining the equivalence of the two formulations.  In addition to publishing the results of his research in three planned journal articles (and eventually in a book), the PI plans to make his work accessible to a wide audience through a series of six public lectures and through his relevant teaching at Cambridge.This project examines the equivalence of the Hamiltonian formulation of General Relativity with the Lagrangian formulation to resolve the problem of time. Hamiltonian General Relativity has been associated with a lack of change in physically real observables since the mid-1950s, whereas the more fundamental Lagrangian treatment (Einstein's equations), like common sense, exhibits changing observables. Many leading physicists have commented on this unacceptable situation, but for various reasons an adequate solution has not been found. Two new definitions of observables have been proposed, one by the PI and another by Pons, Salisbury, and Sundermeyer. The PI seeks to take the crucial next step, of taking the recently-proposed definition of observables and testing them, by studying whether they correctly render equivalent formulations of various theories equivalent in their observational content. The project will shed light on research programs in quantum gravity, exhibits the fruitfulness of interaction between General Relativity and particle physics, and shows the utility of integrated history and philosophy of science for current science.