Shimony is a leading expert on the many fascinating philosophical aspects of quantum mechanics. He has made a number of significant contributions relating to hidden variables, Bell's Theorem, and the quantum mechanical measurement problem. Recent work includes projects on geometric (i.e. non-dynamic) phases, on stochastic modifications of the Schroedinger Equation, and on two-particle interferometry. Additional interests in the foundations of probability theory, as applied to statistical mechanics and to inductuctive logic are being pursued. Stachel has completed critical studies on aspects of quantum mechanics, including one on the Finkelstein-Putnam-Bub approach to quantum logic. He has also advanced an approach to the foundations of the special theory of relativity based on the use of measuring rods alone.
Stachel is playing a leading role in this project. Volume I: The Student Years (1879-1901) has been completed, and work has begin on a multi-volume history of relativity. In addition to the origins of the theories of relativity, this history will emphasize the technical developments (theoretical and applied) and experimental results of the theory. Research is also being conducted into the foundations of space-time theories, such as the concept of simultaneity in Newtonian, special- and general- relativistic theories, an algebraic foundation for general relativity, and a two-plus-two formulation of general relativity.