PIRSA:09020038

deBroglie-Bohm and the Timeless Mechanics of Jacobi

Westman, H. (2009). deBroglie-Bohm and the Timeless Mechanics of Jacobi. Perimeter Institute. https://pirsa.org/09020038

Westman, Hans. deBroglie-Bohm and the Timeless Mechanics of Jacobi. Perimeter Institute, Feb. 10, 2009, https://pirsa.org/09020038 

          @misc{ pirsa_PIRSA:09020038,
            doi = {10.48660/09020038},
            url = {https://pirsa.org/09020038},
            author = {Westman, Hans},
            keywords = {Quantum Foundations},
            language = {en},
            title = {deBroglie-Bohm and the Timeless Mechanics of Jacobi},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {feb},
            note = {PIRSA:09020038 see, \url{https://pirsa.org}}
          }

Hans Westman

Talk number
PIRSA:09020038
Collection
Talk Type
Subject
Abstract
A standard canonical quantization of general relativity yields a time-independent Schroedinger equation whose solutions are static wavefunctions on configuration space. Naively this is in contradiction with the real world where things do change. Broadly speaking, the problem how to reconcile a theory which contains no concept of time with a changing world is called 'the problem of time'. In this seminar we shall study this problem using a reformulation of Newtonian mechanics due to Jacobi (Jacobi's timeless mechanics) which allows one to study the problem of time without all the technical difficulties present in quantized general relativity. We show explicitly that Jacobi's timeless mechanics is a straightforward counterexample to the claim that all first class constraints generate gauge transformations, i.e. physically indistinguishable states. The implications of this is unclear. By making use of deBroglie-Bohm trajectories we derive a necessary and sufficient condition for a time-dependent Schroedinger equation to emerge for subsystems. The importance of 'strong' entanglement between subsystem and environment for the emergence of time is stressed.