Time symmetry in operational theories


Hardy, L. (2021). Time symmetry in operational theories. Perimeter Institute. https://pirsa.org/21060084


Hardy, Lucien. Time symmetry in operational theories. Perimeter Institute, Jun. 04, 2021, https://pirsa.org/21060084


          @misc{ pirsa_21060084,
            doi = {10.48660/21060084},
            url = {https://pirsa.org/21060084},
            author = {Hardy, Lucien},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Time symmetry in operational theories},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060084 see, \url{https://pirsa.org}}


The standard operational probabilistic framework (within which Quantum Theory can be formulated) is time asymmetric.  This is clear because the conditions on allowed operations include a time asymmetric causality condition.  This causality condition enforces that future choices do not influence past events.  To formulate operational theories in a time symmetric way I modify the basic notion of an operation allowing classical incomes as well as classical outcomes.  I provide a new time symmetric causality condition which I call double causality.  I apply these ideas to Quantum Theory proving, along the way, a time symmetric version of the Stinespring extension theorem using double causality.  I also propose the idea of a conditional frame of reference.  We can transform from the time symmetric frame of reference to a forward or a backward frame of reference.  This talk is based on arXiv:2104.00071.