Abstract

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.