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The laws of quantum mechanics that govern the atomic and molecular building blocks of our physical world are fundamentally time symmetric. What then allows us to conclude that time moves forward rather than backwards? Clues to this puzzle have long been thought to reside in the process of wave function collapse: a quantum system can be initialized in a superposition of states but will collapse randomly into a classically allowed state if it is measured. Recent experimental innovations allow us to examine quantum measurement as a continuous process, revealing the evolution induced by measurement. An open question in continuously measured systems is the presence of time reversal symmetry in this process. The persistence of forward/backward symmetry in quantum measurement allows for new tests of causality which can be constructed with time reversed quantum feedback loops. The purpose of this research is to investigate the origins and degree of time symmetry in continuously measured quantum systems, and to examine the extent to which quantum systems and measurements validate or question the notion of determinism. Ultimately, this can reveal whether an arrow of time exists as a physical reality or as a construction of our perception of the physical world.