Dr. Jonathan Dowling
Louisiana State University
Quantum Measurement in the Timeless Universe
One of the fundamental rules of quantum theory, known as the measurement postulate, forces the future to be treated very differently from the past. This observation has come to be known as the "quantum mechanical arrow of time." This leads to a deep paradox, however, when we attempt to use quantum theory to describe gravity and cosmology, because our theories of gravity and cosmology do not describe how physical objects change with time; instead, they describe how physical objects change with respect to each other. In a very literal sense, the physical laws describing the universe itself are timeless. Our goal is to reconcile this timeless nature of the universe with quantum theory's definite "arrow of time." To accomplish this, we need to go back to the foundations of quantum theory and re-write the measurement postulate itself, using the modern-day tools of information theory. By invoking the field of information theory, we expect that the resulting framework should not only describe the emergence of time's arrow, but that it will also enable us to make fundamental statements about what we as observers can learn about our universe from within universe itself.
General covariance has imposed on physics a new language in which our conception of time is fundamentally altered. Dynamics is no longer about evolution in an external time variable - instead, dynamical quantities evolve with respect to one another. This understanding of reality forces us to confront foundational issues in the formulation of quantum theory. In particular, those features of quantum theory, which rely on the familiar notion of "instants of time" (for example the statistical interpretation of quantum mechanical states, and the measurement postulate itself) must be re-evaluated in the context of covariant quantum theory. We have proposed a framework for accomplishing this, which identifies quantum measurement in terms of entanglement and information, and appears to solve basic problems of correspondence with established Schroedinger-picture mechanics. We will build on this foundation, with emphasis on generalizing the formalism to encompass the covariant analogs of powerful informationtheoretic tools and results - a formalism we will use to answer fundamental questions about accessible information in quantum cosmology, and to identify an emergent quantum mechanical arrow of time within timeless cosmologies; concepts that are well-known in the context of quantum information, but lacking from our current understanding of the universe.
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