The Quantum Equivalence Principle and Quantum Coordinate Systems

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The two pillars of fundamental physics are General Relativity and Quantum Theory. Each is very successful in its own realm. However, there is a deep problem: they do not fit together. The problem of Quantum Gravity is to find a new physical theory that reduces to General Relativity and Quantum Theory in situations where these theories have been found to be empirically correct. This is the holy grail of fundamental physics. This proposal concerns a new approach to this problem. In fact, Einstein himself faced a similar problem. He realized in 1907 that Special Relativity and Newtonian Gravity were incompatible. He spent the next eight years resolving this problem with many twists and turns along the way. His starting point was what he called "the happiest thought of my life" - that there is no way to distinguish whether an elevator we are in is falling under gravity or floating in space. Locally (in a small enough elevator) these two situations are equivalent. This idea is called Einstein's equivalence principle. More technically, we can always find a frame of reference in which the effects of gravity disappear.   In Quantum Theory any dynamical quantity is subject to indefiniteness. For example, there is no-matter-of-the-fact as to whether a particular particle fired at a screen with two slits goes through one slit or the other. In General Relativity causal order (the order of events in  time) is itself subject to dynamical laws. Hence we expect indefinite causal structure in a theory of Quantum Gravity.  This represents a radical departure from previous physical theories. Usually we think of a state evolving in time. We cannot do this in a theory of Quantum Gravity since to do so requires an ordered sequence of events. We have to tackle the problem of indefinite causal structure head on to make progress.  I will employ the notion of a quantum frame of reference (introduced by Aharonov and Susskind in the 1960's) which allows us to be in a quantum superposition of different frames of reference. Here I propose the quantum equivalence principle (which I recently introduced): that it is always possible to find a quantum frame of reference such that, in the vicinity of any given point, we have definite causal structure. Einstein's equivalence principle provides a way to tame gravity without removing it from the picture. Analogously, the quantum equivalence principle offers a way to tame indefinite causal structure. Students will learn how to frame a problem first in conceptual, then in mathematical terms. They will understand key concepts such as causality, ontology, and operationalism and learn mathematical methods such as tensor analysis, linear algebra, and probabilistic methods. These skills are very transferable and have applications, for example, to Quantum Information, and to big data set analysis.   Students trained trained in these techniques will strengthen the Canadian workforce both inside and outside academia.