This award is for a doctoral dissertation research improvement grant. The Co-PI, the doctoral candidate, is working under the supervision of his mentor, the PI, on a project whose central aim is to generalize a foundational account of time reversibility in physics. The PI has requested support for the Co-PI to engage in intensive training with two researchers at the University of California at Irvine who specialize in the topic of his dissertation. The requested funds will be used to support a five week research stay in Southern California, from February 1 - March 6, 2011.
Intellectual Merit
The requested funds will provide the Co-PI with an important opportunity to work face to face with top researchers in his field as he strives to develop a rigorous, unified foundation for the meaning of time reversal, which stems from a symmetry principle. Although the physics community recognizes the important implications of a certain definition time reversibility, there is little attention paid as to why this definition is chosen and not some other. This project aims to fill that gap. Substantial improvements to the Co-PI's dissertation are likely to come about as a result of this research visit. In the longer term, the Co-PI expects to use a similar approach (using symmetry principles) to analyze related concepts in physics such as physical equivalence.
Potential Broader Impacts
Although the work is of particular interest to philosophers of science, in that it seeks to explicate a central concept in the foundations of modern physics, it will also be of interest to physicists who are concerned with the conceptual basis for time reversibility, a concept considered of fundamental importance in the practice of physics. The Co-PI plans to disseminate the results of his research at philosophy of science conferences, at physics conferences, and through publications in peer-reviewed journals in both fields. Doing so will serve to contribute to and to enhance interdisciplinary interaction.
In the Spring of 2011, Bryan Roberts received NSF grant #1058902, entitled "Doctoral Dissertation Research: Symmetries in the foundations of quantum theory." The question Roberts hoped to answer was how one can understand the distinction between "past" and "future" in the context of modern physics. In particular, Roberts was interested in how quantum theory, our most fundamental theory of matter, deals with this distinction. The question is philosophical, but it is one that requires the techniques of modern physics to answer. The NSF awarded Roberts the opportunity to travel to the University of California in Irvine and in San Diego, to receive both training in the mathematical and philosophical foundations of quantum theory, together with guidance during his investigation, from renowned experts in the field Craig Callender and David Malament. The training that Roberts received during this trip was intensive, and not available at his home university. This preparation and guidance led him not only to answer the question he was asking, but to discover an unexpected new result, which he explored and developed over the course of his dissertation. There were two major findings. First, Roberts assumed that, whatever time reversal means, there must be at least one fundamental system that does not distinguish between the past and the future. Such a system is called "time reversal invariant." For example, if we take a movie of a completely empty vacuum, then winding that movie in reverse will look no different. He then found that, once the mathematical constraints of quantum theory are adopted, together with some assumptions about the non-triviality of the system, the essential meaning of time reversal within the theory could be derived: it is described by a particular kind of transformation, and its precise properties could be determined. Moreover, the result was robust: Roberts showed that this derivation of the meaning of time reversal applied both when Einstein's theory of special relativity is in play (that is, in relativistic quantum field theory), and when it is ignored (in "ordinary" quantum mechanics). Second, there was an unexpected finding that appeared over the course of this investigation. This was the discovery that the invariance of a system under time reversal is closely connected to invariance under translations in space, and to uniform changes in velocity (Galilei boosts). These latter two symmetries are not quite sufficient to establish time reversal invariance. However, with the addition of a further requirement, that there be no 'internal degrees of freedom' like spin or charge, Roberts found that time reversal invariance can be mathematically established, i.e., that in that context quantum theory does not distinguish between past and future. Put another way, the result showed that if a system has a "fundamental arrow of time," in that it distinguishes between past in future at the level of quantum mechanics, but is nevertheless invariant under spatial translations and Galilei boosts, then it must have internal degrees of freedom like spin or charge. This unexpected finding was further developed and explored over the course of the dissertation. From a broader perspective, this research led to a number of new discoveries about the nature of time and its "arrow," which would not have been available without NSF funding. Roberts presented his findings at the universities he was visiting, and was later invited to present them internationally at the University of Bristol and University of Oxford to present these results. The final findings were described in articles that are publicly available on philsci-archive.pitt.edu, and are currently under review by major journals in the field.
