Since I joined UTEP my main line of research has been to contribute to the resolution of the philosophical and physical problem at the foundations of dynamics. For instance, theories of dynamical systems, such as classical mechanics and quantum physics, often assume the existence of a prior, absolute, and independent space-time background which conflicts with the lessons of general relativity, which appears to the deny the existence of such independent framework (background independence). In quantum mechanics, the a priori existence of entities comes into question in contrast with other theories of dynamics. In philosophy these problems fall under the ambit of metaphysics and are part of the problem of motion, which dates back to Presocratic philosophers and includes questions regarding the nature of time, space, and identity.
My research approach has centered primarily on figuring out a way to treat motion in physics consistently and fundamentally, that is, treating motion is ontologically prior to space and time (a dynamic relational approach). In addition, my aim has been to cultivate the bridge between fundamental technical questions and the phenomenological experience of motion. So besides contributing to the debate over the dynamics of a quantum theory of gravity, I have contributed to the question of motion, and gained insight into the problem in the process, from pursuing the question from a distinct perspective: the examination of the concepts of space, time, motion, and individuation of indigenous cultures of Mesoamerica, focusing primarily on the Maya. I have written a book length manuscript and several articles on the organic metaphysics of the classic Maya. I also attempt to make the ideas of these two distinct technical fields available to a broad audience.
I have co-edited a volume on the foundations of physics as a way to help popularized the current treatment of these foundational problems to a wide audience and am now preparing another volume on the question of time in quantum gravity, also for non-specialists. I have also contributed a paper on the problem of motion as part of a popular series book on virtual worlds.