Carl H. Brans

I have been a member of the Loyola University physics faculty from 1960 to present. During that time I have also been a visiting Professor of Physics, Princeton University, 1973-74, visitor Institute for Advanced Study, Princeton, 1993, and visiting Professor at the Institut fuer Theoretische Physik, Koeln, Fall 1998.

My research interests center on general relativity, quantum theory, and related mathematical problems and their interaction with the physics of space-time. In addition to NSF grants, I was the 1998 Recipient of Humboldt Senior Research award which enabled me to spend time visiting Friedrich Hehl and his relativity group in Cologne.

My Princeton PhD thesis had the apparently oxymoronic title, Mach’s Principle and a varying Gravitational Constant (unpublished). This and early work in collaboration with Robert Dicke led to a scalar-tensor modification of standard Einstein theory generally now known as Jordan-Brans-Dicke theory published in the Physical Review, 124, 925 (1961). Experimentation in the 1960’s and 1970’s, indicate that parameters of this theory must be such as to distinguish it only insignificantly from standard Einstein theory in the solar system context. However, recent speculations resulting from superstring theory and from cosmology have led to a re- awakening of interests in the possibility of an additional universally coupled scalar field under the guise of the dilaton and/or inflaton. Consequently I have revisited the role of scalar fields in general relativity, especially in relation to the question of positive energy wormholes.

In unrelated work from the 1960’s and 1970’s I developed a complete and effective invariant classification of four dimensional Ricci flat geometries, a type of post-Petrov approach, leading to some results on exact vacuum metrics. I have also been interested in questions related to the true operational significance of Bell’s theorem and the foundations of quantum interpretation. From about 1995 on, my primary current research efforts have been in the study of applications of exotic (non-standard) differential structures on R^4 and other topologically simple manifolds to the spacetime models necessary for physics. I have published several papers on these subjects with Duane Randall (Loyola), and Torsten Asselmeyer-Maluga (Berlin). Torsten and I have also co-authored a research monograph surveying these new developments in differential topology and their relationship to physics. The book, intended for both physicists and mathematicians, has been published in January, 2007, as Exotic Smoothness and Physics: Differential Topology and Spacetime Models, World Scientific Press. Torsten has also edited a collection of papers as a Festschrift for my 80^th birthday published as At the Frontier of Spacetime: Scalar-Tensor Theory, Bells Inequality, Machs Principle, Exotic Smoothness (Fundamental Theories of Physics) 1st ed. 2016 Edition.

As of 2019, my retirement work has been primarily devoted to exploring (learning and re-learning) some basic and hopefully fundamental topics in algebraic and differential topology.