arXiv subjects

Ronald Anderson

Publications and source records attributed to Ronald Anderson.

3 recordsLinked to original sources

arXiv2006

Interpreting Mathematics in Physics: Charting the Applications of SU(2) in 20th Century Physics

The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has played in three key episodes in 20th century physics - intrinsic spin, isospin, and gauge theory and electro-weak unification. We also briefly consider its role in loop quantum gravity. Each episode has led to new physical notions of a space other than the traditional ones of space and spacetime, and each has had associated with it a complex and in places, contested history. The episodes also reveal ways mathematical structures provide resources for new physical theorizing and we propose our study as a contribution to a need Roger Penrose has identified to develop a "profoundly sensitive aesthetic" sense for locating physically relevant mathematics.

physics.hist-ph↗

arXiv1994

Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.

hep-th↗

arXiv1992

Quaternions and the heuristic role of mathematical structures in physics

One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are already part of successful physical theories serve as good guides for the development of new physical theories. The principle is a more formal presentation and extension of a position stated earlier this century by Dirac. Quaternions form an excellent example of such a generalization, and we consider a number of the ways in which their use in physical theories illustrates this principle.

hep-ph↗