What is a path for creating new theoretical physics? Presenter: William M. Pezzaglia Jr. (wpezzag@clifford.org)

Department of Physics, Santa Clara University, Santa Clara, CA 95053, USA

Presentation to Society of Physics Students (SPS), 98Jan14, Santa Clara University

Abstract In response to suggestions from SPS students I will discuss the the following:

(1) Just how does one do "new" physics? Many of you have participated in experimental physics research projects at Santa Clara Univ (and Slac). But can mere mortals (i.e. undergraduates) involve themselves in the development of new fundamental theories?

(2) Just as tensors allowed Einstein to see further, can the introduction of a better mathematical language lead to new physics? William Kingdon Clifford was the translater of Riemann's works, and the first to propose curvature was related to gravity. In 1876 he introduced an extraordinary geometric algebra, in which one can add a vector to a scalar to a plane. However, due to his untimely death and historical accidents, it was replaced by the much more limited (and flawed) Gibbs vectors which still appear in your physics books. Recent revival and new extensions hold promise for completely new approaches to unified physical theories, in particular the descriptoin of spin in quantum theory and gravitation.

(3) Pilot programs at UC Davis, Univ of Windsor (Ontario), and Univ of Barcelona have shown that undergraduates can more quickly learn and apply Clifford vectors than Gibbs vectors; becoming quite excited with the interpretation of "i" as the volume of 3 space, seeing "planes" as things that cause rotations (or Lorentz transformations), and being able to do divergence, curl and gradient in a single equation. Possible projects at Santa Clara are participation in writing papers for the American Journal of Physics, development of symbolic manipulation programs (in Maple or Mathematica) and help in creating an on-line web book.

See also the following talk at the Santa Clara Univ. Math Department Colloquium, Jan 20, 1998, Why does "real" physics need "imaginary" numbers? A history of physical applications of geometric algebras.

• Index of other talks at: http://www.clifford.org/wpezzag/talks.html • This URL: http://www.clifford.org/wpezzag/talk/1998sps/98sps.pdf • Updated: 2007Dec26

Index to Transparencies I. Introduction (Title Page) II. Epistemology (Metaphysics)

• A. What is this thing called Physics? • B. The Character of Physical Law • C. The Scientific Process, New Theory

o What is a good theory?

III. Geometric Algebra • A. Quaternions

o 1. Anticommutivity is Perpendicularity o 2. Quaternionic Algebra o 3. Rotations

• B. Vectors, Matrices, Tensors o 1. Grassmann’s Extended Quantities o 2. Gibbs Vector Algebra o 3. Why use Gibbs Vectors in Physics? o 4. Rotations with Matrices vs. Quaternions

• C. Clifford Algebra o 1. History of Abstract Algebras o 2. William Kingdon Clifford o 3. The Clifford Group o 4. Vector Algebra o 5. Geometric Calculus

IV. Pan-Dimensional Physics • A. Poly-Geometric Laws

o 1. Special Relativity o 2. Electrodynamics with Spin o 3. Electrodynamics in 3D

• B. Metamorphic Transformations o 1. Special Relativity o 2. Automorphism Invariance in 4D o 3. The Spin Contribution

• C. Generalized Curvature o 1. Dimensional Democracy o 2. Papapetrou Equation Derivation o 3. Pan-Dimensional Curvature

V. Epagogy • The Poly-Dimensional Principles • Clifford: Geometry is the gateway to Science

VI. References