Abstract
The 2002 Oersted Medal Lecture by David Hestenes concerns the many advantages for education in physics if geometric algebra were to replace standard vector algebra. However, such a change has difficulties for those who have been taught traditionally. A new way of introducing geometric algebra is presented here using a four-element array composed of traditional vector and scalar products. This leads to an explicit 4 × 4 matrix representation which contains key requirements for three-dimensional geometric algebra. The work can be extended to include Maxwell's equations where it is found that curl and divergence appear naturally together. However, to obtain an explicit representation of space–time algebra with the correct behaviour under Lorentz transformations, an 8 × 8 matrix representation has to be formed. This leads to a Dirac representation of Maxwell's equations showing that space–time algebra has hidden within its formalism the symmetry of 'parity, charge conjugation and time reversal'.