A new relativistic quantum mechanics has been developed that extends the realm of applicability of both Maxwell electromagnetism and relativistic quantum mechanics. The quantum world should be at least “complex”, as opposed to merely “real”. A proper basis of non-commutative relativistic space-time, the Space Time Algebra, championed by David Hestenes, contains both the complex algebra and the quaternion algebra as sub-algebras. Identifying two symmetric non-commuting 4-spaces within this, space-time and inverse space-time, allows an understanding of the nature of inter-action, as described by our recent paper (van der Mark, M.B.;. Williamson, J.G. Relativistic Inversion,. Invariance and Inter-Action. Symmetry June 2021, 13, 1117). From these basis spaces can be derived a further 4 dynamical degrees of freedom, describing current, electric field, magnetic field and quantum spin respectively. These, together, describe the real 3-D space of experiment and experience. With the exception of quantum spin-space, these spaces are very familiar to any physicists, as current, electric field and magnetic field. In particular crystal structure is largely defined by relationships in electric field space, a space with three and only three components. Thinking in spin-space (and the related magnetic field space), however, leads to new insights in physics, chemistry and collective phenomena in the solid state. These will be explored briefly with reference to relativistic wave-functions for light and matter and with examples in atomic and molecular chemistry, the fractional quantum hall fluid, and (high temperature) superconductivity.
This talk was presented to The Fanaaten, 09/09/21.