A New View of Minkowski Space, and its Effects in Relativistic Quantum Mechanics

Since Minkowski in 1908 announced the merger of space and time there has never been an explanation of its real-and-imaginary structure ($x$,$y$,$z$,\textit{ict}). An explanation is now available that was unknown in 1908: The imaginary component in the 4-vector is a necessary consequence of negative curvature in the background position 3-space, and its time dependence comes from the changing curvature radius under the Hubble expansion in cosmic time (Smith, F. T., Ann. Fond. L. de Broglie [AFLB], \textbf{35}, in press, (2010)). These observations confirm an especially symmetric extension of special relativity previously reported (Smith, F. T., AFLB, \textbf{30}, 179, (2005)), based on a direct product of two Lorentz groups, one generated by velocity boosts and the other by translations in a Hubble-expanding hyperbolic position space. The symplectic symmetry of the direct product group makes it possible to extend a fully Hamiltonian dynamics and quantum mechanics smoothly throughout the relativistic regime. Some resulting changes in special relativity will be described, including fully covariant $n$-body relativistic Schr\"{o}dinger and Dirac equations.