A Relativistic Algebraic Approach to the Q/C Interface: Implications for “Quantum Reality”

Abstract

Clifford's geometric algebra, in particular the algebra of physical space (APS), provides a new relativistic approach to the Quantum/Classical interface. It describes classical relativistic dynamics in quantum terms: spinor amplitudes with projectors describe classical motion and satisfy the Dirac equation of relativistic quantum theory. Some basic properties such as the spin-1/2 nature of elementary systems are seen to be a simple result of the geometry of physical space. The nature of "quantum reality" is constrained: the pure state of any single fermion is fully polarized and determines an exact spin direction, but an entangled pair can be unpolarized. Measurements can form or break entanglement, or they can transfer it between particle pairs. Quantum "weirdness" can arise from the need to use amplitudes of entangled systems. Mathematics Subject Classification (2000). 15A66, 81P15, 81R25, 83A05.

An Online Calculator for Quantum Computing Operations Based on Geometric Algebra

“…A quantum bit can be modelled in different ways in GA, as shown by Baylis in [2], using the complex geometric algebra Cl(2, C) 2 with two spatial basis vectors; or Cafaro and Mancini [4], as well as by Doran and Lasenby [5], using four basis vectors in a real algebra. These approaches are briefly depicted in [6].…”