Space: The Anti-Euclidean Metric From The Structure Of Rotations

Standard treatments of 3-space assume that the choice between Euclidean (+ + +) and anti-Euclidean (- - -) metrics is independent of the physics, and therefore arbitrary. A careful analysis of the orientation preserving nature of rotations in 3-space shows that only the anti-Euclidean metric is consistent with a real algebraic description. The Euclidean metric can be used to represent rotations by patching up the mathematics using complex numbers. We mention the Clifford algebras associated with the spacetime metrics (+ - - -) and (- + + +), and indicate that ii electromagnetism is set up in the correct spacetime metric, complex numbers need not be used.