space reversal

The input is in yellow, going from (-5 -5 -5 -5) to zero. The space reflection in blue, (-5, 5, 5, 5) to zero, is a mirror operation around the origin. The time reflection, (5, -5, -5 -5) to zero, in green requires you recall how the yellow input collection of events came onto the stage, so the green back it out. The reflection of both time and space, (5, 5, 5, 5) to zero, in red looks like a continuation of the yellow. Deep in quantum field theory they tell the odd tale of antiparticles going backward in time looking like particles going forward in time. Such an animated story now looks more reasonable.

Time requires memory, space needs mirrors. These do not look the same animated. If animation starts off like it ends up, then time reversal is in play. While time reversal can involve a minimum of one event on a screen, space reflection requires matching pairs of events. In math, imaginary basis vectors are represented as a 90 degree rotation in the complex plane. There is no difference except in label between real and complex numbers. The complex plane misleads. Real numbers have a graph that is undirectional - one times one is one - so real numbers can live without the imaginaries. Imaginary graphs have a directional graph - 1 times i is i, while i times -i is 1 - and there is no way to do multiplication with only an imaginary basis.

There are three directions in space, and three complex basis vectors. Flipping a space variable, or equivalently taking the conjugate of a complex basis vector, means using a mirror around the point (t, 0, 0, 0). Whatever time it is, a space reflection makes another point appear on the "other side". What was left handed now looks right handed. If you see pairs of points swing together around the origin, suspect the work of space reflection or conjugation.