Space and Time Reversal Are Different

Posted by doug
Time and space reversal do not look the same which makes the difference between real and imaginary numbers concrete.
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.
q_graph -dir vp -out space_and_time_reversal -loop 0 -box 5 -command 'q_add_n -5 -5 -5 -5 0.005 0.005 0.005 0.005 1000' -color yellow -command 'q_add_n -5 -5 -5 -5 0.005 0.005 0.005 0.005 1000 | q_conj | q_x_scalar -1' -color green -command 'q_add_n -5 -5 -5 -5 0.005 0.005 0.005 0.005 1000 | q_conj' -color blue1
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\begin{align*} q\to q' &= q^* \quad \textup{space reversal}\\ q\to q' &= -q^* \quad \textup{time reversal} \end{align*}