Space Reversal Uses Mirrors

summary:

Reversal in space is only about mirrors.

description:

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.

command:

q_graph -dir vp -out space_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' -color blue

youtube link:

Space Reversal

youtube embed:

Outside video:

math

equation:

$q\to q'=q^*$

sage notebook:

quaternion conjugates - space reversal

numbers:

space_reversal.povray.100.1000.numbers