The Norm Requires a Clock

summary:

The norm of spacetime is only about time.

description:

The input is in yellow. The conjugate of the input is in blue, a 3D spatial reflection. The norm that results from multiplying yellow and blue is in green. Nailed to the origin, no ruler is needed, only a watch to record how long into the future is any spacetime norm.

command:

q_graph -box 6 -loop 0 -dir vp -out norm -command 'q_add_n -2 -3 1 2 .004 .003 -.0005 -.003 1000' -color yellow -command 'q_add_n -2 -3 1 2 .004 .003 -.0005 -.003 1000 | q_conj' -color blue -command 'q_add_n -2 -3 1 2 .004 .003 -.0005 -.003 1000 | q_norm' -color green

youtube link:

The Norm

youtube embed:

Outside video:

iPod downloads:

norm.povray.100.1000.animation.scan_.m4v

math

equation:

norm(q) = q^* q

sage notebook:

Quaternion Norms

numbers:

norm.povray.100.1000.numbers