Complex Numbers Move Straight

summary: 

Complex numbers are constrained to move with their basis vectors, unable to explore all of spacetime.

description: 

Complex numbers have some freedom to move in space. The 3 straight lines indicate a choice of Cartesian basis vectors, but other basis vectors could have been chosen. Complex numbers are used extensively in quantum mechanics. Yet the obvious limitations in the animations suggest we should rebuild the foundations of complex-valued quantum mechanics. Sounds like a lot of work!

command: 
q_graph -out complex -dir vp -loop 0 -box 5 -command 'q_add_n -3 4 0 0 .002 -0.008 0 0 1000' -color yellow -command 'q_add_n 4 0 4 0 -.006 0 -0.008 0 1000' -color blue -command 'q_add_n -6 0 0 -6 .012 0 0 .012 1000' -color green
youtube embed: 
math
equation: 

(2 q + q^* + (i q i)^*) / 2 = (t, x, 0, 0)
(2 q + q^* + (j q j)^*) / 2 = (t, 0, y, 0)
(2 q + q^* + (k q k)^*) / 2 = (t, 0, 0, z)

tags
Math Tag: 
real numbers
complex numbers
Programming Tag: 
command line quaternions
q_add_n