wave equation

The Wave Function of a Wave Equation Shifted and Marked

Posted by doug

summary:

Each and every photon is identical to every other, but by coloring in those where t = 0, we can cheat and see the phase.

description:

Part of the great mystery of quantum mechanics is that all particles are identical. There is no adding a tag or painting one red while the rest are yellow. As a programmer, we can cheat, do something not allowed in Nature, and mark all those where t = 0 in red. The shift is the same as before, but now we can spot its trail.

What is so tricky in quantum mechanics is not the vectors - those we can always point at with our fingers. Instead it is the scalars that provide the challenge, the unpointables. Each scalar is connected to three vectors to make 3 complex numbers, but the scalar can be shared by other events. The scalar become the thread within a pattern of events, and between separate patterns of events. It is wonderfully ironic that the simplest core component can be so confusing by playing many roles.

command:

q_graph -out amp_shifted_marked -dir int14 -box 1.6 -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 0 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 -.1 | q_add_n_m 0 0 0.003 0 1 1000' -color red -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 1000 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 0 | q_add_n_m 0 0 0.003 0 1000 1000' -color yellow

math

equation:

$\phi = (cos(\omega t + \delta), sin(\omega t + \delta), k ~ \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi$
$\textrm{red} = (cos(\delta), sin(\delta), k ~ \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi$

The Wave Function of a Wave Equation Shifted

Posted by doug

summary:

A phase shift is added to a wave function, but you cannot tell due to the periodic boundary condition.

description:

A change in the phase was included. Each event above another event has a different starting time due to the phase shift, but given enough time, all the same locations in spacetime are experienced, so the pattern looks the same.

command:

q_graph -out amp_shifted -dir int14 -box 1.6 -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 1000 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 0 | q_add_n_m 0 0 0.003 0 1000 1000' -color yellow

math

equation:

$\phi = (cos(\omega t + \delta), sin(\omega t + \delta), k \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi$