Charge Photons Creation

From the post "Why Should Amplitude Remain Constant?", it was argued that a change in parameter $n_i\rightarrow n_f$ changes $\lambda_n$ and $a_{\psi\,n}$ but does not change $A_n$.  $\lambda_n$ is orthogonal to $a_{\psi\,n}$ and both are orthogonal to $A_n$.

Since,

$c=f_n\lambda_n=\cfrac{\lambda_n}{T}$

$T=\cfrac{\lambda_n}{c}$

where $T$ is along the $t_c$ time dimension.

$2\pi a_{\psi\,n}=i\lambda_n$

$\lambda_n=-i2\pi a_{\psi\,n}$

So,

$T=\cfrac{-i2\pi a_{\psi\,n}}{c}$

$iT=\cfrac{2\pi a_{\psi\,n}}{c}$

$iT$ is a time dimension perpendicular to $T$.  It is either $t_T$ or $t_g$.  $iT$ is not any of the two space dimensions as $a_{\psi\,n}$ does not affect $A_n$.

$iT$ is separately,

$iT=t_T$

 $iT=t_g$

for the two type of charges.

A change in $a_{\psi\,n}$, therefore changes $t_T$ or $t_g$, and a change in $\lambda_n$ changes $t_c$.

As long as $a_{\psi\,n}$ and $\lambda_n$ are valid solutions to the wave equation,  the particle is still a wave in 2 space dimensions and one time dimension $t_g$ or $t_T$ after the changes (ie the particle is not destroyed).  That means $v=c$ along both $t_c$ and, $t_T$ or $t_g$.

If a change forces $v\gt c$ along $t_g$ or $t_T$, the energy is released along that dimension instead.  $v$ remains constant at $c$.  If a changes results in $v\lt c$, energy is absorbed along the same time dimension, such that $v$ increases to $c$ again.  In both changes, other orthogonal dimensions are not affected.  The particle has no access to other dimensions in which it is not oscillating, and not existing (The charge exist along $t_c$).  So the charge has access to $t_c$, two space dimensions and $t_T$ or $t_g$.

A slow down in time $t_c$ is associated with greater then light speed, $v_s\gt c$ in space.  When time returns to normal, $v_s=c$, the particle velocity is at light speed.  (Time speed changes after the particle has reach light speed in space).  As such a change along $t_c$, the time dimension in which the particle exist, is coupled to the space dimension, ($s$) along which it travels ($c^2=v^2_s+v^2_{tc}$).  As the particle returns to light speed in $t_c$, it is in light speed in $s$.

Taken altogether,  changes in $a_{\psi\,n}$ and $\lambda_n$ of a particle creates another wave in the same set of dimensions as the particle, as long as the final $a_{\psi\,f}$ and $\lambda_f$ are still valid solutions to the wave equation.  If the particle is destroyed, there is then no light speed constrain on the dimensions involved and no emission/radiation of energy would be required.  That the original particle is not destroy is itself a constrain leading to the creation of the new particle.

The diagram above shows that changes in $a_{\psi\,n}$ and $\lambda_n$ of charges lead to the creations of two types of photons oscillating along $t_g$ or $t_T$, existing along $t_c$.  These are charge photons associated with each type of charge.

Makan Time!  If you are Swedish it means something else.