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.
