This post is wrong, the math in the post "Into A Pile Of Deep Shit" dated 09 Jun 2016 is wrong.
From the post "Equating To A Indefinite Integral" dated 10 Jun 2016
\(\cfrac{\Delta E}{\Delta t}=P=\dot{x}F_{\rho}\)
as \(\Delta t\rightarrow 0\)
but from the post "Into A Pile Of Deep Shit" dated 09 Jun 2016,
\(\cfrac { dq }{ dx } =2\dot { x }\cfrac { \partial \, \psi }{ \partial \, x }\)
and
\({ q_{a_{\psi}} }=2\dot { x }F_{\rho}|_{a_{\psi}}\)
Why is,
\({ q_{a_{\psi}} } =2P|_{a_{\psi}}\)
??
Why is the total flux through the spherical surface at \(x=a_{\psi}\) twice the power \(P\) when we cross \(x=a_{\psi}\) with velocity \(\dot{x}\)?
\(P\) is in the space dimension only, \({ q_{a_{\psi}} }\) of the particle oscillates in one space dimension and one time dimension. When time and space dimensions are equivalent, then to account for the time dimension, twice the power is needed. Another way to see this is that, energy input to the system in one dimension is shared equally with the other dimension, eventually only half the energy remains in the dimension receiving energy input.
Otherwise the partial differential maths in the post "Into A Pile Of Deep Shit" dated 09 Jun 2016, is wrong.
It is likely that the maths is wrong.
