\(\Delta t*v_s=\cfrac{v_{boom}}{c}*v_s=S\) --- (*)
from the post "Light Speed Back In Time" also dated 15 Jan 2018, might change to,
\(\Delta t*v_s=\left(1-\cfrac{v_{boom}}{c}\right)*v_s=S\) --- (**)
The former expression (*) suggests an absolute change in \(t\) and the latter expression (**) might suggest a relative change in \(t\) with respect to the photon that remains at light speed \(c\). But consider this;
if
\(1-\cfrac{v_{boom}}{c}=\cfrac{\Delta}{\text{refer.}}\)
\(\cfrac{v_{boom}}{c}=\Delta\)
then,
\(\text{refer.}=\cfrac{\cfrac{v_{boom}}{c}}{1-\cfrac{v_{boom}}{c}}=\cfrac{v_{boom}}{c-v_{boom}}\)
Which reminds of the expressions,
\(E=mc\int ^{c}_{v_{boom}}{ dv }\)
\(E=mc\int ^{c}_{c-v_{boom}}{ dv }\)
This implies that \(\text{refer.}\) is with reference to the a photon at speed \(c-v_{boom}\) instead of \(c\). ie the situation when \(v_{boom}\) flips sign. Given \(v_{boom}\), numerically, it is possible that,
\(c-v_{boom}\) and \(c+v_{boom}\)
that the torus collapse to a photon going in the opposite direction.
Expression (*) should be used, where \(c\) is the reference.
