\(F.c=\cfrac{dKE}{dt}\)
\(KE\) is as defined in the space dimension \(\cfrac{1}{2}mv^2\)
\(F.c=\cfrac{1}{2}m\cfrac{dv^2}{dt}\)
with \(v=c\)
\(F.c=m.c\)
with \(m=\cfrac{1}{c}\)
\(F.c=\cfrac{1}{c}.c=1\)
However, force density \(F\) was derived as,
\(F=i\sqrt{2mc^2}.G.tanh\left(\cfrac{G}{\sqrt{2mc^2}}(x-x_z)\right)\)
where we make \(x_z=0\). When \(m=\cfrac{1}{c}\),
\(F=i\sqrt{2c}.G.tanh\left(\cfrac{G}{\sqrt{2c}}(x)\right)\)
Is it possible logically that,
\(F.c=\sqrt{2c}.G.tanh(\theta_{\psi}).c=1\)
from which,
\(G=\left(\cfrac{1}{c}\right)^{3/2}.\cfrac{1}{\sqrt{2}.tanh(\theta_{\psi})}\)
where \(\theta_{\psi}=\cfrac{G}{\sqrt{2c}}(a_{\psi})\)
\(\cfrac{1}{c}\) is the inertia of a particle in the time dimension.
\(G\) is not the gravitational constant, but the constant of proportionality in the derivation for \(F_{\rho}\).
\(\cfrac{1}{c}\) was derived with the consideration of \(F_{\rho}\), both basic particles and big particles with \(n\) constituent basic particle shares the same \(F_{\rho}\) expression. Both basic particles and big particles have the same inertia \(\cfrac{1}{c}\). When \(F_{\rho}\) is scaled by \(m\),
\(F_{\rho}\to m.F_{\rho}\)
then inertia,
\(\cfrac{1}{c}\to \cfrac{m}{c}\)
\(m.F_{\rho}\) is due to \(m\) distinct basic particles or \(m\) distinct big particles.
\(\psi\) is energy density without material mass. Inertia in the time dimension is the resistance to change in energy as expressed as,
\(\Delta E=\cfrac{d\,KE}{dt}\)
Both basic particles and big particles although with different \(a_{\psi}\) are made of the same \(\psi\). They both have the same resistance to a change in energy in the time dimension, as such they both have the same inertia. With \(m\) distinct particles, each will present the same resistance, as such there is \(m\,\,\,times\) the individual inertia to a change in energy.
\(\Delta E=\cfrac{d\,KE}{dt}\)
Both basic particles and big particles although with different \(a_{\psi}\) are made of the same \(\psi\). They both have the same resistance to a change in energy in the time dimension, as such they both have the same inertia. With \(m\) distinct particles, each will present the same resistance, as such there is \(m\,\,\,times\) the individual inertia to a change in energy.
Good night.
