From the post "Resistance In Time, Not Futile",
\(Z_{1Do}=\cfrac{1}{\sqrt{2}}\sqrt{\cfrac{\mu_o}{\varepsilon_o}}=\sqrt{\cfrac{\mu_o}{\sqrt{2}}\cfrac{1}{\sqrt{2}\varepsilon_o}}\)
ie,
\(\mu_o\rightarrow\cfrac{\mu_o}{\sqrt{2}}\)
and
\(\varepsilon\rightarrow\sqrt{2}\varepsilon_o\)
and so,
\(\psi\rightarrow\sqrt{2}\psi\)
in one space dimension, where \(\psi\) was defined as,
\(\psi=\cfrac{1}{2\mu_o}B^2=-\cfrac{1}{2}\varepsilon_oE^2\)
for \(\psi\) oscillating between two dimensions, from the post "Maybe Not". In the presence of a time dimension,
\(\psi\lt\psi_{DTo}\le\sqrt{2}\psi\)
The right hand side of this bound corresponds to the time dimension presenting no resistance to \(\psi\) and the left hand side of this range corresponds to the time dimension presenting the same resistance to \(\psi\) as a space dimension. Within this range of \(\psi\), is the value of
\(m_{\rho\,po}c^2=\int^{2x_z}_{0}\psi_{DTo}d\,x\)
where the photon oscillates between one time dimension and one space dimension, manifests fully as energy, \(\psi\).
\(\int^{2x_z}_{0}\psi d\,x\lt m_{\rho\,po}c^2\le\sqrt{2}\int^{2x_z}_{0}\psi d\,x\)
\(0\lt m_{\rho\,po}c^2-\int^{2x_z}_{0}\psi d\,x\le\left(\sqrt{2}-1\right)\int^{2x_z}_{0}\psi d\,x\)
\(0\lt m_{\rho\,particle}c^2\le\left(\sqrt{2}-1\right)\int^{2x_z}_{0}\psi d\,x\)
We have a bound on the mass density of any particle manifesting \(\psi\), assuming that photon is pure energy and that it is so, because of a reduction in resistance to \(\psi\) in the time dimension. And since,
\(\sqrt{2}-1=0.4142\lt 0.5\)
less than half of the possible \(\psi\) is manifested as mass, (\(E=mc^2\) equivalent) .
