Photon Tells More

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) .