What If The Particles Are Photons?

From the post "Pressure, Energy Per Unit Vol" dated 12 Dec 2017,

$P=\cfrac{2}{3}\rho_n*\cfrac{4}{3}\pi{(2c)^3}*\cfrac{1}{2}m_av^2_{rms}$

but,

$\rho_n=\cfrac{dn_s}{df}=\cfrac{8\pi}{c^3}f^2$

so,

$P=\cfrac{2}{3}*\cfrac{8\pi f^2}{c^3}*\cfrac{4}{3}\pi{(2c)^3}*\cfrac{1}{2}m_av^2_{rms}$

$P=\cfrac{8^3}{9}\pi^2* f^2*\cfrac{1}{2}m_av^2_{rms}$

We have just mix wave and particles which would make sense only if $v_{rms}=c$, in the time dimension, where the particles are photons.  In the time dimension, one particle occupies the time volume,

$Vol_{time}={T^3}=\cfrac{1}{f^3}$

per unit time volume per particle is,

$per\, time\, volume, particle=\cfrac{1}{T^3}=f^3$

density per particle volume in the time dimension,

$\rho_n=1$

and

$E=m_ac^2$

So,

$P=\cfrac{8^3}{18}\pi^2*f^2*m_ac^2=1*f^3*m_ac^2$

only if,

$f=\cfrac{c}{\lambda}=\cfrac{8^3}{18}\pi^2=280.73541407543064515$

where in the time dimension all entangled particle in a spherical volume of radius $r=2c$ is considered a single particle; a photon at light speed.  And total energy within such a volume/entity is conserved between the time and space dimension.

If we define $\lambda=10^{6}$  then

$c=280735414.07543064515$

or

$c=\cfrac{8^3}{18}\pi^2*10^{6}$

If $c=299792458$,  then

$\lambda=1.0678825790017675793e6$

which is just nonsense because light speed is just fine defined as $299792458\,ms^{-1}$.  What about

$f=280.73\,Hz$   ???

What happened when you flash photons (light at whatever wavelength) at this frequency at someone?  This frequency engage all entangled photon within the spherical volume $r=2c$.  Do photons start oozing from the time dimension?  All such photons are entangled.

Total nonsense...