I Don't Know...

What happens when we jiggle this transformed particle in the time dimension at,

$f=280.73\,Hz$

???

I don't know...

Maybe to be consistent, we consider a volume of size,

$Vol_{time}=\cfrac{4}{3}\pi T^3=\cfrac{4}{3}\pi* \cfrac{1}{f^3}$

instead.  In which case,

$P=\cfrac{8^3}{18}\pi^2*f^2*m_ac^2=1*\cfrac{3}{4\pi}*f^3*m_ac^2$

 $f=\cfrac{4*8^3}{3*18}\pi^3=1175.942\,Hz$

a low hum...

And we shall keep the factor  $\cfrac{4}{3}\pi=4.1888$ in mind.

$f=f=\cfrac{4*8^3}{3*18}\pi^3$

Maybe this is part of the reason we needed $\mu_o=4\pi\times10^{-7}$.  The factor  $\cfrac{1}{3}$  can be removed by considering $3R$ in place of $R$ in the post "What If The Particles Are Photons?" dated 12 Dec 2017, as we move from one direction to all 3D space in a volume containing $P$. 

Have a nice day.