Sunday, June 27, 2021

Another Resonance In Cubic Time And Spherical Space

 If we consider, a cube in the time dimension again and a sphere in the space dimension. 



From the post "Freaking Out Entanglement" dated 14 Dec 2017 (corrected as),

\(\cfrac{8^3}{6}\pi^2*f^2*m_ac^2=1*\cfrac{3}{4\pi}*f^3*m_ac^2\)

instead of a sphere in time we use a cube,

\(\cfrac{8^3}{6}\pi^2*f^2*m_ac^2=1*\cfrac{1}{Vol_{cube}}*m_ac^2\)

The centroid to vertex distance, \(r\) of a cube of edge \(a\) is,

\( r=\cfrac{\sqrt{3}}{2}a=T\)

if this is equal to \(T\) (a unit of time) then its volume is given by,

with \(a=\cfrac{2}{\sqrt{3}}T\),

\(Vol_{cube}=\left(\cfrac{2}{\sqrt{3}}T\right)^3\)

This approach is consistent with that taken for other platonic solids.  Previously, in the post "What If The Particles Are Photons?" dated 12 Dec 2017, we had used simply \(T=a\) and had obtained a value of \(f=280.735\,\,Hz\). 

With \(T=\cfrac{\sqrt{3}}{2}a\) however,

\(\cfrac{8^3}{6}\pi^2*f^2*m_ac^2=1*\left(\cfrac{\sqrt{3}}{2}f\right)^3*m_ac^2\)

where \(T=\cfrac{1}{f}\),

\(f=\cfrac{8^3}{6}\left(\cfrac{2}{\sqrt{3}}\right)^3\pi^2=131.379\pi^2=1296.661\,\,Hz\)

What is this frequency?  square 1296-661 Hz