Monday, June 27, 2016

And Light Speed Has A Pulse...

From the post "Just When You Think c Is The Last Constant" dated 26 Jun 2016,

\(c=\sqrt { \cfrac { 38.5*(32\pi ^{ 4 }-1) }{ 64*3.135009*\pi .ln(cosh(3.135009))tanh(3.135009) }  *\left( \cfrac {3.135009}{ 0.7369 }  \right) ^{ 3 }}\)

Since,

\(\left( \cfrac { 3.135009 }{ 0.7369 }  \right) ^{ 3 }=77\)

\(c=\sqrt { \cfrac { \frac { 77^{ 2 } }{ 2 } *(32\pi ^{ 4 }-1) }{ 64*3.135009*\pi .ln(cosh(3.135009))tanh(3.135009) }  } \)

We generalize the above expression,

\(c=n\sqrt { \cfrac {(32\pi ^{ 4 }-1) }{ 128\pi\theta_{\psi}ln(cosh(\theta_{\psi}))tanh(\theta_{\psi}) }  } \)

where given \(n\), \(\theta_{\psi}\) is fixed.

\(n.a^3_{\psi\,c}=a^3_{\psi}\)

as \(n\) basic particles reform into one particle, a sphere of radius \(a_{\psi}\).

\(a_{\psi}=\sqrt [  3]{n  }.a_{\psi\,c} \)

and

\(\theta_{\psi}=\cfrac{G}{\sqrt{2mc^2}}a_{\psi}=\cfrac{a_{\psi\,c} G}{\sqrt{2mc^2}}\sqrt [  3]{n  }\)

\(G\) is not the gravitational constant, it is still unknown.

We have,

\(\left(\cfrac{c}{n}\right)^2=\cfrac {(32\pi ^{ 4 }-1) }{ 128\pi\theta_{\psi}ln(cosh(\theta_{\psi}))tanh(\theta_{\psi}) }\)

where \(\theta_{\psi}\) is proportional to \(\sqrt [  3]{n  }\)

A plot of xln(cosh(x))tanh(x) gives,


and a plot of 1/(xln(cosh(x))tanh(x)) and 3/x^2 gives,


Both curves coincide only at \(x=1\).  In the expression for \(c\), \(c\) is not a constant but changes with \(n\).  It is an expression for \(c\) that is valid only at the point \(n=77\) with the assumption that,  

\(\theta_{\psi}=\cfrac{G}{\sqrt{2mc^2}}a_{\psi}\approx\pi\)

which delimits the particle size to be less than or equal to,

\(\theta_{\psi}=\cfrac{G}{\sqrt{2mc^2}}a_{\psi}=\pi\)

\(n=77\) is not a more fundamental constant, changing \(n\) does not change \(c\) in reality, but changes the magnitude of the charge.

And light speed has a pulse...