March 11th, 2018, 10:42 am
Just a mathematical coincident between the proton mass and the proton radius (possible proton radius) or something more to it?
\(r_p=\frac{\hbar}{2m_Pc}\sqrt{\frac{1}{2\alpha-\alpha^2}}\approx 0.872015\times 10^{-15} \mbox{ m}\)
or even simpler from the reduced Compton of the proton
\(r_p=\frac{\bar{\lambda}_P}{2}\sqrt{\frac{1}{2\alpha-\alpha^2}}\approx 0.872015\times 10^{-15} \mbox{ m}\)
where \(m_P\) is the proton mass (CODATA), \(\alpha\) fine structure, and \(\hbar\) is the reduced Planck constant. And a particle with reduced Compton equal to half the proton radius if travel at speed \(c(1-\alpha)\) will have relativistic mass equal to the proton mass, that is how I found equation above. That would be rather fun, a particle traveling (rotating?) with speed \(c(1-\alpha)\) and relativistic mass equal to the proton mass, surrounded by a particle (electron) traveling with speed \(c\alpha \). And naturally \(c(1-\alpha)+c\alpha=c\), conservation of velocity particle pair.
or just some correlation versus causality?