De Broglie's paper refers to his theorem
A periodic phenomenon is seen by a stationary observer to exhibit the frequency $ν_1=h^{-1}m_0c^2\sqrt{1-\beta^2}$ that appears constantly in phase with a wave having frequency $ν=h^{-1}m_0c^2/\sqrt{1-\beta^2}$ propagating in the same direction with velocity $V=c/\beta$.
where,
$\beta$=Velocity of periodic matter/ speed of light
$m_0$=proper mass
$c$=velocity of light
$ν_1$=refers to frequency of the periodic oscillation as seen by the fixed observer
$ν$= refers to frequency obtained by equating E=hν=m$c^2$
De Broglie also provides a proof for this theorem. He calculates the phase of the two waves($ν_1$ and $ν$) and shows that the two waves maintain equal phase for any given distance x travelled by the waves.
He calculates phase of $ν_1$ at time t by calculating $ν_1\cdot t$. He then goes on to calculate phase of $ν$ by calculating $ν\cdot(t-\frac{\beta \cdot x}{c})$.I have a question here. Can someone explain how does the factor $(t-\frac{\beta \cdot x}{c})$ comes into play for calculating phase of $ν$
Another question, What does $ν$ frequency obtained through energy relation (hν) indicates. Is it a hypothetical frequency that has no relation to real world?
The full de broglie paper can be downloaded from http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf . I am referring to Chapter 1 'The Phase Wave' derivation.
