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 $V=c/\beta$.


  • $\beta$=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.

  • $\begingroup$ Are you saying that the first relation is for a fixed observer and a fixed source? What is the observer fixed relative to? $\endgroup$ – ggcg May 8 at 20:39
  • $\begingroup$ @ggcg as I understand there is some periodic oscillation of a moving particle. If an observer watches the moving particle from a fixed reference, he sees the frequency to be lesser. $\endgroup$ – Karthick S May 9 at 2:32

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