3

I came across the derivation, present all across the web, which utilized Einstein's energy mass equivalence equation and energy of a photon. It goes like this: $$ E = mc^2,\;\;E = h f \;\;[f = \text{frequency} ]\;\;\Rightarrow \;\;hf = mc^2\\ \frac{h c}{\lambda} = mc^2 \;\;[\lambda = \text{wavelength}]\\ \frac{h}{\lambda} = p, \;\;\;\frac{h}{p} = \lambda,\;\;\;\frac{h}{mv} = \lambda $$ With this, I have a problem with every step (like converting $mc$ to $p$ and then to $mv$)? IS this really correct? How?

Supposing we use, $E/c = p$ for a photon, then isn't it still wrong? Aren't we using EM radiation to find an associated wave? Aren't these completely different? Could someone please help with the real one?

Qmechanic
  • 201,751
Adam Karlson
  • 199

1 Answers1

5

When de Broglie published his proposed relationship he attempted to show that it was compatible with the Planck relation and Special Relativity; his arguments are quite detailed, and heuristic.

His goal was to show convincingly that if waves had particle properties, then particles must have wave properties --and he invoked Special Relativity as a principle in a variety of ways.

As you have noted, the de Broglie relation is trivially valid for the momentum of light; his arguments try to show that this relationship is the only possibility for a matter wave. But in the end one cannot derive this relationship: it is a physical hypothesis, and has to be shown experimentally.

So ultimately these "demonstrations" don't matter; even if they were to give all of de Broglie's arguments they would still be flawed. For more of the flavor of the original argument, see https://en.m.wikipedia.org/wiki/Matter_wave

Peter Diehr
  • 7,165