At the expense of any pretensions of historical accuracy,
I am going to see how many interesting conclusions we can
draw from one simple hypothesis posed by
Louis Victor Pierre Raymond duc de Broglie
in his 26-page doctoral thesis in 1924.
It had been shown two decades earlier
that light, which is certainly a wave,
comes quantized in clumps like particles
(called photons) with the energy of each photon
equal to Planck's constant times its frequency: ,
where
J-s is Planck's constant.
(It was the explanation of this phenomenon in 1905
that won Albert Einstein the Nobel prize.
Relativity was just gravy.)
It had already been shown earlier still
(in the late Nineteenth Century)
that an electromagnetic wave carries both energy E
and momentum p, in the ratio E = pc where
c is the speed of light. This ratio holds also
for quantized photons, which therefore have momentum
.
But for any wave,
,
so