3-The big step
That’s one small step for man, one giant leap for mankind
.Neil Armstrong on the moon
To people like us who live with established ideas , these ideas may appear self evident specially if the idea is not merely an idea anymore but has become an empirical fact after being confirmed by many observations and experiments. We rarely can estimate how much originality in thinking was necessary to first come to the idea.
De Broglie's idea of matter waves is one of these ideas. It is important not only because of the creative thinking behind its invention, but also because of the far-reaching consequences in the scientific developments that followed it.
De Broglie thought: "If light or generally electromagnetic waves have quantized properties, maybe this dual nature is not restricted to light alone, maybe material particles -of which we know that they are countable entities since millikans discovery of elementary electric charge- , are not only particles but they might have wavelike properties "
This idea was the essence of the Ph.D. thesis defended by Louis de Broglie in Paris 25 November 1924 . His dissertation was accepted only after a certain resistance.(Einsteins good reference contributed to the acceptance) .
In his work he tried to find the relationship between the wave properties like wavelength, frequency and the known mechanical quantities like energy momentum1. He formulated the dispersionsrelation for electron waves namely the relation between wave length and the frequency.
If the idea of electron waves was correct, electron beams should show interference effects as any other wave phenomena.2 This was in fact experimentally demonstrated in 1927 – by Davisson and Germer in USA and by G.P. Thompson in scotland- 3. Experiments with electrons of various energies confirmed De Broglies dispersionsrelation.
But something very strange seemed to happen in the interference experiments. This is discussed in the next chapter.
1. In nonrelativistic limit namely when the velocity v is much smaller then light velocity c the momentum is given by mv (m the mass of the particle) For greater v the relation is not linear in v anymore but by a small increase in velocity , the momentum increases rapidly going asymptotically to infinity when v comes closer to c .
2. Waves from two coherent sources (coherent: oscillating whitout uncontrolled relative phase shifts) like a plane wave passing through double slits create a stationary wavy pattern in space. If it is a light wave, dark and bright stripes appear on a paper/plate placed at some distance behind the slits
3. Hey,Tony 1987 p.27