Waves or Particles?

A French Prince and Waves of Matter

Einstein had shown that light waves could behave like particles. Could particles behave like waves? In 1923, French Prince Louis de Broglie, generalised Einstein's work from the specific case of light to cover all other types of particles. This work was presented in his doctoral thesis when he was 31. His thesis was greeted with consternation by his examining committee. Luckily, Einstein had received a copy in advance and vouched for de Broglie. He passed! de Broglie thought that the waves were not just strange abstractions – he said they could be measured! The simple but profound importance of de Broglie's ideas become even more clear when expressed with simple mathematics for photons.

We start with Einstein's famous equation which relates energy 'E' of an object to its mass 'm' and the speed of light 'c'

E = m c² = m c c.

de Broglie realised that 'm c' was simply the photon momentum, p (mass x velocity). So, we can now write

E = p c.

The speed of light 'c' can also be expressed as

c = f ,

where 'f' is the frequency of the light and is its wavelength.

Remember that we also know from Planck's work that

E = h f.

Putting all this together we have

h f = p f .

Or equivalently

h / p = ,

i.e.: as the wavelength of light decreases, the momentum of the photons increases.

Related Laureates