5.1   What's the Matter?

• Reminds us of the things we have learned  which we're now going to bring together to  investigate wave-particle duality.

We discussed in Chapter 1 the curious double personality of light:  in the most familiar things it does – like diffraction – it behaves like a wave but in other ways its properties make more sense if we picture it as being made up of particles, which we call photons.  Thus we are forced to accept the idea of wave-particle duality: that light is what it is, but that in our attempts to model its properties, we sometimes have to approximate it one way, sometimes the other.

We also introduced the idea, in Chapter 1,  that  if light, which we normally think of as a wave, can also be a particle, it doesn’t seem entirely unreasonable that something we normally think of as a particle can also behave, in some situations, like a wave. Applying this idea to an electron, for example, we saw that by postulating that electrons in atoms behave like standing waves, we could possibly find a way to explain their quantised energy levels.

We have covered a lot of ground since then.  With the help of special relativity, we have learned to relate the total energy of a particle to its mass and its momentum and crucially for us, we have learned that a photon, even though it has no mass, does have momentum. This, coupled with what we have also learned about how to describe waves mathematically, has now set us up to develop a wave theory of particles. So let’s get started.