Waves of what?

What do wave ideas tell us about light?

In thinking about the production of dark and light fringes on a screen as light passes through two slits to create interference effects, the basic questions of interest are:

Where on the screen will photons of energy arrive?

Where are the light places, where are the dark places?

These questions are answered by using wave ideas, and thinking about trip times and possibly path differences. At places where wave theory tells us that the amplitudes of the interfering waves add constructively, we can expect to find lots of photons arriving. Where wave theory tells us that the amplitudes of the waves add to nothing through destructive interference, we can expect not to find photons arriving.

In this way we use wave ideas to predict the probability of photons arriving at certain places. In fact, the probability of photons arriving is proportional to the square of the amplitude of the resultant wave at that point. With these procedures in mind, we might say that light waves are probability waves telling us where photons of energy are most likely to arrive.