(Credit to Don Marolf in this section. I basically follow his order)
The experiment was performed by Thomas Young in 1800, and demonstrated that Fermat's least time principle could not be the last word to describe light. The experiment is utterly simple. Young took a source of light (had to be the sun? find out), and caused it to shine on an opaque screen with a small slit in it, a few tenths of a millimeter wide. On the far side of this screen, he put another screen, this time with two parallel small slits, so that the light shining through the first screen could illuminate (and therefore shine through) them. Whatever light finally came through all three of the slits was used to illuminate a screen several meters away, which Young could observe. The experimental setup is shown in fig. 7.4.
What Young saw is rather remarkable. The screen was lit up with a pattern of parallel bands of light, which repeated for about a centimeter before they faded out and became too dim to see. There were several bands, not just one or two. It is instantly clear that Fermat's principle cannot predict this behavior, simply because that principle, by construction, predicts a unique least time path. Even with different combinations of slits considered, there is no way for it to produce so many actual paths for light to have taken. Something else is requred.
Without explaining it completely, we can make the following suggestive observations. We saw that ripples, as waves, can add, meaning that the values of the height field, excited at the same place by two ripples, is the sum of the values either would have caused. Waves, however, as we have seen in the pictures, involve both positive and negative deviations. Two positive numbers add to make a larger positive number, and two negative numbers add to produce a larger negative number, but a positive and a negative number, appropriately chosen, can add to produce zero. In particular, two waves created by different sources can combine to produce very complicated resulting motions, which can be large in some places, either positively or negatively, but can also be zero in others, because the waves `cancel each other'.
Young, seeing the pattern of bright and dark bands on the screen, postulated that somehow, light must be a wave, and that the brightness of the light was related to how big the wave was at some place. He had no idea in what it might be a wave, but he also didn't have to. We can recognize a ripple, whether it is on the surface of a pond or in the edge of a glass, or even in the hot air over a desert road. This is why the distinction between the wave, and the field that it is a wave in, is important. Without being able to measure the field in which light is a wave, or indeed even caring whether it existed, Young could measure and predict properties of the wave itself, such as how long the cycles were and what patterns could be produced when waves emanated from two different sources (his two secondary slits) to shine on the same screen. All he needed were the characteristics of the waves themselves, and the crucial assumption that they had this property of superposition.
We will show Young's explanation of the behavior of light through the two slits in explicit detail in the first chapter of Part III, where we will also pursue its ramifications to discover a whole technology for predicting wave properties. For now, suffice it to observe that wave addition has the intriguing property that two `something's can add to make `nothing', and that nothing is exactly what Young saw in the dark spaces between his bands. Further, historically, we note that Young was able to predict exactly the right distance between the light and dark bands, which was the first compelling evidence that light should be described as a wave, at least under some circumstances. It is important that such a description is possible only if: i) the wave exists, which implies certain characteristics of the field that supports it, and ii) it has the property of superposition. Both of these properties will be very important to us in understanding later topics.
Finally, it is very important that we can predict properties of excitations like waves, even when we cannot measure or for that matter even understand what fields they are created in. This was useful for Young, who had no way to know that the fields mattered, much less what they were. Maxwell, with his seminal understanding of Electricity and Magnetism, related those waves to Electric and Magnetic fields, which he thought were measureable (hence classical) fields. The whole world agreed with him for nearly half a century, and made very good experimental predictions. Then, gradually in the 1930s and 1940s after the quantum interpretation of fields had been reasonably well developed in other contexts, it became increasingly clear that the electric and magnetic fields that Maxwell thought were classical were in fact quantum mechanical fields. They were not intrinsically measureable at all. A large category of measurements happen to extract secondary properties from them in such a way that it looks very much like one is measuring the field itself. Once again, the elusive field required re-understanding. Meanwhile, the wave predictions remained intact. The only importance of the fundamental groundwork-shifting being done to the meanings of the fields was, that previous wave predictions were shown simply to be approximations of various kinds. People had to agonize over the correct new interpretations of the fields with each experimentally driven revolution, but the outcome of the new interpretations was simply that they showed how to compute new and better refinements to the previous approximate conclusions. Of course, they also revealed new and unsuspected phenomena, which the previous predictions would have gotten disastrously wrong, as Fermat's principle would have done for Young's experiment.
These are the basic properties of all fields that we will need. We now turn our attention to certain technical considerations, which we must understand in order to make sense of what we actually see.