Quantum Man: Richard Feynman's Life in Science Read Free Page B

provides important evidence that light behaves, in this instance, like a wave.
    Amost thirty years before Huygens’s work, Fermat too reasoned that light should travel more slowly in dense media than in less dense media. Instead of thinking in terms of whether light was a wave or particle, however, Fermat the mathematician showed that in this case one could explain the trajectory of light in terms of a general mathematical principle, which we now call Fermat’s principle of least time . As he demonstrated, light would follow precisely the same bending trajectory determined by Snell if “light travels between two given points along the path of shortest time.”
    Heuristically this can be understood as follows. If light travels more quickly in the less dense medium, then to get from A to B (see figure) in the shortest time, it would make sense to travel a longer distance in this medium, and a shorter distance in the second medium in which it travels more slowly. Now, it cannot travel for too long in the first medium, otherwise the extra distance it travels would more than overcome the gain obtained by traveling at a faster speed. One path is just right, however, and this path turns out to involve a bending trajectory that exactly reproduces the trajectory Snell observed.

    Snell’s law
    Fermat’s principle of least time is a mathematically elegant way of determining the path light takes without recourse to any mechanistic description in terms of waves or particles. The only problem is that when one thinks about the physical basis of this result, it seems to suggest intentionality , so that, like a commuter in Monday-morning rush-hour listening to the traffic report, light somehow considers all possible paths before embarking on its voyage, and ultimately chooses the one that will get it to its destination fastest.
    But the fascinating thing is that we don’t need to ascribe any intentionality to light’s wanderings. Fermat’s principle is a wonderful example of an even more remarkable property of physics, a property that is central to the amazing and a priori unexpected fact that nature is comprehensible via mathematics. If there is any one property that was a guiding light for Richard Feynman’s approach to physics, and essential to almost all of his discoveries, it was this one, which he thought was so important that he referred to it at least two different times during his Nobel Prize address. First, he wrote,
    It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling you can show the relationship. . . . it was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. . . . I think it is somehow a representation of the simplicity of nature. I don’t know what it means, that nature chooses these curious forms, but maybe that is a way of defining simplicity. Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.
    And later (and more important for what was to come), he added,
    Theories of the known, which are described by different physical ideas, may be equivalent in all their predictions and are hence scientifically indistinguishable. However, they are not psychologically identical when trying to move from that base into the unknown. For different views suggest different kinds of modifications which might be made and hence are not equivalent in the hypotheses one generates from them in one’s attempt to understand what is not yet understood.
    Fermat’s principle of least time clearly represents a striking example of this strange redundancy of physical law that so fascinated Feynman, and also of the differing “psychological utilities” of the different prescriptions. Thinking about the