It all comes together

Nobody could be blamed for becoming confused about all these aspects of light. We based geometrical optics on Fermat's principle of least time. In wave optics we considered the wave nature of light. Now we are talking about vector amplitudes!

In fact, these methods are equivalent mathematically. Vector amplitudes in Feynman's formalism add and subtract in an identical manner to the superposition of waves. The vector amplitudes representing paths of the same single photon are more mysterious, but the mathematical result is the same.

Instead of talking about 'histories' and 'rotating arrows' let us visualise two trains of waves, which follow different paths and come together again. Paths which are near to the quickest path are almost equal in length. The waves arriving at B are almost exactly in phase, and the resultant amplitude at B is large. Waves which take longer, more 'roundabout' routes can arrive at B with any phase value. In general a large number of such waves coming together will cancel out.

What then is new?

The new and very powerful theory developed by Feynman extends the formalism to include the most basic particle of matter, the electron. His theory not only considers how (i) a photon can go from place to place, but also (ii) how an electron can go from place to place, and (iii) how an electron can emit or absorb a

Figure 14.14 When the path lengths differ significantly, there is a random phase difference between waves arriving at B.

photon. These, according to Feynman, are the three basic actions from which all the phenomena of light and electrons arise. They form the basis of quantum electrodynamics.

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