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3-8: Summary of Part 3

Let us summarize what we have learned in Part 3.
(1) It was clarified that the law of equipartition of energy that is inevitably derived from the classical theory (Newtonian mechanics and Maxwellian electromagnetism) is not satisfied for the heat capacities of solids at low temperature and for the cavity radiation. This was a deadlock which the classical theory came to.
(2) It was made clear that the deadlock would be overcome by introducing Planck's hypothesis of energy quanta, i.e., the energy is not a continuous quantity but exists in a form of "grains" (energy quanta).
(3) Extending Planck's hypothesis, Einstein proposed the hypothesis of light quanta, i.e., light exists in a form of "particles" and it is absorbed into atoms as a whole unit instantaneously. This particle nature of light was confirmed by experiment.
The particle of light was called photon, and has been admitted into the brotherhood of "particles" like electrons or protons.
The particle nature of light can never be explained with the classical theory. It is an amazing property from the point of view of the classical theory.

[The Particle Nature and the Wave Nature of Light]
Although the particle nature of light was made clear, yet its wave nature has not been denied. The fact that light causes the diffraction and the interference cannot be understood on the basis of the particle nature.
Let us consider Young's experiment with a double-slit by which T. Young (UK, 1773 - 1829) confirmed the wave nature of light for the first time.
A schematic drawing of Young's experiment is given in the following figure.

Young's double-slit experiment

A monochromatic light from a point source passes through the two thin slits, S1 and S2, and makes an interference fringes (striped pattern) on the screen. An example of the interference fringes is shown in the following picture.

The above picture (A) represents the picture of the pattern on the screen when only one of the slits is open, and (B) shows the picture of the striped pattern on the screen when both the slits are open.
The reason why such a striped pattern appears on the screen in the double-slit experiment is as follows:

Path difference in Young's experiment

As seen in the above figure, the incident monochromatic light (electromagnetic wave) passes through both the slits separately. The two groups (beams) of light, one passing through the slit S1 and the other the slit S2, interfere with each other after having passed through each slit. Let us assume that the distance between the two slits is d. Here we think of the path of beams from the slit S1 (or S2) to a point A on the screen. If the path difference

is equal to an integral multiple of the wavelength, then the two beams reinforce each other at the point A and constructive interference occurs. If the path difference is equal to where n is an odd integer, destructive interference occurs and a dark fringe results. Thus there appears an striped interference pattern on the screen.
If we assume that light is "particles", one particle cannot pass through two slits simultaneously so that such a interference pattern as in the above picture (B) never appears. The experimental fact that there actually appear the interference fringes on the screen implies that light must be waves and a wave passes through the double slits partially and simultaneously to make an interference pattern.
Looking at these facts, we have to consider that light must be particles at one moment and waves at another moment. Then, when is it particles? And when is it waves? This is a quite difficult question. What is the true feature of light?
The answer to this question has first been given by the construction of Quantum Mechanics. Until then, physicists could not help changing their attitudes depending on what kind of problem they met with. They adopt the particle theory on one occasion and the wave theory on the other. Someone told a joke that they obey the particle theory on Monday, Wednesday and Friday in a week, and the wave theory on Tuesday, Thursday and Saturday.
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