Absolutely Small - Michael D. Fayer [22]
To describe the interference effect, the mathematical formulation in terms of Maxwell’s wavefunctions was not changed at all. However, the physical meaning of the wavefunction was redefined. Instead of the amplitude of an electromagnetic wave in a certain region of space, such as leg 1 or leg 2 of the interferometer, the wavefunction was redefined as describing the number of photons in a region of space. Previously, the wavefunction was taken to give the amplitude of the wave in a region of space, and this amplitude could be used to calculate the intensity. After the redefinition, the wavefunction was taken to tell how many photons were in a region of space, say leg 1 of the interferometer, and the intensity could still be calculated. This redefinition seemed perfectly reasonable, but it was wrong! The entire description of half of the photons going into each leg of the interferometer is fundamentally wrong. The correct description required the leap to thinking quantum mechanically.
FIGURE 5.1. The beam of light is composed of photons that hit a 50% reflecting mirror. In the initial incorrect description of the interference effect in terms of photons, it was thought that half of the photons go into each leg of the interferometer. The photons from each leg cross in the overlap region, and it was believed that the photons from one leg interfere with photons from the other leg to produce the interference pattern. The idea that photons from one leg interfere with photons from the other leg is not correct.
Many things are wrong with the picture that half of the photons go into each leg of the interferometer and then come together and interfere with each other. The simplest experiment that shows the problem with this description is the intensity dependence of the interference pattern (the lower right portion of Figure 5.1). The shape of the interference pattern observed in the overlap region of the interferometer is independent of the intensity used to create it. For a given method of detection, a piece of photographic film or a digital camera, note that if the intensity is turned up it will take less time to acquire a high-quality pattern, but the shape of the pattern is unchanged. That is, the separation and shapes of the peaks and nulls in the pattern are unchanged. As discussed in Chapter 3, the periodicity of the pattern depends on the crossing angle of the beams and the wavelength of light. It does not depend on the intensity. If the intensity is reduced, it will take more time to collect the pattern, but the pattern will not change shape. A standard red laser pointer puts out 1 mW (milliwatt), which is one thousandth of a watt, or 0.001 J/s (joules per second). The red color is approximately 650 nm, that is, the wavelength λ = 650 nm. Using λν = c and E = hν where h is Planck’s constant, ν is the frequency of the light, and c is the speed of light, one photon of 650 nm light is about 3 × 10-19 J. So the 1 mW laser pointer is emitting about 3 × 1015 photons per second, that is 3 thousand trillion photons per second. If this is the input beam for the interferometer, the interference pattern will be very easy to record and, in fact, if the fringe spacing is big enough (see Chapter 3, the discussion of fringe spacing following Figure 3.4), you will be able to see the interference pattern with your eyes.
Imagine turning the intensity down and down. Soon, you will not be able to see the interference