Absolutely Small - Michael D. Fayer [36]
7
Photons, Electrons, and Baseballs
PHOTONS, ELECTRONS, AND BASEBALLS are all described with quantum theory in the same way, but quantum theory isn’t necessary to describe baseballs. Baseballs act as classical particles and behave in a manner that is accurately described by classical mechanics. If photons, electrons, and baseballs all have the same quantum mechanical description, why do only baseballs act as classical particles? The answer is that baseballs are large in the absolute sense. Here, we will see why photons and electrons need a quantum theory description but baseballs do not. Real physical situations are discussed that bring out both the wavelike and particlelike nature of quantum particles, that is, absolutely small particles.
WAVES OR PARTICLES?
When a particle is in a superposition state, a wave packet, we have some knowledge of its position and some knowledge of its momentum. So are photons, electrons, and so on waves or particles? The answer is that they are wave packets. Whether they seem to be particles or seem to be waves depends on what experiment you do, that is, what question you ask. In the photoelectric effect, the photons act like particles. One photon hits one electron, and kicks it out of the metal (Figure 4.3). The photon is a wave packet formed from a spread of momentum eigenstates. The width of the spread, Δp, results in a relatively well-defined position, that is, a relatively small Δx. Thus, the photon wave packet is more or less well defined in position, so that it can act like a particle of light in the photoelectric effect. In the interference experiment (Figure 5.1), the photons act like waves. This may not be surprising because the wave packet is, in fact, a superposition of waves, but not waves in the normal classical sense, but rather probability amplitude waves. In the discussion of the interference phenomenon, the photon wave is discussed as if it is a single probability amplitude wave. Now it is clear that it is actually a wave packet, composed of a superposition of waves. When it hits the beam splitter, it becomes a superposition of the two translation states, T1 and T2. The probability amplitude waves in T1 interfere with their corresponding waves in T2, to produce the interference pattern as discussed above.
DIFFRACTION OF LIGHT
So a photon acts like a particle in the photoelectric effect, but it can also act like a wave. An experiment that clearly shows the wavelike properties of photons is diffraction of light from a diffraction grating. It is possible to see diffraction using a music compact disk (CD) and a bright light or sunlight. The CD has very fine grooves on its surface. These are the tracks on which the information is stored. As explained below, when white light from the sun or a light bulb falls on the CD, the grooves diffract the light, sending different colors in particular directions. Different parts of the CD make a range of angles relative to your eye, which causes the appearance of different colors emanating from different parts of the CD.
Diffraction from a grating is used in many optical instruments, called spectrometers. These instruments separate the different colors of incoming light so that the colors can be analyzed individually. A recording of the colors of light from a particular source is called a spectrum. For example, stars emit different colors of light depending on their temperature. Taking a spectrum of the light from a star can provide a great deal of information about the star. Star light traveling through space will encounter molecules in space. As discussed in Chapter 8 and subsequent chapters, different molecules absorb different colors of light. Star light traveling to Earth has some of its colors partially absorbed by the molecules in space. Astronomers mount spectrometers on telescopes and take spectra to determine what types of molecules are in space between a particular