Section 2: Mysteries of Light
Figure 3: This furnace for melting glass is nearly an ideal blackbody radiation source.
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The nature of light was a profound mystery from the earliest stirrings of science until the 1860s and 1870s, when James Clerk Maxwell developed and published his electromagnetic theory. By joining the two seemingly disparate phenomena, electricity and magnetism, into the single concept of an electromagnetic field, Maxwell's theory showed that waves in the field travel at the speed of light and are, in fact, light itself. Today, most physicists regard Maxwell's theory as among the most important and beautiful theories in all of physics.
Maxwell's theory is elegant because it can be expressed by a short set of equations. It is powerful because it leads to powerful predictions—for instance, the existence of radio waves and, for that matter, the entire electromagnetic spectrum from radio waves to x-rays. Furthermore, the theory explained how light can be created and absorbed, and provided a key to essentially every question in optics.
Given the beauty, elegance, and success of Maxwell's theory of light, it is ironic that the quantum age, in which many of the most cherished concepts of physics had to be recast, was actually triggered by a problem involving light.
Figure 4: The electromagnetic spectrum from radio waves to gamma rays.
The spectrum of light from a blackbody—for instance the oven in Figure 3 or the filament of an electric light bulb—contains a broad spread of wavelengths. The spectrum varies rapidly with the temperature of the body. As the filament is heated, the faint red glow of a warm metal becomes brighter, and the peak of the spectrum broadens and shifts to a shorter wavelength, from orange to yellow and then to blue. The spectra of radiation from blackbodies at different temperatures have identical shapes and differ only in the scales of the axes.
Figure 5: Spectrum of the cosmic microwave background radiation.
Source: © NASA, COBE. More info
Figure 5 shows the blackbody spectrum from a particularly interesting source: the universe. This is the spectrum of thermal radiation from space—the cosmic microwave background—taken by the Cosmic Background Explorer (COBE) satellite experiment. The radiation from space turns out to be the spectrum of a blackbody at a temperature of 2.725 Kelvin. The peak of the spectrum occurs at a wavelength of about one millimeter, in the microwave regime. This radiation can be thought of as an echo of the primordial Big Bang.
Enter the quantum
In the final years of the 19th century, physicists attempted to understand the spectrum of blackbody radiation but theory kept giving absurd results. German physicist Max Planck finally succeeded in calculating the spectrum in December 1900. However, he had to make what he could regard only as a preposterous hypothesis. According to Maxwell's theory, radiation from a blackbody is emitted and absorbed by charged particles moving in the walls of the body, for instance by electrons in a metal. Planck modeled the electrons as charged particles held by fictitious springs. A particle moving under a spring force behaves like a harmonic oscillator. Planck found he could calculate the observed spectrum if he hypothesized that the energy of each harmonic oscillator could change only by discrete steps. If the frequency of the oscillator is ( is the Greek letter "nu" and is often used to stand for frequency), then the energy had to be 0, 1 , 2 , 3 , ... n, ... where n could be any integer and h is a constant that soon became known as Planck's constant. Planck named the step a quantum of energy. The blackbody spectrum Planck obtained by invoking his quantum hypothesis agreed beautifully with the experiment. But the quantum hypothesis seemed so absurd to Planck that he hesitated to talk about it.
Figure 6: Max Planck solved the blackbody problem by introducing quanta of energy.
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The physical dimension—the unit—of Planck's constant h is interesting. It is either [energy] / [frequency] or [angular momentum]. Both of these dimensions have important physical interpretations. The constant's value in S.I. units, 6.6 x 10-34 joule-seconds, suggests the enormous distance between the quantum world and everyday events.
Planck's constant is ubiquitous in quantum physics. The combination h/2 appears so often that it has been given a special symbol called "hbar." This symbol appears in the upper-right-hand corner of these pages.
For five years, the quantum hypothesis had little impact. But in 1905, in what came to be called his miracle year, Swiss physicist Albert Einstein published a theory that proposed a quantum hypothesis from a totally different point of view. Einstein pointed out that, although Maxwell's theory was wonderfully successful in explaining the known phenomena of light, these phenomena involved light waves interacting with large bodies. Nobody knew how light behaved on the microscopic scale—with individual electrons or atoms, for instance. Then, by a subtle analysis based on the analogy of certain properties of blackbody radiation with the behavior of a gas of particles, he concluded that electromagnetic energy itself must be quantized in units of . Thus, the light energy in a radiation field obeyed the same quantum law that Planck proposed for his fictitious mechanical oscillators; but Einstein's quantum hypothesis did not involve hypothetical oscillators.
An experimental test of the quantum hypothesis
Whereas Planck's theory led to no experimental predictions, Einstein's theory did. When light hits a metal, electrons can be ejected, a phenomenon called the photoelectric effect. According to Einstein's hypothesis, the energy absorbed by each electron had to come in bundles of light quanta. The minimum energy an electron could extract from the light beam is one quantum, . A certain amount of energy, W, is needed to remove electrons from a metal; otherwise they would simply flow out. So, Einstein predicted that the maximum kinetic energy of a photoelectron, E, had to be given by the equation .
The prediction is certainly counterintuitive, for Einstein predicted that E would depend only on the frequency of light, not on the light's intensity. The American physicist Robert A. Millikan set out to prove experimentally that Einstein must be wrong. By a series of painstaking experiments, however, Millikan convinced himself that Einstein must be right.
The quantum of light energy is called a photon. A photon possesses energy , and it carries momentum /c, where c is the speed of light. Photons are particle-like because they carry discrete energy and momentum. They are relativistic because they always travel at the speed of light and consequently can possess momentum even though they are massless.
Although the quantum hypothesis solved the problem of blackbody radiation, Einstein's concept of a light quantum—a particle-like bundle of energy—ran counter to common sense because it raised a profoundly troubling question: Does light consist of waves or particles? As we will show, answering this question required a revolution in physics. The issue was so profound that we should devote the next section to reviewing just what we mean by a wave and what we mean by a particle.