Warped Passages (21 page)

Satellites have recently measured the spectrum of this cosmic microwave background radiation (which is what Figure 40 shows). It looks almost precisely like the spectrum of a blackbody with a temperature of 2.7 degrees K. The measurements tell us that deviations are smaller than one part in ten thousand. In fact, this relic radiation is the most accurately measured blackbody spectrum to date.

When asked in 1931 how he had come up with his outrageous assumption that light is quantized, Planck responded, “It was an act of desperation. For six years I had struggled with the blackbody theory. I knew the problem was fundamental and I knew the answer. I had to find a theoretical explanation at any cost…”
^*
For Planck, light quantization was a device, a kludge that gave the correct blackbody spectrum. In his view, quantization was not necessarily a property of light itself, but could instead have been a consequence of some property of the atoms that were radiating the light. Although Planck’s conjecture was the first step in understanding light quantization, Planck himself did not fully comprehend it.

Five years later, in 1905, Einstein made a major contribution to quantum theory when he established that light quanta were real things, not merely mathematical abstractions. Einstein was a very busy man that year, developing special relativity, helping to prove that atoms and molecules exist by studying the statistical properties of matter, and providing a validation of quantum theory—all while he was working at the Swiss patent office in Bern.

The particular observation that Einstein interpreted using the hypothesis of light quanta, thereby enhancing its credibility, is known
as the
photoelectric effect
. Experimenters shone a single frequency of radiation onto matter, and that incoming radiation propelled electrons out. Experiments had shown that bombarding material with more light, which carries more total energy, did not change the maximum kinetic energy (energy of motion) of the emitted electrons. This is contrary to what intuition might suggest: larger incident energy should surely produce electrons with larger kinetic energy. The limit on the electron’s kinetic energy was therefore a puzzle. Why didn’t the electron absorb more energy?

Einstein’s interpretation was that radiation consists of individual quanta of light, and only a single quantum will donate its energy to any particular electron. Light is delivered to an individual electron like a single missile, not like a blitzkrieg. Because only one quantum of light ejects the electron, more incident quanta would not change the energy of the emitted electron. Increasing the number of incident quanta makes the light eject more electrons, but it doesn’t influence the maximum energy of any particular electron.

Once Einstein interpreted the results of the photoelectric effect in terms of these definite packets of energy—the quantized units of light—it made sense that the emitted electrons always had the same maximum kinetic energy. The most kinetic energy an electron can have is the fixed energy that it receives from the quantum of light minus the energy required to eject the electron from the atom.

Using this logic, Einstein could deduce the energy of the light quanta. He found that their energy depended on the frequency of the incident light exactly as Planck’s hypothesis predicted. To Einstein, this was clear evidence that light quanta were real. His interpretation gave a very concrete picture of light quanta: a single quantum hit a single electron, which it thereby ejected. It was this observation and not relativity that earned Einstein the Nobel Prize for Physics in 1921.

Oddly enough, however, although Einstein acknowledged the existence of quantized units of light, he was reluctant to accept that these quanta were actually massless particles, which carried energy and momentum but had no mass. The first convincing evidence for the particle nature of the quanta of light came from the 1923 measurement of
Compton scattering
, in which a quantum of light hits an electron
and is deflected (see Figure 41). In general, you can determine a particle’s energy and momentum by measuring its deflection angle after a collision. If photons were massless particles, they would behave in a well-defined manner when they collided with other particles such as electrons. Measurements showed that the quanta of light behaved precisely as if the quanta were massless particles that interacted with the electrons. The inexorable conclusion was that light quanta were indeed particles, and we now call these particles
photons
.

Figure 41.
In Compton scattering, a photon (γ) scatters off a stationary electron (e
^-
) and emerges with a different energy and momentum.

It’s perplexing that Einstein was so resistant to the quantum theory that he helped to develop. But his reaction is no more remarkable than Planck’s response to Einstein’s quantization proposal—which was disbelief. Planck and several others praised Einstein’s many achievements, but qualified their enthusiasm.
^*
Planck even said, somewhat disparagingly, “That he missed the target in his speculations, as, for example, in his hypothesis of light-quanta, cannot really be held too much against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk.”
^†
Make no mistake. Einstein’s conjectured light-quanta were right on target. Planck’s comment merely reflects the revolutionary nature of Einstein’s insight and the initial reluctance of scientists to accept it.

Quantization and the Atom

The story of quantization and the old quantum theory didn’t end with light. It turns out that
all
matter consists of fundamental quanta. Niels Bohr was next in line with a quantization hypothesis. In his case, he applied it to a well-established particle, the electron.

Bohr’s interest in quantum mechanics developed, in part, from attempts at the time to clarify the atom’s mysterious properties. During the nineteenth century, the notion of an atom was unbelievably vague: many scientists didn’t believe that atoms existed other than as heuristic devices that were a useful tool but which had no grounding in reality. Even some of the scientists who did believe in atoms nonetheless confused them with molecules, which we now know to be composites of atoms.

The atom’s true properties and composition were not accepted until the beginning of the last century. Part of the problem was that the Greek word “atom” meant a thing that could not be divided, and the original picture of the atom was indeed one of an unchanging, indivisible object. But as nineteenth-century physicists learned more about how atoms behave, they began to realize that this idea had to be incorrect. By the end of the century, radioactivity and
spectral lines
, the specific frequencies at which light is emitted and absorbed, were some of the best-measured properties of atoms. Yet both of these phenomena showed that atoms could change. On top of that, in 1897, J.J. Thomson identified electrons and proposed that the electron was an ingredient of the atom, which meant that atoms had to be divisible.

At the beginning of the twentieth century, Thomson synthesized the atomic observations of the time in his “plum pudding” model, named after the British dessert containing isolated pieces of fruit stuck in a bready blob. He suggested that there was a positively charged component spread throughout the atom (the bready part), with negatively charged electrons (the pieces of fruit) embedded inside.

The New Zealander Ernest Rutherford proved this model wrong in 1910, when Hans Geiger and a research student, Ernest Marsden, performed an experiment that Rutherford had suggested. They discovered a hard, compact atomic nucleus, much smaller than the atom
itself. Radon-222, a gas produced in the radioactive decay of radium salts, emits alpha particles, which we now know to be helium nuclei. The physicists revealed the existence of the atom’s nucleus by shooting alpha particles at atoms and recording the angles at which the alpha particles scattered. The dramatic scattering they recorded could arise only if there were a hard, compact atomic nucleus. A diffuse, positive charge spread throughout the extent of the atom could never have scattered the particles so widely. In Rutherford’s words, “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
^*

Rutherford’s results disproved the plum pudding model of the atom. His discovery meant that the positive charge was not spread throughout the atom, but was instead confined to a much smaller inner core. There had to be a hard central component, the nucleus. An atom, according to this picture, consisted of electrons that orbited a small central nucleus.

In the summer of 2002 I attended the annual string theory conference, which happened to be held that year at the Cavendish Laboratory in Cambridge. Many important pioneers of quantum mechanics, including two of its heads, Rutherford and Thomson, did much of their important research there. The hallways are decorated with reminiscences of the exciting early years, and I learned some amusing facts while wandering the hallways.

For example, James Chadwick, the discoverer of the neutron, had studied physics only because he was too shy to point out that he had mistakenly waited in the wrong line when matriculating. And J.J. Thomson was so young when he became head of the lab (he was twenty-eight) that a congratulation read, “Forgive me if I have done wrong in not writing to wish you happiness and success as a professor. The news of your election was too great a surprise to permit me to do so.” (Physicists aren’t always the most gracious.)

Yet despite the coherent picture of the atom that had developed by the early twentieth century at the Cavendish and elsewhere, the
behavior of its components was about to wreak havoc with physicists’ most fundamental beliefs. Rutherford’s experiments had suggested an atom consisting of electrons that traveled in orbits around a central atomic nucleus. This picture, simple as it was, had an unfortunate drawback: it had to be wrong. Classical electromagnetic theory predicted that when electrons orbited in a circle, they would radiate energy through photon emission (or, classically speaking, electromagnetic wave emission). The photons would thereby remove energy and leave behind a less energetic electron, which would orbit in ever smaller circles, spiraling in towards the center. In fact, classical electromagnetic theory predicted that atoms could not be stable, and would collapse in less than a nanosecond. The atom’s stable electron orbits were a complete mystery. Why didn’t electrons lose energy and spiral down into the atomic nucleus?

A radical departure from classical reasoning was required to explain the atom’s electron orbits. Pursuing this logic to its inevitable conclusion exposed chinks in classical physics that could be filled only by the development of quantum mechanics. Niels Bohr made just such a revolutionary proposal when he extended Planck’s notion of quantization to electrons. This, too, was an essential component of the old quantum theory.

Electron Quantization

Bohr decided that electrons couldn’t move in just any old orbit: an electron’s orbit had to have a radius that fit a formula he proposed. He found these orbits by making a lucky and ingenious guess. He decided that electrons must act as if they were waves, which meant that they oscillated up and down as they circulated about the nucleus.

In general, a wave with a particular wavelength oscillates up and down once over a fixed distance; that distance is the wavelength. A wave that goes around a circle also has an associated wavelength. In this case the wavelength sets the extent of the arc over which the wave will go up and down once as it winds around the nucleus.

An electron that orbits in a fixed radius cannot have any wavelength.
It can only have a wavelength that would permit the wave to go up and down a fixed number of times. That implied a rule for determining the allowed wavelengths: the wave has to oscillate an integer
^*
number of times when going around the circle that defined the electron’s orbit (see Figure 42).