The two-pendulum clock-developed in 1921 by William Hamilton Shortt-squeezed just about the last ounce of perfection out of mechanical clocks. If significant gains were to be made, a new approach was needed. As we shall see, new approaches became available because of man's increased understanding of natureparticularly in the realms of electricity, magnetism, and the atomic structure of matter. In one sense, however, the new approaches were undertaken within the framework of the old principles. The heart of the clock is today, as it was 200 year ago, some vibrating device with a period as uniform as possible. Furthermore, the periodic phenomena today, as before, involve the conversion of energy, to and fro, between two different forms. In the swinging pendulum we have energy being transferred back and forth repeatedly from the maximum energy of motion-kinetic energy—at the bottom of the swing, to energy stored in the pull of the earth's gravity-or potential energy-at the top of the swing. If the energy does not "leak out" because of friction, the pendulum swings back and forth forever, continually exchanging its energy between the two forms. Energy appears in many forms-kinetic, potential, heat, chemical, light ray, electrical, and magnetic fields. In this discussion we shall be particularly interested in the way energy is transferred between atoms and surrounding fields of radio and light waves. And we shall see that resonators based on such phenomena have achieved Q's in the hundreds of millions. THE QUARTZ CLOCK-Q=105-106 The first big step in a new direction was taken by the American scientist Dr. Warren A. Marrison with the development of the quartz crystal clock in 1929. The resonator of this clock is based upon the so-called "piezoelectric effect." In a sense even the quartz crystal clock is actually a mechanical clock because a small piece of quartz crystal vibrates when an alternating electric voltage is applied to it. Or, conversely, if the crystal is made to vibrate it will generate an oscillatory voltage. These two phenomena together are the piezoelectric effect. The internal friction of the quartz crystal is so very low that the Q may range from 100,000 to 1,000,000. It is no wonder that the quartz resonator brought such dramatic gains to the art of building clocks. The resonant frequency of the crystal depends in a complicated way on how the crystal is cut, the size of the crystal, and the particular resonant frequency that is excited in the crystal by the driving electric voltage. That is, a particular crystal may operate at a number of frequencies in the same way that a violin string can vibrate at a number of different frequencies called overtones. The crystal's vibration may range from a few thousand to many millions of cycles per second. Generally speaking, the smaller the crystal the higher the resonant frequencies at which it can vibrate. Crystals at the high-frequency end of the scale may be less than one millimeter thick. Thus we see that one of the limitations of crystal resonators is related to our ability to cut crystals precisely into very small bits. The crystal resonator is incorporated into a feedback system that operates in a way similar to the one discussed on page 37. The system is self regulating, so the crystal output frequency is always at or near its resonant frequency. The first crystal clocks were enclosed in cabinets 3 meters high, 22 meters wide, and 1 meter deep, to accommodate the various necessary components. Today quartz-crystal wrist watches are available commerciallywhich gives some indication of the great strides made in miniaturization of electronic circuitry over the past few years. The best crystal clocks will keep time to one millisecond per month, whereas lower quality quartz clocks may drift a millisecond or so in several days. There are two main reasons that the resonant frequency of a quartz oscillator drifts. First, the frequency changes with temperature; and second, there is a slow, long-term drift that may be due to a number of things, such as contamination of the crystal with impurities, changes inside the crystal caused by its vibration, or other aspects of "aging." Elaborate steps have been taken to overcome these difficulties by putting the crystal in a temperature-controlled “oven,” and in a contamination-proof container. But just as in the case of Shortt's two-pendulum clock, a point of diminishing return arrives where one must work harder and harder to gain less and less. NUCLEUS ATOMIC CLOCKS-Q = 105 - 109 The next big step was the use of atoms (actually, at first, molecules) for resonators. One will appreciate the degree of perfection achieved with atomic resonators when he is told that these resonators achieve Q's over 100 million. To understand this we must abandon Newton's laws, which describe swinging pendulums and vibrating materials, and turn instead to the laws that describe the motions of atoms and their interactions with the outside world. These laws go under the general heading of "quantum mechanics," and they were developed by different scientists, beginning about 1900. We shall pick up the story about 1913 with the young Danish physicist Niels Bohr, who had worked in England with Ernest T. Rutherford, one of the world's outstanding experimental physicists. Rutherford bombarded atoms with alpha particles from radioactive materials and came to the conclusion that the atom consists of a central core surrounded by orbiting electrons like planets circling around the sun. But there was a very puzzling thing about Rutherford's conception of the atom: Why didn't atoms eventually run down? After all, even the planets, as they circle the sun, gradually lose energy, moving in smaller and smaller circles until they fall into the sun. In the same manner the electron should gradually lose energy until it falls into the core of the atom. Instead, it appeared to circle the core with undiminished energy, like a perpetual motion machine, until suddenly it would jump to another inner orbit, releasing a fixed amount of energy. Bohr came to the then revolutionary idea that the electron did not gradually lose its energy, but lost energy in "lumps" by jumping between definite orbits, and that the energy was released in the form of radiation at a particular frequency. Conversely, if the atom is placed in a radiation field it can absorb energy only in discreet lumps, which causes the electron to jump from an inner to an outer orbit. If there is no frequency in the radiation field that corresponds to the energy associated with an allowed jump, then no absorption of energy can take place. If there is such a frequency, then the atom can absorb energy from the radiation field. The frequency of the radiation is related to the lump or quantum of energy in a very specific way: The bigger the quantum of energy, the higher the emitted frequency. This energy-frequency relationship, combined with the fact that only certain quanta of energy are allowed-namely, the ones associated with electron jumps between specific orbits-is an important phenomenon for clockmakers. It suggests that we can use atoms as resonators, and furthermore that the emitted or resonant frequency is a property of the atom itself. This is a big advance because now we don't have to be concerned with such things as building a pendulum to an exact length or cutting a crystal to the correct size. The atom is a natural, nonman-made resonator whose resonant frequency is practically ELECTRON EMIT ABSORB immune to the temperature and frictional effects that plague mechanical clocks. The atom seems to be approaching the ideal resonator. But we are still a long way from producing an atomic resonator. How are we to count the "ticks" or measure the frequency of such a resonator? What is the best atom to use? How do we get the electron in the chosen atom to jump between the desired orbits to produce the frequency we want? We have partially answered these questions in the section on "Pushing Q to the Limit," on page 37. There we described a feedback system consisting of three elements-an oscillator, a high-Q resonator, and a feedback path. The oscillator produces a signal that is transmitted to the high-Q resonator, causing it to vibrate. This vibration in turn, through suitable electronic circuitry, generates a signal proportional to the magnitude of the vibration that is fed back to the oscillator to adjust its frequency. This process goes around and around until the high-Q resonator is vibrating with maximum amplitude; that is, it is vibrating at its resonant frequency. In the atomic clocks that we shall be discussing, the oscillator is always a crystal oscillator of the type discussed in the previous section, whereas the high-Q resonator is based upon some natural resonant frequency of different species of atoms. In a sense, atomic clocks are the "offspring" of Shortt's twopendulum clock, where the crystal oscillator corresponds to one pendulum and the high-Q resonator to the other. In 1949, the National Bureau of Standards announced the world's first time source linked to the natural frequency of atomic particles. The particle was the ammonia molecule, which has a natural frequency at about 23,870 MHz. This frequency is in the microwave part of the radio spectrum, where radar systems operate. During World War II, great strides had been made in the development of equipment operating in the microwave region, and attention had been focused on resonant frequencies such as that of the ammonia molecule. So it was natural that the first atomic frequency device followed along in this area. The ammonia molecule consists of three hydrogen atoms and one nitrogen atom in the shape of a pyramid, with the hydrogen atoms at the base and the nitrogen atom at the top. We have seen how the rules of quantum mechanics require that atoms emit and absorb energy in discrete quanta. According to these rules the nitrogen atom can jump down through the base of the pyramid and appear on the other side, thus making an upside-down pyramid. As we might expect, it can also jump back through the base to its original position. The molecule can also spin around different axes of rotation: The diagram shows one possibility. Each allowed rotation corresponds to a different energy state of the molecule. If we carefully inspect one of these states, we see that it actually consists of two distinct, but closely spaced, energy levels. This splitting is a consequence of the fact that the nitrogen atom can be either above or below the base of the pyramid. The energy difference between a pair of levels corresponds to a frequency of about 23,870 MHz. To harness this frequency a feedback system is employed consisting of two "pendulums": a quartz-crystal oscillator and the ammonia molecules. The quartz-crystal oscillator generates a frequency near that of the ammonia molecule. We can think of this signal as a weak radio signal being broadcast into a chamber of ammonia molecules. If the radio signal is precisely at the resonant frequency of the ammonia molecules, they will oscillate and strongly absorb the radio signal energy, so little of the signal passes through the chamber. At any other frequency the signal will pass through the ammonia, the amount of absorption being proportional to the difference between the radio signal frequency and the resonant frequency of the ammonia. The radio signal that gets through the ammonia is used to adjust the frequency of the quartz-crystal oscillator to that of the ammonia resonant frequency. Thus the ammonia molecules keep the quartz-crystal oscillator running at the desired frequency. The quartz-crystal oscillator in turn controls some display device such as a wall clock. Of course, the wall clock runs at a much lower frequency-usually 60 Hz, like an ordinary electric kitchen clock. To produce this lower frequency the crystal frequency is reduced by electronic circuitry in a manner similar to using a train of gears to convert wheels running at one speed to run at another speed. Although the resonance curve of the ammonia molecule is very narrow compared to previously used resonators, there are still problems. One is due to the collision of the ammonia molecules with one another and with the walls of the chamber. These collisions produce forces on the molecules that alter the resonant frequency. Another difficulty is due to the motions of the molecules-motions that produce a "Doppler shift" of the frequency. We have observed Doppler frequency shifts when we listen to the whistle of a train as it approaches and passes us. As the train comes toward us, the whistle is high in pitch, and then as the train passes by, the pitch lowers. This same effect applies to the speeding ammonia molecules and distorts the results. Turning to the cesium atom instead of the ammonia molecule minimizes these effects. The Cesium Resonator-Q = 107 - 108 The cesium atom has a natural vibration at 9,192,631,770 Hz, which is, like that of the ammonia molecule, in the microwave part of the radio spectrum. This natural vibration is a property of the atom itself, in contrast to the ammonia natural frequency, which results from the interactions of four atoms. Cesium is a silvery |