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?t...7<)1CS Precise Measurement of Time Norman F. Ramsey Long before the earth supported life, it was subject to marked periodicities: the change from day to night and the change in seasons. These periodicities had a profound effect on the evolution of biological organisms; most animals have a circadian rhythm which leads them to need sleep at approximately 24-hour interval even if they are confined to an artificial environment with no periodic changes in lighting. The all-toofamiliar j t lag that human beings experience when traveling long distances east or west demonstrates the difficulty that they have re etting their internal biological clocks. The periodicities in man's physical environment and in his biological nature clearly must have affected his development of the concept of time. That d velopment has in tum been closely intertwined with the ability to measure time, and in some respects the very meaning of time is defined by the methods used to measure it. The fundamental features of any clock are a mechanism to provide regular periodicity, such as the rotation of the earth, the successive in:ersions of an hour glass, or the motion of a pendulum; a source of energy to maintain motion without significantly affecting the periodicity; and a means for counting the periods and displaying the time. In discuss'omran &msey IS Hrggins Professor of Plrysics Emmtus at Han.~t~rd Umvrn;rty and ttru recently a visrtmg fellow at tire Joint iiiSirtute for l.Aoomtory Astroplrysrcs m Boulder, Colorado. His erptrimmtal work lras ranged from molecular OCams to particle plrysics, and Ire lras concentmted on prtcist measumnmt of tire tlectnc and 11ragnetrc properties of m1clcons, nuclei, atoms, and molecules. He IS the mventor of the separated OSCillatory field method used m atomic beam clocks md co·mventor of the hydrogen masu. He IS currently president of tire Umted Chapters of Phi Beta Kappa . Address: Lyman Plrysrcs l.Aooratory, Han.~t~rd Univrn;rty, Cambridge, MA 02138. ~::! American Scientist, Volume 76 ing the characteristics of clocks, it is necessary to distinguish between three different but related properties: accuracy, reproducibility, and stability. Accuracy measures the degree to which a clock agrees with the value specified in the definition of the unit of time. Reproducibility is a measure of the extent to which properly adjusted independent devices of the same design agree. Stability is a measure of the degree to which a device gives the ~e results in successive intervals of time. Because the stabil- Tradition has it that in 1583, Galileo compared the motion of a swinging lamp with his pulse and discovered that the lamp's period of oscillation was approximately independent of its amplitude (1). This observation provided the scientific basis for the use of pendulums in clocks. Although Galileo recognized the value of his discovery for keeping time, it was 73 years before the Dutch scientist and clockmaker Christian Huygens devised a suitable mechanism, called an escapement, to maintain the oscillations and made the first successful pendulum-controlled clock. Clearly technology transfer The unprecedented was slow. Twenty years later, Huygens combined some ideas of Robert accuracy and stability Hooke with his own escapement of atomic clocks mechanism and produced a dock whose periodicity was provided by have revolutionized an oscillating balance wheel retimekeeping and strained by a spiral spring. This clock was the forerunner of clocks and exact measurement watches with balance wheels and in many fields hairsprings. The pendulum clock continued to provide the most accurate timekeeping for the next two ity and accuracy of a clock are pri- and a half centuries. The accuracy of marily detennined by the mechanism both pendulum and balance wheel providing the periodicity, this feature clocks improved steadily up to the is emphasized in discussions of the twentieth century, as compensations were introduced to diminish the efprecise measurement of time. Various devices and mecha- fects of changing external conditions nisms have been used over the cen- such as temperature (2). By the midturies as sources of periodicity for dle of the twentieth century, the stameasuring time. Many prehistoric bility of the best gravity pendulum monuments are oriented to detect clocks was approximately 2 x 10- 8 . the summer solstice. Solar indicators were used by early man to divide the Quartz crystal clocks day into measurable subunits; as civilization advanced, these were super- Time and frequency are closely relatseded by water clocks, candles, and ed, since frequency is by definition hourglasses, most of which had inac- the number of cycles of osdllation curacies worse than 1,000 seconds a per second (hertz). Provided the day (Fig. 1). Since there are approxi- counting of the cycles is correct, an mately 100,000, or Hf, seconds in a accurate measurement of time proday, this corresponds to an accuracy vides an equally accurate measurement of frequency; conversely, a deof one part in 100, or 10- 2• Figure 1. Human beings have searched over the centuries for ever more precise ways to measure time. The earliest mechanical device for telling time-originated in ancient Egypt and subsequently developed by the Greeks and Romans-was the water clock, or clepsydra. The relatively sophisticated clepsydra shown here consists of a reservoir for supplying water, a float in a receiving vessel that rises with the water level to indicate on a cylindrical scale the passage of time, and a siphon, drum, and gear wheels to empty the vessel at the end of the day and rotate the scale 1/365 of a full -------------------Ff. ,.,rht L \7 F,.•. F15 n l tum. vice oscillating at a stable frequency can be the source of the periodicity that is measured by a dock. The earliest clocks, as we have seen, were developed primarily for measuring the passage of time. However, the initial incentive for the development of tuning forks, quartz crystal oscillators, and atomic clocks was the measurement of frequency . The oscillatory motions of a vibrating olid can provide a measurement of frequency or periodicity that can serve as the basis of a clock. It is difficult to maintain the vibratory motion with most substances, but certain cry tals have the property of piezoelectricity (literally, "pressure" electricity). Piezoelectricity is polarization ( hift in the relative locations of positive and negative charges) produced by mechanical strain in certain cry tal ,· and it i al o the inverse effect whereby a crystal become strain d when electrically polarized. The piezoelectric property permits a cry tal to be coupled to an electronic circuit to maintain the vibrations and to count them . Although the phenomenon was discovered by Pierre and Jacques Curie in 1880 and piezoelectric crystals were subsequently used by Nicholson and Cady in an electronic oscillator, the first clock driven by a quartz crystal wa developed only in 1928 by Horton and Morrison (3). Of all the known crystals, single crystals of quartz (silicon dioxideSi02) have been found to be the best for measuring time and frequency because of their piezoelectric properties, hardne s, low internal dissipation, durability, uniformity, availability in sufficiently large sizes, and capability of being cut into wafers whose characteristic vibration frequencies are nearly independent of temperature. A quartz crystal is shown in Figure 2, along with some ..... r • :: • , ,. ,..>f "'. , . r ~ ~ ~ '· of the cuts that provide suitable wafer . The best quartz clocks are highly stable (2 x 10- 13), but they are much worse for reproducibility (1 x 10- 7) and war e still for accuracy, since new crystal usually have to be calibrated experimentally against other frequency standards. Quartz clocks do, however, have the advantage over other more accurate and stable devices that they are inexpensive and portable, as evidenced by quartz wristwatches. The adaptation of quartz oscillators to small watches required major innovations, includ- ing the cutting of the crystal in a tuning fork shape, as shown in Figure 3, to provide a convenient natural period of oscillation in a crystal of small size. Atomic clocks Although quartz clocks achieve remarkable stability, the greatest accuracy, reproducibility, and stability have been achieved by atomic clocks, which now provide the basis for defining the second as the unit of time. The measured periodic motion of atomic clocks arises from the magnet1988 january-February ~ ,J' ,._ i . 0 0 , ·~ ..; •• ~; • l • : . -~ 43 i(" mler,lCllon of the hcavv nucleus of the atom with it light electrons. The nuclei of most atoms are magnetized like compass needles. Just as a spinning top tilted at an angle precesses about the vertical under the influence of gravity, the nucleus precesses about the field created by the electrons' magnetism. The axis and angular momenta of the spinning motions of the nucleus and electrons and the resulting precessional motion are shown in Figure 4. The precessional frequencies and the angular momenta are be t expressed in terms of quantum mechanics. For the atoms most often used in atomic clocks, only two states of relative orientation between the angular momentum of the nucleus and that of the electrons are permitted, one in which they are as nearly parallel as possible and the other in which th y are as nearly antiparallel as possible. If the difference in energy between the two state is W1 - W2, then the clas ical precesional frequency corresponds to the quantum mechanical frequency f = (WI - W 2) I h Since this internal precessional frequ ncy was first observed in optical spectroscopy as a very small splitting of spectral lines, it is often called the hyperfine frequency. It is determined by atomic properties which Figure 2. The Curie brothers discovered the phenomenon of piezoelectricity-vibr~tions in cryst.Us c~used by mech~nic~l strilin-in 1880, but it was not until the 1920s th~t ~ clock was invented to use the property as ~ source of periodicity. Single cry t.Us of quartz an cut into w~fers (the sh~ded rectMtgles shown here, for example) whose frequency of vibr~tion is neuly independent of temperature. 44 American Scientist, Volume 76 mounting pedestal Figure 3. For use in wristw~tches, qu~rtz cut in the shape of a tuning fork with prongs ~bout 5 mm long x 0.8 mm wide and 0.03 mm thick. Gold tuning pads on the ends of the prongs allow trimming to precise frequencies. oscill~tors ~re are constant in time (except for small variations due to fluctuating external magnetic and electric fields), so it provid~ an excellent basis for a highpreci ion dock. Before such a clock can be built, however, there must be a suitable means for observing and counting this internal atomic periodicity. The first method for accurately measuring hyperfine frequencies was provided by molecular beam magnetic resonance (Fig. 5). It was developed starting in 1937 by I. I. Rabi and his associates (4, 5). The apparatus is evacuated to a pressure less than 10 7 torr, to avoid collisions of the atoms with the background gas. Cesium atoms are most commonly used. They are heated in the oven to raise their vapor pressure to a point where significant numbers of them pass through the oven's slit jaws, forming a beam. The inhomogeneous field of a magnet deflects the beam, since the force on the north pole of the electrons' magnetic dipole moment is different in magnitude from that on the south pole. The beam then passes through the main part of the apparatus, where it experiences a weak static magnetic field and an even weaker perpendicular oscillatory magnetic field. Beyond the field region the atoms are deflected again by a second inhomogeneous magnetic field. The beam then strikes the hot-wire ionizer of the detector, where each atom gives up an electron and becomes a positive ion which is electrically counted. If the frequency of the oscillating magnetic field equals the hyperfine frequency given in the equation above, the orientation of the electrons' spin angular momentum is reversed by the resonant oscillatory field; the force on the atom is in tum reversed, and the beam follows the indicated path with a maximum of detected intensity. If, on the other hand, the frequency of the oscillating field is far from the hyperfine frequency, no resonant reorientation of the electrons' magnetic moment will occur, and the beam will be directed downward by the second inhomogeneous magnet with the result that the detected intensity will decrease. The detected intensity can then be used through a normal feedback circuit to adjust slightly the frequency of a quartz crystal oscillator, which provides the oscillating magnetic field that induces the atomic transitions. In this fashion, the oscillator frequency is stabilized to the internal atomic prece ional frequency . In Rabi's resonance method, the oscillatory magnetic field extended uniformly all the way through the region with the static magnetic field (see Fig. 5). However, in 1949 I showed that there were many advantages to concentrating the oscillatory magnetic field in two shorter regions at the beginning and end of the region with the static magnetic field (6). The resonances can then be much narrower, and the first-order Doppler shift is eliminated. (The first-order Doppler shift for electromagnetic waves is analogous to the familiar increase in pitch of the whistle on an approaching locomotive; it corresponds to the compression of waves as the source approaches an observer. The second-order Doppler shift is much smaller than the ftrst, arising from the well-known effect-explained by the special theory of relativity-that rapidly moving clocks appear to run slowly.) Although Rabi and his associates first discussed the possibility of atomic clocks before 1945, many improvements in subsequent years by Jerrold Zacharias and others (5, 7) were required to achieve the present accuracy of to- 13 • The atomic cesium clock was so far superior to all previous clocks that in 1967 the international defmition of the second was changed from one based on the motion of the earth about the sun to 9,192,631,770 periods of the cesium atom. A variety of atomic and molecu- Jar resonance devices were developed in the 1950s as possible alternatives to the atomic cesium beam (5). Among the most effective were those that employed atoms such as rubidium stored along with a neutral buffer gas such as helium in bottles whose inner surface were coated with waxes similar to dotriacontane (C32 H 66). The atoms were optically pumped with circularly polarized light into preferred states. Ammonia (NH 1) masers (devices for amplifying microwave by stimulated emission of radiation) were developed by Townes and others. None attained a great accuracy a the atomic beam ce ium clocks, but when less accuracy is ufficient, an optically pumped rubidium clock is often used because of it lower cost and lighter weight. For many purpo s such as measurement in radio a tronomy, which need the highest pos ible stability over period of a few hours, the Figure 4. The greatest accuracy, tabihty, and reproducibility ue provided by atomic dock , which take advantage of the periodic magnetic interactions of nuclei and electrons. In this schematic diagram, a nudeu precesses about the field created by the electrons' magnetism, with the vector I representing the spin angular momentum of the nudeu , J that of the electrons, and F the resultant or vector um of the two. The precessional motion is shown by the circle. best existing clocks are atomic hydrogen masers (Fig. 6), which Daniel Kleppner and I invented in 1960 (8). An intense electrical discharge in the ource converts commercially available molecular hydrogen (H 2) into atomic hydrogen (H). The atoms emerge from the source into a region that has been evacuated to a pres ure below 10 t. torr. A beam of diverging atoms enters the state-selecting mag- net, which has three north poles alternating in a circle with three south poles. By symmetry the magnetic field is zero on the axis of such a magnet and increases away from the axis. The low-energy hyperfme state of atomic hydrogen, called the F = 0 state, has the characteristic that its energy decreases with increasing bottle for ten seconds and using the same aperture for entrance and exit is extremely low. Masers have very low noise levels, especially when the amplifying element is an isolated single atom. The major disadvantage of the hydrogen maser is that the atoms collide with the wall at intervals, In 1967 the international definition of the second was changed from one based on the motion of the earth about the sun to 9,192,631,770 periods of the cesium atom magnetic field. Just as a ball runs downhill to where the energy is lower, the atoms in the low-energy state will move away from the axis to where their energy is still lowerthat .is, the beam of these atoms will be dispersed as in Figure 6. Conversely, most of the atoms in the high-energy F = 1 state will be drawn toward the axis, and thus those atoms are focu d. Atoms in the high-energy state enter the srna!J aperture of the storage cell, a 15-cm diameter bulb coated with teflon on the inside. If these atoms are exposed to microwave radiation at the hyperfine frequency, more atoms will go from the higher energy state to the lower, and the released energy will make the microwave radiation stronger-that is, the device will be an amplifier, a maser. If the storage ce!J i placed inside a tuned cavity, an oscillation at the re onance frequency will be increased in magnitude until an equilibrium value is reached, at which level the oscillation will continue indefinitely. The energy to maintain the oscillation comes from the continuing supply of hydrogen atoms in the high-energy state. The atomic hydrogen maser has unprecedentedly high stability due to a combination of desirable features. The atoms reside in the storage bulb much longer than in an atomic beam apparatus, and as a result the resonance line is much narrower. They are relatively free and unperturbed while radiating, unlike the atoms in most optically pumped rubidium ce!Js, which collide frequently with buffer gas atoms. The first-order Doppler shift is removed, since the average velocity of atoms stored in a changing slightly the hyperfine frequency and giving rise to a wall shift of two parts in 10 11 • The wall shift can be experimentally determined by measurements with bulbs of different diameters or with a deformable bulb whose surface-to-volume ratio can be altered. Since the shift is constant, its exi tence mostly affects the maser's accuracy rather than its stability. Over periods of several hours, the hydrogen maser's stability is better than 1 X 10- IS. Future improvements It might appear that there is little room for improvement in the measurement of time. That is not the case. The state-selecting magnets of atomic beam clocks can be replaced with laser beams, and two beams of atom can go through the transition region in opposite directions to reduce the harmful effect of phase shifts. New coating materials that result in smaller and more stable wall shifts may be developed for hydrogen masers, including superfluid liquid helium and teflon-like oils or greases. Atomic time standards based on lasers and related quantum devices are being developed at much higher frequencies. Measurements to the same fraction of a cycle at higher frequencies correspond to smaller fractions of the frequency. The firstorder Doppler shift is large, but various ingenious methods have been devised to reduce or eliminate it. Saturated absorption spectroscopy and two-photon spectroscopy employ two laser beams at the same frequency going in opposite directions so that the first-order shifts 1988 January-February ·•..!'; . - . . .. ~ ~ •: . ~~ . ~ ·"'J. _, ( 45 be stored for long interval in trap and since there are no wall effects, trapped ions have attractive feature as time and frequency standards. Until recently, the ions had high velocities in the traps and consequently large Doppler shifts. Used in combination with the laser cooling method discu sed below, however, ion traps are very effective. More recently, various techniques have been invented to trap neutral atoms with nonuniform laser beams (10, 11). The forces arise in some cases from the gradient of a beam's electric field and in other cases from the momentum imparted to an atom when it scatters a photon. Although some of the traps are quite shallow, the laser cooling techniques help to overcome this disadvantage. [For more on atom trapping and cooling, see the interview with Steven Chu in this issue of American Scien- \ tist.] Laser cooling is a method by which a beam of light can be used to damp the velocity of an atom or ion (11, 12). The basic mechanism utilizes a laser beam tuned lightly lower in frequency than a strongly allowed resonance transition. When the vemagnet A magnet 8 locity of the ion or atom is directed against the laser beam, the light fredetector quency in the ion's frame is Doppler shifted closer to resonance, and the light scattering takes place at a higher rate than when the velocity is in the oven I wave gu1de cav1ty same direction as the laser beam. Since the photons are reemitted in Figure 5. One me~ns for meuuring the hyperfine frequency of ~tom shown in Figure 4 is random directions, the net effect over the atomic be~m magnetic reson~nce ~ppuatus. To ~void l~rge numbers of collisions a motional cycle is to damp the ion's between ~toms ~nd the surrounding gu, pressure in the apparatus is kept below 10-7 torr. A velocity by absorption of photon mobeam of atoms is boiled out of the oven, deflected by the inhomogeneous magnetic field of mentum. Using pairs of counterprom~gnet A, md subjected to ~ we~k static m~gnetic field in the main put of the ~ppu~tus. As the bum m~kes its first md second pu~ge through the w~ve guide c~vity, it is pagating laser beams along each of subjected to ~ we~ker perpendicular oscill~tory magnetic field; it is then deflected ~gain by three mutually perpendicular axes, the inhomogeneous m~gnetic field of m~gnet 8 ~nd fin~lly converted to po itive ions by ~ one can obtain a three-dimensional hot-wire ionizer in the detector. The ions are counted electric~lly. In the diagram, m~gnets A laser-cooled region in which the atand 8 h~ve been rot~ted 90" ~bout ~ vertic~! axis to show the tips of their poles. The oms move very sluggishly; such a photogr~ph shows the cesium ~tomic be~m clock ~t the Nation~ Bure~u of Standuds. E<lch region is frequently called "optical end of the clock hu both ~n oven ~nd ~ detector, so that the ~ppuatus can be operated in molasses." Atoms have been lasereither direction. (Photogr~ph courtesy of N~tion~ Bureau of Stmduds.) cooled to less than 0.0003 K, and narrow resonances have been obcancel (9-11). Concurrent with the can be trapped in a static uniform served with a single cooled and development of stable oscillators at magnetic field in combination with a trapped ion. The laser cooling not much higher frequencies, intense ef- suitable nonuniform electrostatic only overcomes the first-order Doppforts have also been made to multiply field (Penning trap) or in suitable ler broadening but also virtually elimand divide such frequencies so that nonuniform electric fields whose po- inates the second-order Doppler valid comparisons can be made be- larities and gradients alternate in shift, which remains in all atomic tween standards at all frequencies. time at radio frequencies (Paul traps). clocks unless the atoms are sufficientAlthough ions cannot be stably Dehmelt and his associates (10) pio- ly cooled. It is too soon to say which comtrapped in static electric fields, it has neered the use of traps for studying been known for a long time that they atomic spectroscopy. Since ions can bination of trapping and cooling will ~~--~--I/ ~I I Amt>rican Soentist. Volume 76 ' • '. ,. ... ) : . . "'! ' . .. ... • . .. - · be most effective, but there is a high probability that one or more of the new techniques we have examined will lead to even more stable periodicities, which can in tum provide the basis for even more stable atomic docks. Time and relativity The measurement of time is so accurate today that relativistic effects on clocks are directly observable. According to the special theory of relativity, if two observers with clocks are moving relative to each other at a constant relative velocity, each will find that the other's clock is going at a lower rate than his own clock. Thi relati\ is tic effect has been demonstrated by a comparison of two atomIC dock · l'lCion! and after one of them wa carried on a high-speed aircraft. As a re ult of thi variation, the idea of simultaneity for two events at different locations 'Io es its meaning. If two observer moving relative to each other view two events at different locations, one observer may conclude that the events are simultaneous, while the other will be convinced that they are not; or one observer mav conclude that event A precedes event B, while the second observer concludes that B precedes A. But the reordering of events can never be so great that the cause of an event seems to occur after the event itself. It might seem that the different dock rates would lead to such horrible ambiguities that the concept of time would be useless. That is not the case. Each observer has his own "proper time," which is the time as measured by an accurate dock kept with him at all times. Then, if one knows the relative velocities of different observers, one can calculate their proper times by the well-known mathematical relations of the special theory of relativity. Einstein's general theory of relativity overcomes the limitation of his special theory to constant relative velocities by including acceleration and gravitation. One consequence of the general theory is that the rate of a dock depends not only on its apparent velocity but also on its gravitational potential-for example, a dock far from earth will go at a slightly faster rate than one dose to the earth. microwave cav1ty source Figure 6. In the atomic hydrogen maser, which measures time with high stability over periods of a few hours, hydrogen atoms pass through a low-pressure region (lo-• torr) into a state-selecting magnet. In the magnet, atoms in the low-energy hyperfine state (F 0) diverge from those in the high-energy hyperfine state (F 1). Most of the latter enter the storage cell, a 15-cm diameter bulb whose inner surface is coated with teflon. Exposed to microwave radiation, these atoms release their energy. The radiation takes on the extra energy, continuing indefinitely at the frequency for which the energy transfer is greatest, the hyperfine frequency. The oscillations of the microwave radiation that emerges through the coaxial cable provide the periodicity required for a highly stable atomic clock. The photograph shows an atomic hydrogen maser with the side and front panels removed. The source of hydrogen atoms is at the top of the maser, and the storage cell is at the bottom. Twenty-two masers like the one shown here are in use worldwide for radio astronomy, tracking of space probes, and time keeping. (Photograph courtesy of Smithsonian Astrophysical Observatory.) = = 1988 January-February "": :: .. ., .,~. '...,.,{..... .. ;;, 11'. .,... .\'\.: > .., - _... . ~ 47 Time as date The word time i used with two different meanings. One is an interval of time, such as the number of minute required to boil an egg. It is this meaning that has been the subject of my discussion so far. Time is also used in the sense of date, such as 30 seconds past 2:00 P.M., EST, 12 December 1987. Clearly the two meaning are closely related, since the latter is the interval between some agreed starting point and the d signated time (13). Even with international agreement on the definition of the second as the unit of time and on a suitable starting event for the measurement of time as date, there are added complications due to the variable rate of the earth's rotation. If the day and year were defined solely in terms of atomic time, the calendar would change it relation to the sun and stars, to the confusion and inconvenience of astronomers and navigators and eventually even the casual observer. As a result, by international agreement there are occasional leap seconds to correct for the irregular motion of the earth. The international time scale is based on what is called Coordinated Universal Time, or urc. The stan- jects in our olar system, and from the velocitie and gravitational potentials of transported clocks. Care is required even in the definition of synchronization. Ambiguities can be avoided on the surface of the earth by utilizing a "coordinate time" on an underlying nonrotating system and then calculating by known relativistic principles the relationship between this coordinate time and the measured time on the surface of the rotating earth (14). Need for precise measurement of time It might seem that there should be no need for measurements of uch high accuracy as those already achieved, much less those contemplated with future improvements; but there are many applications, some of which push cprrent techniques to their limits. In radio astronomy one looks with a parabolic reflector at the radio waves coming from a star, just as in optical astronomy one looks with a telescope at the star's light waves. Unfortunately, the wavelength of the radiation is about a miJJion times longer than the wavelength of light, so the resolution of the normal radio telescope is about a million times The unit of length has recently been defined as the distance light travels in a specified time, and the basic units for voltage and resistance soon will be defined in terms of time dards laboratories of a number of major nations contribute measurements from their own cesium clocks to the Bureau international de l'heure in Paris, which averages them to obtain the trrc. Leap seconds are introduced with adequate warning at the beginning or middle of the year when required to prevent the urc from differing from navigators' time by more than 0.7 seconds. At present a leap second is introduced approximately every year and a half. Allowance must be made for different relativistic effects over the surface of the earth and in nearby space. As we have seen, such effects arise from the rotation and orbital motion of the earth, from the gravitational potential of the earth and other obAmerican Scientist, Volume 76 ) i< .... ~: ' Jl ' '~·"<.'' " , J' ,• • • r worse than that of an optical telescope, depending as it does on the ratio of wavelength to telescope aperture. However, if there are two radio telescopes on opposite sides of the earth looking at the same star and if the radio waves entering each are matched in time, it is equivalent to a single telescope whose aperture is the distance between the two telescopes, and the resolution of such a combination exceeds that of even the largest single optical telescope. For precise matching in time, each of the two radio telescopes needs a highly stable clock. Precision clocks are also needed to measure the periods of pulsarsstars that emit their radiation in short pul es-and the changes in their pe- riods, which sometimes occur smoothly but sometimes abruptly. Of particular intere t are millisecond pulsars, whose remarkable constancy of period rivals the stability of the best atomic clocks. In fact, one of these pulsars is so stable that it may eventually be suitable as a standard of time over long periods (15). Another millisecond pulsar is part of a rapidly rotating binary star that is slowly changing its period of rotation. This change can be attributed to loss of energy by the radiation of gravity waves-the first experimental evidence for the existence of gravity waves. Accurate measurements of time permit measurements of the variability of quantities that were once thought to be constant. As we have seen, the rotation period of the earth, which once served as the ba is for defining the unit of time, is now known to vary by a few parts in a hundred million from winter to summer and from year to year. Some of the variation is regular and some unpredictable. Different atomic clock rates have been accurately compared over long periods of time to see if there might be changes in their relative rates which could correspond to a change with time in the fundamental physical constants, but no such change has yet been discovered. Precision clocks make possible an entirely new and more accurate navigational system, the global positioning system, or GPS. A number of satellites containing accurate atomic clocks transmit signals at specific times so that any observer receiving and analyzing the signals from four such satellites can determine his position to within ten yards and the correct time within one hundredth of a millionth of a second (10- 8 s). Time can be measured so accurately that wherever possible other fundamental measurements are reduced to time measurements. Thus the unit of length has recently been defined as the distance light travels in a specified time, and the basic units for voltage and resistance soon will be defmed in terms of time. Accurate clocks have provided important tests of both the special and general theories of relativity. In one experiment, the periodic rate of a hydrogen maser carried in a rocket 10,000 krn up changed with speed and altitude by the amounts predict- ed by the . pecial and general theories (16, 17). In other experiment ob rvers have mea urcd the delay predicted by relativity for radio waves passing near the sun. Future improvements in the stability of clocks should make possible even more rigorous te ts of fundamental theories. 5. N . F. Ramsey. 1983. References 8. N . F. Ramsey. 1968. The atom1c hydrogen maser. Am . SCJ . 56:420. 9. F. T. Arecchi, F. Strumia, and H . Walther, eds. 1983. Admncrs in lAser Spectroscopy. L D. J. Boor;tin. 19 3. TI1r Discot'frers Random House. 2. D. S. Landes. 1983. RI.'!.IQ/ution 111 Timl'. Harvard Univ. Pre s. 3. W. G Cady. 1964. Pu•welrctncJty. Dover. 4. F. Ramsey. 1956. Mokru/ar Beams. Oxford Univ. Pre. . H1~tory of atom1c clock'>. f. Rt>s . NilS 88:301. Thi' arti le contain'> L' h.'ns1ve references to the urigmal publication on the ubJL'Ct. 6. N . F. Ramsey. 1980 The method of uccessive oscillatory fields. Phys . To.tay 33(7):25. porc: Scientific Pubbshers. 13. J. Jesperson and J. Fitz-Randolph. 1977. From Surul~als to Atomic Clocks. US National Bureau of Standards. . Ashby and D. W. Allan. 1979. Practical implications of relativity for a global coordmate time scale. Radio Sci. 14:649. 15. Rawley, L. A., j . H . Taylor, M. M. Davis, and D. W. Allan. 1987. Millisecond pulsar I'SR 1!137 + 21 : A highly stable clock. SCJmct 14. 7. H. Hellw1g, K. M. Evenson, and D. J. Wineland . 197 . Time, frequency and physical measurement. P!JJ~S . Today 31(12):23. Plenum. 10. T. W. Hansch andY. R. Shen, eds. 1985. lAser Spt-ctroscopy, vol. 7. Springer-Verlag. 11. D. J. Wineland and W. M . ltano. 1987. Laser cooling. Phys . Today 40(6):34. "That' 12 R. S. Van Dy k, Jr., .md N . Forto;on, ed~ . 1984. Atom1c Physits, vol 9. Smga- orne of my earlier work." 238:761. 16. R. F. C. Vessot et al. 1980. Test of relanvistic gravitation with a space-borne hydrogen maser. Phys. Rev. Lett. 45:2081. 17. J. P. Tumeaure, C. M . Will, B. F. Farrell, E. M Mattison, and R. F. C. Vessot. 1983. Test of the principle of equivalence by a null gravitational red-shift experiment. Phys . R1.'1.1. D 27:1705.