Relativity and Clocks

RELATIVITY AND CLOCKS

Carroll 0. Alley

Universityof Maryland CollegePark, Maryland

Sumnary be mentioned.

In this centennial year of the birth of Albert The internationaltimekeeping communityshould Einstein, it is fittingto review the revolutionary takegreat pride in the fact that the great stabil- andfundamental insights about time whichhe gave ity of cont-mporaryatomic clocks requires the us inthe Restricted Theory of Relativity (1905) first practical applications g Einstein's General and inthe conseqences of the Principle of Equiv- Theory of Relativity.This circumstance can be ex- alence (l'. . .The happiest thought of my life.. .") pected to produce a better understanding among whichhe developed (1907-1915) into histheory of physicists andengineers of the physical basis of gravityas curved space-time, the General Theory of gravity as curvedspace-time. For slow motions and Relativity. weak gravitational fields, such as we normally experience on theearth, the primary curvature is It is of particularsignificance that the ex- thatof &, notspace. A body falls,according traordinary stability ofmodern atomicclocks has toEinstein's view, not because of the Newtonian recentlyallowed the experimental Study and accur- forcepulling it tothe earth, but because of the ate measurement of thesebasic effects of motion properties of time: clocksrun slower when moving and gravitationalpotential on time. Experiments andrun faster or slower, the higher or lower re- with aircraft flights and laser pulseremote time spectively they are in the earth's gravity field. comparison(Alley, Cutler, Reisse, Williams, et al, 1975)and an experiment with a rocketprobe (Vessot,Levine, et al, 1976) are brieflydes- Some Eventsin Einstein's cribed. Intellectual Development

Properunderstanding and allowance for these Figure 1 shows Einstein in his study in Berlin remarkableeffects is now necessary for accurate several years after he hadbrought the General global time synchronizationusing ultrastable Theoryof Relativity to its complete form in 1915. clocks,transported by aircraft, and forthe cor- He alwaysregarded this theory as his major accom- rectoperation of navigational systems such as the plishment,although his other outstanding contribu- NAVSTAR/Global Positioning System. tions to physics would place him among the greatest physicists of thiscentury even without the General Theory. His stature as a scientistand his charac- Introduction ter as a man are appropriately symbolized in the cartoonof Herblock which appeared in The Washing- It is anhonor to be asked to review the sub- ton Post shortly after his death on April 18, 1955. ject of relativityand clocks for the 33rd Frequen- (Figure 2). Thisdrawing is includedhere for an cyControl Symposium in this centennial year of the additional reason. birth of Albert Einstein which occurred in Ulm, Germany on March 14, 1879. I am pleased to attempt Imaginesomeone observing the Earth from the a brief summary of the subject. position of Herblock'sobserver, taken to be a spaceship far removed from thesolar system, The plan is to recall first some ofthe signi- located among the nearby stars but at great dis- ficant events in Einstein's intellectual life by tances fromeach of them, not moving with respect showing hisphotographs at variousages. Next, the to the Sun,and equipped with standard cesium restricted("special'') theory of relativity(re- atomicclocks with which to measure time. This stricted,that is, to inertialframes of reference) observer Is clearlyaware of Einsteinian time. The will besketched, followed by the implications of onehundred years which have elapsed on Earth since the Principle of Equivalence that gravity curves Einstein's birth would be recorded by theHerblock light beams andaffects the rate ofclocks, the observerto be about 46 secondslonger due to the cluesthat led to theidea of gravity as curved effectsof gravitational potential difference (29 space-time,the General Theory of Relativity. Re- secondsfrom the Sun's potential and .t2 seconds cent experiments which have been able to measure fromthe Earth's potential) and orbital motion of andstudy some ofthe effects of motion and gravity theEarth (%l5 seconds).In the next section, I on time will bebriefly described. Finally, the wishto recall and explain these fundamental ef- practical matter of including relativity in modern fects on time which Einstein originally revealed to clocksynchronization and navigational systems will usby pure thought.

4 To continuewith Einstein's life, Figure 3 Einstein.This led to employment therefor seven shows his earliest known picture at the age of fruitfulyears from 1902 until 1909. He had a nat- about5. This is when he first saw a magnetic uralaptitude for evaluating the feasibility of the compassand began to wonderabout its behavior. patentapplications, leaving time andenergy to Figure 4 shows him inelementary school in Munich wonder aboutphysics. Often in later life when at theage of 10. He is secondfrom the right in askedfor advice byyoung scientists, he would rec- thefront row. Figure 5 showshim at theage of ommend, withhis experience at the patent office in 14. He hadbegun toread Euclidean Geometry two mind,that they not be dependent for their liveli- years earlier and a year later was to become a hood on theproduction of scientific results be- highschool dropout because of dissatisfaction causeof his concern with the corrupting influence withthe methods of teaching in his Munich gym- ofthe need to be successful. In Figure 8, he is nasium. He spent a happy yearin Northern Italy shown at theage of 26 at his desk at thePatent where hisfamily had moved, travellingand con- Officein the year 1905 when he publishedthree tinuinghis own studies. At theage of 16, he remarkablepapers in the Annalen der Physik: One attemptedto enroll in the Swiss Federal Institute introducingthe light quantum intophysics, one ofTechnology (Eidgenzssische Technische discussingthe theory of the BrownianMotion and Hochschule)in Zurich, but failed the entrance ex- providingthe clinching argument for skeptics of aminationoverall, although he impressed the exami- theexistence of atoms, and the third, "On the nerswith his knowledgeand abilityin physics Electrodynamicsof Moving Bodies,"containing his andmathematics. These examiners recommended that revolutionaryinsight about the relative nature of hespend a yearin the high school in Aarau, simultaneityand the non-absolute nature of time, Switzerland,and then enter the ETH, since noen- thefundamental key to his restricted theory of tranceexamination was requiredof graduates of relativity. About hisyears at the Patent Office, Swisssecondary schools. Figure 6 shows the 16 andMarcel Grossmann's help in obtaining the posi- yearold Albert Einstein (far right, first row) in tion,he wrote in a letterof condolence to Gross- the Aarauclassroom of an excellent teacher, Dr. mann's widow in1936, "...This saved my life; not JostWinteler. It was duringthis period that that I wouldhave died without it, but I wouldhave Einsteinbegan to think about what a beam of light beenintellectually stunted", and, in the last year would look like if somehow he were able to move of his life, "The greatestthing that Marcel Gross- fast enough to catch up with it. pkFrw-1 shows mann didfor me as a friend".There was, however, him as a student at the ETH inZurich, where he a thirdmajor thing that Grossmann did for succeeded in disappointing and alienating his Einstein. When heneeded to learn differential professors by attendingthe required classes only geometryand thetensor calculus in order to give sporadicallywhile pursuing independent studies. mathematicalform to his idea of gravity as curved (He particularlyliked to spend time inthe elec- space-time,he turned to Grossmann who had special- tricity andmagnetism laboratory and in the study izedin the subject and was a member ofthe faculty ofMaxwell's Theory of the electromagnetic field, ofmathematics at the same ETH inZurich when which was notthen taught at the ETH). He passed Einstein was a member ofthe physics faculty there the few requiredexaminations only with the help from1912 to 1914.Figure 9 shows Einsteinin a of hisfriend, Marcel Grossmann, who was a model playful mood at the California Institute of Technol- student,attending lectures and takingcareful ogy in the early 1930's while Figure 10 showshim notes,which he lent to Einstein. The famous at the Institute for AdvancedStudy inPrinceton mathematician, Hermann Minkowski, who lectured at wherehe spent the last twenty-two yearsof his the ETH and later contributedthe geometrical life. pointof view to space-time and relativity, said, on learningof Einstein's 1905 paper on restricted If these tidbits have stimulated you to want relativity, "Oh, thatEinstein, always missing to learn more aboutEinstein's life, there is no lectures - I really would nothave believed him better book to begin with than the brilliant bio- capable of it!" On anotheroccasion, he referred graphyby Professor Banesh Hoffmann, Albert to Einstein as "a lazy dog". Einstein,Creator andRebel.4 Many ofthe facts statedabove, along with many ofthe photographs, Becauseof these attitudes, which seem to weretaken from this book. It hasthe added virtue havebeen shared by other members of the faculty, ofexplaining Einstein's physics in a particularly Einsteincould not obtain an academic position or clear way. Some of theremarks in the next sec- a permanentjob of any sort for about a yearand tionsof this talk follow the approach ofHoffmann. a halfafter he graduated. (As a teacherin a university, I reflectoften, when looking at these picturesof Einstein during his student years, how Brief Review of Restricted easy it is tocompletely misjudge a student'strue ("Special")Relativity abilities.Conventional teaching in universities has changed little sinceEinstein's student days, Thisreview will be much too concentrated for and we haveyet to react to his criticisms. A thosepeople whomay be encountering the ideas for recent essay by MartinKlein2 on Einstein and the thefirst time. However, I shall assume that most Academic Establishment is particularlypertinent peoplein this audience have had some prior contact as are Einstein's own essayson education3). withthe subject so that we canrecall the funda- Finally, his good friendMarcel Grossmannpre- mentalconcepts quickly. vailed onGrossmann's father who was acquainted withthe director of the Swiss Patent Office in The restriction is toreference systems which Bern to intercede and obtainan interview for move with respect to one another with constant

5 velocity,and in any one of which a body at rest his time at thePatent Office, he sat boltupright remains at rest and a freely movingbody moves in in bed with the realization that time is notabsol- a straight line - theso-called inertial systems. -Ute. The situation described is only "apparently The adjacentdiagram shows theconventional repre- irreconcilable". The simultaneity of separated --events is relativeto the inertial observer. Dif- ferent inertial observers will not agree on whether two spatiallyseparated events are simultaneous. For some observers,they may besimultaneous, but otherobservers will noteven agree on whichevent occursbefore the other. This fundamentalrealiza- tion about time hashad profound consequences for _.-all of physics!! xEinstein's Prescription for Comparisonof Time z z' The following illustration shows Einstein's prescriptionfor time comparison and affords the J opportunityof introducing space-time diagrams: sentation of two suchsystems in relative motion. A fundamentalpostulate is that the laws of physics, electromagnetismand all other parts of physics, as well as dynamics,are to be the same inevery inertial system. This has the conse- quencethat no experiment carried out within an inertialsystem can distinguish it fromany other suchsystem. This is therestricted (special) Principle of Relativity.

Thesecond fundamental postulate which Ein- stein identified had to do with the velocity of light in empty space.gLight travels with a defi- Let the vertical axis measure time innano-seconds nitespeed (c =3 x 10 meters persecond) for and thehorizontal axis measure distance (one di- everyinertial observer which does not dependon mension) infeet (2.30 cm).Then theplot of a themotion of its source. moving light pulse will make anangle of 45' since c % 1 footper nano-second. The prescription is These two postulates appear to be hopelessly simple.Send out a pulse at time tl, let it be inconflict. Consider the two inertialsystems reflected at thedistant event, and return to the illustrated,each ofwhich has a lightsource at observer at time t . One assumesthat the time of reflection assignea by the observer in midway between tl and t 3:

~. speed v t=t2=t1+7(t3-t)=t1 1 -It +It relative 12123 to A its center. When the two lightsources are abreast The same measurementsof time will also yield the of eachother, let them flashsimultaneously, send- distanceto the event by usingthe radar equation: ing out light wave frontsin the forward and back directions for observer A and for observer B. (Thesecould be railroad cars, in Einstein's own x=A(t example, orspace ships, appropriate to our own 2 3 - epoch.For simplicity, we arelimiting ourselves toonly one dimension.) In his own system, A would Thediagram is called a Minkowskidiagram after see thepulses reaching the ends at the same time, Einstein's distinguished professor of Mathematics buthe would observe the backward travelling wave at the ETH who developedthis geometric way of frontreach the back end system B before the of lookingat space-time in 1907. forwardtravelling wave frontreaches the front end of system B. How couldobserver B measure Modern Observersand Minkowski Diagrams thatthe speed of light was c in both directions, as A would surelymeasure? Does thisnot violate Themodern observer will beequipped with: the postulate of relativity, by which A and B shouldagree on the laws ofphysics? 1. AtomicClocks 2. ShortPulse Lasers You know well the resolution of this dilemma, 3. FastPhoto-detectors which came to Einstein after many yearsof musing 4. EventTimers andbafflement. On awakingone morning during

6 The &-Calculus. By sendingand receiving thelocus of all suchreflection are the events he shortlightpulses andrecording the times (epochs) regardsas simultaneous with his origin even to ofsuch events, one can measure the space-time t' = 0. (The same even t to which A assignst=O). coordinatesof distant events, as we have just This X'-axis makes the same anglewithorespect to seen.In addition, the technique lends itself to thelocus of lightpropagation, the 45 line, as a very clear way ofdeveloping the conceptual thet'-axis. The lightpropagation lines, shown structure of relativity, as was first done by dashedin the figure, are the same forboth obser- Bondi.5Consider the following diagram in which versbecause of the invariance of the speed of theworld line of B is representedin the space- light. They areoften called the light cone. time diagramof A. The geometrization ofspace-time, as pointed A B out by Minkowski in1907, amounts to this: There tt is anabsolute space-time, which is "sliced up" by differentinertial observers in different ways, as shown inthe following diagram (for one space dimension)

Minkowski'sAbsolute Space-Time (1907)

-- 'Locus of :vents which A d/"' "Sliced up" in regards as stmultaneous differentways with his origin event t=O by inertial observers Observer B hasthe same equipment as A, in particular a standardatomic clock. Because of the X motionof B relative to A, lightpulses emitted by A with a time interval T between them will be received by B with a stretched time interval kT \ -\ K'' becauseof the additional distance travelled by B betweenreception of pulses. This is justthe6 'Light speed same familiarDoppler effect. It is aneasy exercise for all to show thatthe relativistic Doppler factor k is given by Some referenceevent is chosenand a light cone is associatedwith it. Ifthis reference event is chosen as theorigin event for several inertialobservers, their time andspace axis are plotted as shown.Observer C is moving tothe leftwith respect to observer A. The distancein thediagram along the time andspace axes which locusof the events which A regards as The corresponds to unity will be different for each simultaneouswith his origin event t = 0 as deter- inertialobserver7. The coordinatesfor an event mined by theoperation shows inthe above diagram, aredetermined by parallel projection onto the a pulseless effect at t = -x/cbeing received back timeand space axes for any inertial observer, as at t = xfc.This constitutes A's x-axis.If ob- shown inthe following diagram server B carriesthrough the same operation,as shown inthe following diagram, emitting a pulse at t' = -x'/c and receiving it back at t' = x'/c, +\.. *.

'\Locus of Events which B regards as simultaneous x with his origin event t'=O

/ / \ Space -Time

7 Minkowski showeda veryremarkable property: eventhough t' # t and x' # x inthe above diagrams,there is anexpression which is the same forboth observers, namely8

Reading of moving clock is its own time. ProperTime. Denote by T. This is calledthe square of the invariant inter- -val between the origin event (0,O) and the event (t,x) or (t', X'). Forany two events whose sepa- rationin time is At or At' and whose separation inspace is Ax2 or Ax', it is easily shown that

22 2 2 2 (As)' = c (At) - (Ax)' = c (At') - (Ax') (5) it is present. The curvature of theworld line shows that it experiencesaccelerations. Two neighboringevents along the world line of the clockare shown representing"ticks" of the clock (everysecond, or better, everynanosecond). With respectto the inertial observer, they have a time separation At and a spatialseparation Ax. For the moving observeraccompanying the clock, the 22 2 2 timeseparation between ticks is thetime interval (As)2 = c (At) - (Ax) - (Ay) - (Az)~ actuallyrecorded by the moving clock, which is 2 2 2 (6) called its propertime interval andgiven the = c (At') - (Ax') - (Ay')2 - (Az') symbol AT. The spatialseparation between the ticks for the observer moving with'the clock will andcontinues to be invariant for all inertial bezero, since the clock is always at theorigin of the moving coordinatesystem. If the two tick observers. eventsare close together, the moving observercan beregarded as an inertial observer since his in- This is an extremelyimportant result because will it providedthe mathematical basis for Einstein's stantaneous velocity v changevery little duringthe interval between ticks. Then, denoting later development of histheory of gravity - a curvatureof the flat space-time that we havebeen thetime and space measurements of the moving ob- serverwith primes, discussingin terms of thepreceding diagrams - as we shalldiscuss later on. Minkowski character- izedhis development of thegeometry ofspace- time duringan address to the 80th Assemblyof German Natural Scientists andPhysicians in Cologne on the 21st ofSeptember, 1908 inthe followingfamous excerpt: But At' = AT "The viewsof Space and Time which I wishto lay before youhave sprung from Ax' = 0 the soil of experimentalphysics, and therein lies theirstrength. Hence- and forth,space by itself, and time by itself, are doomed tofade away into Ax = vAt mereshadows, and only a kind of union of the two will preservean independent Equation (7) thus becomes reality."

He was, of course,talking about the slicing up of c2(A~)' = c2(At)2 - (vAt) 2 space-time by differentinertial observers, accom- 22 2 panied by theinvariance of the interval, as we = (C - V ) (At) havejust discussed. or The Effect ofMotion on Clocks 2 V 2 (6~)~= - --T ) (At) (1 L This is most readily described byusing the C invariantinterval. Consider the following Minkowski space-timediagram which represents the motionof a clock with respect to some arbitrary AT = inertialobserver whose coordinate time andspace C axesare displayed. The world line of the moving clock is just thelocus of the events at which

8 relatingthe proper time increment AT ofthe moving a watchdropped on a hard floor from a sufficient clock to the coordinate time increment At ofthe height will probablystop running! However, it is inertialobserver. Note thatthis important result possiblein real situations to keep accelerations has been obtained with very little mathematics. smallenough to avoid significant rate changes by The authorhas successfully taught these ideas to carefulpackaging to reduce shocks and vibrations introductoryphysics students, given several weeks and by sufficiently slow motions of the vehicle for them tobe absorbed gradually. (e.g.aircraft) carrying the clock. The important point is that there is nospecific dependence on If two identicalclocks are synchronized to theinstantaneous acceleration in the theory pre- readthe same when theyare together, and observed dictingthe elapsed proper time for an arbitrary tohave the same rate when together,they will not motionof a clockin space-time. exhibitthe same readingafter being separated and experiencingdifferent routes in space-time before Einstein's 1905 Prediction beingbrought together again, even though their rates will againbe the same. The situation is Inthe 1905 paper, ''On theElectrodynamics of illustrated below for clocks A and B. Moving Bodies",referred to earlier, Einstein made thefollowing statement after developing his ideas about time :

"Thence we concludethat a balance-clock* I atthe equator mustgo more slowly, by I I a verysmall amount, than a precisely l similar clocksituated at one of the polesunder otherwise identical condi- t ions. " Your time is (/li not my time" * / Not a pendulum clock,which is physically a systemto which the earth belongs. Thiscase had to beexcluded." The differencein proper times for clocks A and B The situation is sketchedbelow. The equatorial will be

T (final) - T (initial) = A B

*------

T (final) - T (initial) = B B

surface velocity is about 0.46 meters/second. Equation(12) evaluated in an inertial frame (non- rotating)with origin at thecenter of theearth yields,to first order in v2/c2.

re pre sen ts the coordinate time ofWhere coordinate time t representsthe some in- 0 ertialobserver and vA and vB are the instantaneous velocities of A and B with respect to that inertial observer. The elapsedproper time will bediffer- entfor clocks A and B since their histories or 2 V routesare different. There is a routedependence et- -?t ofelapsed proper time. Colloquially, to para- 2CL phrase a oncepopular song, "Your time is not my time" ! 22 At a pole, v = 0, butat the equator v /2c = 1.18~ Note inequation (12) thatthere is noexpli- If t is one day,the equatorial clock would cit dependenceon the acceleration or higher deriv- runslow with respect to the polar clock by about atives of themotion of the clocks, but only the 102nanoseconds. instantaneousvelocity. This is sometimesreferred to in the literature of relativity as the"clock Ifatomic clocks had existed in 1905 withthe hypothesis".There clearly must be some accelera- stability we havetoday (S2 ns/day) so that the tionfor the clocks to separate and be brought predictioncould have been tested, it wouldhave backtogether again. Any realclock will beinflu- beenfound to bewrong! Why? Becausethe effect enced by accelerationto some extent.For example, ofgravity hadnot been included! Two years were

9 to go by before Einstein discovered the Principle empirical law that all bodies in the of Equivalence in 1907 and drew the conclusion same gravitational field fall with about the influence of gravitational potential on the same acceleration immediately time. The oblateness of thespinning earth causes took on, through this consideration, a decrease in the gravitational potential as one a deep physical meaning. For if moves from the equatorto a pole, getting nearer there is even one thing which falls to the center of the earth. It is remarkable that differently in a gravitational field the effect of this change on clocks is predicted than do the others, the observer to offset exactly the effect of the changeof would discern by means of it thathe surface velocity,so that the correct prediction is in a gravitational field, and that is a null effect. We have performed an experiment he is falling in it. But if such a recently, transporting clocks from Washington, D.C. thing does not exist- as experience to Thule, Greenland andback, which supportsthis has confirmed with great precision- null prediction, and will describe it later. the observer lacks any objective ground to consider himselfas falling in a gravitational field. Rather, he The Principle of Equivalence has the right to considerhis state (Einstein's "Happiest Thought") as that of rest, and his surroundings (with respect to gravitation)as field- Let us now turn to the incorporation of gravi- free. The fact, known from experience, ty into the structure of space-time which in Ein- that acceleration in free fall is in- stein's hands produced the General Theory of Rela- dependent of the material, is there- tivity - no longer restricted to inertial frames fore a mighty argument that the post- of reference. It is my experience that the best ulate of relativity is to be extended way to understand Einstein's theory of gravity is to coordinate systems that are moving through the historical route actually followed by non-uniformly relative to one another. Einstein. The physical ideas came before the full mathematical formulation of curved space-time in- * volving the tensor calculus, which took eight more In this consideration one must natu- years to develop. The key idea came to Einstein rally neglect air resistance." in 1907 when he was working on a summary essay concerning the special theory of relativity for the The following simple diagrams illustrate the yearbook for Radioactivity and Electronics. He point made by Einstein and allow profound conse- described his trainof thought in an essay written quences to be drawn with little or no mathematics! in 1919, "The Fundamental Idea of General Relativ-Consider a laboratory falling freely as shown be- ity in its Original Form", which is not yet pub- low. Objects released with no initial velocity lished, but an excerptwas printed in theNew York Times9 in 1972 when the planned editing and publi- cation ofall hispapers was announced. Free Fall

"I tried to modify Newton's theory of No Local gravitation in such a way that it would Gravltational fit into the theory. Attempts in this Field ! direction showed the possibility of carrying out this enterprise, but they will remain at rest. If the initial velocity is did not satisfy me because they had to not zero, the path of the object will be a straight be supportedby hypotheses without line. This is now very familiar tous from physical basis. At that point, there television and movies of theU.S. astronauts in came to me the happiest thought of my Skylab and the Apollo spacecraft, and the Soviet life [emphasis added] in the following cosmonauts in Salyut and the Soyuz spacecraft. form: freely falling spacecraft constitutes a true Just asin the case where an (local) inertial system. If one imagines the electric field is produced by electro- spacecraft in a region of space free of gravity but magnetic induction, the gravitational subject to the acceleration produced by a rocket field similarly has only a relative engine, as shownon the left below (the "Aclab" of existence. Thus, for an observer in Banesh Hoffmann), the observer inside will experi- free fall from the roofof a house ence effects similar to those in a stationary lab- there exists, during his fall,no gravitational field- at least not in his imediate vicinity. If the observer releases any objects, they will remain,relative to him, in a state of rest, or in a state of uniform motion, independent of their particular chem- ical and physical nature.* The observer is therefore justified in consid- 'Ad&' 'Grovlab' ering his state as one of "rest". The extraordinarily curious,

10 oratory on the surface of a body like the earth wherethere is an accelerationof gravity g. In bath cases, objects released will mve to the floorwith accelerated motion. In the "Aclab" case, thefloor accelerates to the released object, so that any object,regardless of its composition, will behave in the same way. In the "Gravlab" case. it has beenmeasured with increasing accuracy by Galileo, Newton, Elltvlls,Dicke, and Braginsky, "Aclab" "Graviob" that all bodies at thesurface of the earth fall withth same acceleration. The latest measurements,l' using torsionbalance techniques to cm- techniquesof restricted relativity discussed ear- pare aluminum andgold at Princeton University and lier (acceleratedmotion can beanalyzed by using to comparealuminum and platinum at Moscow State a succession of inertial frameshaving the instant- IJnniversitygive anemsvelocity of the accelerated object). The conclusion, as we will show below, is thatthe highclock will run fastwith respect to the low clock.Therefore, by theprinciple of equivalence, in the "Gravlab", thehigh clock will run fastwith respectto the law clock. A clock'srate is predicted to depend on its position in a gravitational field!!

Since we have presented earlier all the math- ematicalmachinery needed to draw this conclusion, let us run brieflythrough the analysis. Con- Implicationsfor Light Propagation struct a space-timediagram for the low andhigh observers in the "Aclab" referredto time andspace Einsteinproposed that the equivalence idea axes of an inertialobserver, a6 shown on the left shouldhold, not only for dynamics,but for all of below. The curvature of theworld lines represents physics,and, in particular,for electromagnetic phenomena, includinglight. If this is the case. Comparison of clocks 8" ''Acid' one can draw some conclusionswithout using any mathematics at all as illustrated in thefollowing diagram. Since the "Aelab" is acceleratingwith

h h ' 111 ' their acceleration with respect to the observer es- "Aclob" "Grovlob" "Aclob" tablishingthe time and space coordinates. They are separated by a vertical distance h when t = 0. Let two successive lightpulses be emitted by the respectto an inertialsystem, and a beam of light low observer a timeinterval T on his would propgate in a straight line in that separated by system, clock. The be received by the to an observer in the "Aclab". the light would ap- pulses will high observerseparated by time interval in accord- pearto follow a curvedpath. If the equivalence to a kT ance with earlier discussion of theDoppler the "Gravlab" is correct.the prediction-would our be factor,equation (3). The velocity whichshould be thatlight follows a curved path when propagating in to evaluate k in that of the high observer a gravitationalfield. In by noting that used addition, when reaches him. the wave fronts associated with the light beam must the first pulse move likeranks of soldiers when turning,the auter soldiers moving fasterthan the inner ones, the v = at(15) ahlc conclusionfallows that the speed of light should increase withheight in a gravitational field!! where a is the acceleration of the "Aclab"and the Implicationsfor the Rate ofClocka approximation is made thatthe separation is still h at this later time so thetransit time = hlc. Imagine two atomicclocks of identical con- It is further assumed thatduring the time T the struction to be at the top andbottom of an "Aclab" velocity will notchange appreciably. as shown below,their readings being comparedby modern observersequipped with short pulse lasers, Then fastphoto-detectors, and event timers as discussed eallier. The rates can becalculated using the

I1 The observer on the ground xat = 0 can estab- k =/=~ -/- (16) lish the coordinates (t,x) of any event by sending 1 - vfc out a light pulse beto reflected back at the time C of the event and received at a later time. The time he assigns to the event is halfway between his Now, by the Principle ofEquivalence, a= g, the emission and reception events as described by acceleration of gravity,so k becomes equation (1). (This is still valid even though the speed of light is not constant in a gravitational field; the time required for the light pulse to go k=Jl+Z& out is the sameas that for it to return). If the 2 procedure is repeated an interval of coordinate time At later, it will define an interval of proper time AT at the higher position,as shown in the Recall that gh is just the Newtonian potential dif- diagram. The essential property is that ference $ if h is small,

gh (18) $ E gh At # AT (21)

so that Time Curvature k = 2 J1 +2$ It is possible to generalize the expression for the square of the invariant interval in restricted relativity, equations(5) and (6), to By the Principle of Equivalence, the situation allow for this effect, and that is just what Ein- would be as shown in the following space-time stein did, writing now diagram. The low and high clocks,are not moving

Low Hlgh

For three spatial dimensions, and using the Newton- ian potential$ to include non-uniform gravitational fields

2 2 As2 = [l +%)c2 (At)2 - (Ax) - (Ay) - (~2)’ C X

so their world lines are straight. The light propagation lines are curved because of the increase Einstein retained the interpretation Asof as mea- of the speed of light with height. The time in- suring the interval between two events in space- terval T becomes stretched tokT, where time, so for the interval between two ticks of a clock, k= dl+& 2 As = CAT (24)

where AT is the interval of proper time recorded This circumstance is what cancalled be the “E- by the clock. If the clock is not moving vature of time.” The elapsed proper time of a clock depends on where is it located in the gravitational field and differs from the elapsedE- --dinate time establishedby an observer, at the surface of the earth, for example, with the aid of light signals. The following diagram shows the or relation for vertical distances. AT = c+At (26) C

tt which is the sameas equation (19), giving the relation between increments of proper time and coordinate time. If the clock ismoving,

Ax = U At, A = U At, A2 = U At (27) X YY

12 and equation(23) becomes (34) 2 (As)’ = ~’(AT)’ = (1 + + ) c (At)’ C (28) All ofthe experiments with atomic clocks which 2 2 - I., +U +UZ (At)’ havebeen done recently, and which we will describe Y below, are a testingof the relationship (34) be- tweenproper time andcoordinate time. whichleads to Analogyof Time Curvatureto the Curvature of a Sphere

Consider a sphere,like the earth, whosecurved surfacepossesses a coordinatesystem of latitude as therelation between proper time and coordinate and longitude, as shown inthe following diagrams. time incrementsfor a clockin motion. The coordinatesof longitude a runsthrough the range 0 to 360. As Einsteindeveloped these concepts during the years 1907 - 1915,and especially during the collaboration with Marcel crossmann from 1912 - 1914,he realized there would also be a curvature As ofspace produced by a gravitationalfield. This As would berepresented by coefficients of the AX)^, (Ay)2,and (Az)’ terms ofthe expression for (As)2 whichwould alsobe functions of position, just as thecoefficient of the c2(At)’ term. The values of these coefficients are determined by his field equationsfor a givendistribution of matter. For a sphericallysymmetric mass distribution,the famous Schwarzschildsolution of the field equa- The coordinate of latituderuns from -90’ to 90’. tions is R is theradius of the sphere. What is thedistance As between two neighboringpoints on the surface of thesphere, differing by Aa and AB? It is not given by

AS)^ = (Aa)’ + (AB)* (Wrong!) (35)

butrather by where

$=- -GM r There are metric coefficients,which depend on position,multiplying the square of the coordinate dif- with M the mass of the central body, r the radial ferentialsto give the true measure of length, or distance, a thelongitude, and B thelatitude. roperlength, between the points. The actual Formotions in weak gravitationalfields such that length will be different for different loca- .. tionson the sphere, even though the coordinate lq< < 1, (32) differentialsare the same. Forexample, consider Aa = 1’ and AB = 0, as shown inthe following ex- C aggerateddiagram. and forslow motions,

2 -v <

onecan neglect the coefficients of the spatial increments,and one is leftwith the equation (23) containingonly the curvature oftime. As = 111.7 km Under the conditions oflow velocity and weak gravityexpressed by equations (32) and (33), one canapproximate equation (29) as At theequator; As will be 111.7 km, while at the latitudeof 45, As will be 78.9 km. The relation betweenthe proper time increment AT and coordinate

13 time increment At in curved space-time is very closely analogous to the relation between the proper length incrementAs and the coordinate of longitude increment Aaon the curved surface of the sphere. The coefficients in relativity are also called metric coefficients. For a network of curvilinear coordinates, x1 and x2, on an arbitrary curved surfaceas shown the proper lengthAs is

' Misner Thorne , Wheeler

There is another way of looking at free motion in the curved space-time produced by masses. Re- call from Einstein's essay that the Principle of Equivalence allows the local cancellation of the effects of gravity by going to a freely falling frame of reference. It can only be local because expressed as: gravitational fields in the real world are not 2 2 2 uniform, as the following diagrams indicate. The (As) = gll(Axl) + 2g12(Ax1) (Ax2) + gZ2(Ax2) (37) extent of the local freely falling frame in both time and spacewill depend on the accuracy with

The great mathematician Gauss made many contribu- tions to the differential geometry of two-dimensional curved surfaces, in particular showing that the curvature can be calculated from the variation 11 of the metric coefficientsgi- on the surface only. These results weregeneralizes to an arbitrary number of coordinates describing n-dimensional curved space by Riemann. This Riemannian geometry furnished many mathematical tools which Einstein AcLab Large GravLob and Grossmann used in the final form of General Paths of dropped Relativity. objects we Converging Paths porallel of dropped objects

Brief Summary of the Curved Space-time Theory of Gravity which measurements are made. These local freely falling frames obviously are local inertial systems In the curved space-time produced by the in that freely moving objects will move in straight ;>resence of matter,2the metric coefficients in the lines as discussed earlier. Inertial systems must 2xpression for (As) being determined by the Ein- be local because only non-uniform gravitational stein field equations, a free objectwill move in fields exist in the real world.The inertial sys- such a way that if one imagines it carrying a clock,tems of large extentas discussed in restricted ;he path it follows in space-time will make its relativity are a fiction. An object moving freely :lapsed proper time a maximum. In technical terms, in a non-uniform gravitational field (curved space- it will follow a so-called geodesic path iswhich time) can be thought asof moving in straight lines :he analog of a great circleon a sphere. Locally, in the flat space-time of restricted relativity in :he path will beas straight as possible in the each of a succession of local freely falling systems :urved space-time. In the words of Professor John which differ in both direction and velocity of mo- heeler, tion. It is clear from equations (12) and associated diagrams that such straight line motion in an "Matter tells space-timehow to curve; inertial system between two events in space-time Curved space-time tells objectshow to produces a proper time difference greater than move. 'l curvilinear motion, since there is some inertial system in which it would be rest, at Hence, the his is graphically represented by the following conclusion that free motion in curved space-time icture and analogy takenfrom the book Gravitation follows a path which produceslj maximum proper time y Misner, Thorne, and Wheeler.l2 The curved sur- difference. Bertrand Russell has referred to this ace of the apple may be thoughtas ofcaused by as the "Principle of Cosmic Laziness." he stem (analog of mass). The ants movingon the urved surface try to move locally as straightas Einstein's theory of gravityas curved space- ossible (geodesics). The result is that the ants time does away with the concept of Newtonian gravi- Id up moving in curved paths about the stem (planettational forces. A body falls to the earth because rbiting the sun). it follows the locally straightest path in curved

l4 space-time. We have seen that forlow velocities the same as coordinate time), was calculated using and weak fields,as exist for most motions on equation (38) for the freely falling earth. earth, the primary curvature is that of time. Thus, from the Einsteinian point of view, bodies In the popular literature on general relativ- -___--fall because of the properties of andtime the ity, the curvature of space is referred to almost behavior of clocks whichwe are discussing. The exclusively since it is somewhat easier to visual- essential property is the relation between proper ize than the curvature of time. However, this is time and coordinate time, equation (34). The quite misleading, since the curvature of time leads curved world line of a falling body results from to all of Newtonian physics lowfor speeds and the elapsed proper time associated with the body weak fields in Einstein's theory, and in this sense can perhaps be regardedas the primary curvature. One should regard mostof these referencesto the curvature of spaceas shorthand for the curvature World Line of space-time. Now that it is possible to measure accurately withmodem atomic clocks, as described Falling in the next sections, the remarkable properties of Einsteinian time,andas the propertiesare, ofne- cessity, used more and more in global timekeeping systems, we can hope for more intuitive understanding of the physics of general relativity. r Curved Some-Time Experimental Measurements

Introduction

T (final) - T(initia1) = dr The experiments which will mainly be described are those of the author and his collaborators with modern cesium beam atomic clocks in aircraft and the experiment with a hydrogen maser in a rocket probe conducted by Vessot and Levine. These experiments were designedto measure primarily the effects of gravitational potential, although the having a maximum value for that aspath compared effects of motionwere necessarily present and were with other paths between the same initial and final also measured. They used macroscopic oscillators event s . controlled by atomic resonances. Before describing them, it is appropriate to mention for completeness The following diagram shows a plot of gravi- some of the earlier observations using direct ra- tational potential $/c2 for the assun a function of distance from its center, along with a schematicdiation from atoms and nuclei. representation of the change in rate of asclock a function of position. This is one way of indicat- Optical Spectroscopy Solar Redshift Observations. The first tests14 of the properties of timeas affected by 7slow fast gravitational potentialwere sought in the shift I - toward the red of the frequency of optical radiation emitted by atoms on the sun and received and Sun c compared on earth with radiation from similar r atoms. The potentia_& difference would predict a shift Af/f n, 2 x 10 . It was very difficult to establish this value with any confidence because of lack of accurate knowledge of pressure-induced frequency shifts in the sun's atmosphere and the complications of Doppler shiftsdue to turbulent ca:thEarth motions of the emitting gas atoms and the surface velocity of the sundue to its rotation. A brief 1, summary with references of these older observations and the attempts to interpret them is given by r Pauli. 15

The choiceof atoms whose spectral lines are ing the curvature of time. At the surface of the little affected by pressure, and the use of rapid sun $/c2 e -2 x Using the value at the earth switching in the earth laboratory from solar radia of the solar gravitational potential, the earth tion to laboratory sourceshas allowed measurement gravitational potential (+/c2= -7 x 10-10 at its with a believable accuracy of about 5%.The exper surface) and the velocity of the earth in its orbit iments were done at Princeton UniversityJ. by around the sun(~30 km/s), the additional46 seconds Brault (1963)16 in France by J. Blamont and F. since Einstein's birthas observed by Herblock's Roddier (1965)l', and in theU.S.A. at Oberlin distant cosmic observer, (whose proper time will beCollege by J. Snider (1972)18.

l5 White Dwarf Redshifts.These observations centrifugeexperiments by H.J. Hay, J.P. S hiffer, havesuffered from lack of precise knowledge of T.E. Cranshaw.and P.A. Egelstaff(1960);2g by W. thesize and mass ofthe objects from which to Kiindig(196 and also by K.C. Turnerand H.A. calculatethe surface gravitational potential. Hill (1964)”;whilestudying other aspects of rela- Sirius B providesthe comparison most widely tivity. The centrifugetechnique has-produced an known, althoughthere are others, such as 40 accuracyof comparison with theory of about 1%. Eridani B. Theaccuracy is probablyno better than 15 to 20%.19,20 Thevery large accelerations associated with thesemotional effects, as well as the acceleration MovingAtoms. The firstcontrolled measure- ofthe muons instorage rings discussed below,have ments of the relativistic effects ofmotion were no intrinsic effect on therelation between proper 21 carriedout by H.E. Ivesand G.R. Stilwell(1941). timeand coordinate time as givenin equation (11). Theymeasured the“transverse Doppler effect“ (that is, thedifference between coordinate time AstronomicalObservations from the Moving Earth andproper time by examiningthe light from excited atomsmoving in a collimated beam, much carebeing The analysisof many typesof observations in- takento average out the first order Doppler ef- volvesthe transformation from a referencesystem fect. The accuracyof comparison with theory is “attached” to thecenter of mass of thesolar system difficultto assess -- perhaps 5 to 10%. Similar in whichcalculations are more easilydone, to the experimentshave been performed by G. Otting referencesystem associated with the earth. Such 23 (1939) .22 H.L. Mandelbergand L. Witten(1962) observationsinclude the measurement of changing quotean accuracy of 5% in their more recentver- pulsarperiods, very long baseline interferometry, sion ofthe experiment. lunarlaser ranging, deep space tracking of spacecraft, and planetaryranging. All involvethe use Using a beam of high velocity Na atomsand ofstable atomic clocks on theearth. The differ- laser techniquesfor the cancellation of first encebetween proper time on the earth and coordinate orderDoppler effects, the “time dilation” has time inthe solar system is therefore essential in beenrecent1 measured by J.J. Snyderand J.L. theanalysis of the results of theobservations. Hall (1975)2xto 0.5%. A particularlyclear discussion of tsf transformation is givenby J.B. Thomas (1976). With Helium-Neon lasers stabilized byMethane, theexpected shift of frequency of 0.542 per de- HighEnergy Physics gree in the Methanedue tothe change of rms velocity with temperature has been observed with ChargedPion Lifetime. This has been measured anuncertainty of 10% by S.N. Bagayevand V.P. by A.J. Greenberg, et al, (1969>32 in a beam from Chebotayev (1972). 25 theLawrence Radiation Laboratory’s 184-inch cyclo- tronwhere the factor (1 - v2/c2)-$had the value Mb’ssbauer Gamma Ray Spectroscopy 2.4.The accuracy of the lifetime determination compared withthe previously measured value of 26 Effectof Gravitational Potential. The dis- nanosecondsfor the lifetime at rest agreeswith coveryby MBssbauer that the frequency shift asso- the relativistic prediction to 0.4%. ciated with the recoil of the nucleus when emitting or absorbing a y-rayphoton could be very small MovingMuons. The differencebetween coordi- when thenucleus transferred its momentum to the nate time intervals andproper time intervals has solid of which it was a part opened the way to beenmeasured using the decay of muons.The life- veryhigh resolution y-ray spectroscopy. The ap- time of rapidly moving muons increased by the plicationof the technique to a terrestrial factor(1 - v2/c2)-4.The most accurate measure- measurement was first made by R.V. Poundand G.A. ment,about 2%, hasbeen made in a storage ring at Rebka (1960)26using a 22.6 meter vertical path in Center for Nuclear Res arch (CERN) in Genevaby a tower at HarvardUniversity. The potential Farley, et al, (1966). ’’ The factor (1 - v2/c2)-’ differenceproduces a frequencyshift Af/f ‘L had a valueof 12. Earlier, but much less accurate, 2.5 x which was measuredwith about 10% measurementshad been made as early as 1941 by Rossi accuracy. Later Pound and J. Snider(1965)27 and ~a113~by studying as a functionof altitude the improved themeasurements to an accuracyof about survivalof muons producedby cosmic rays in the 1%. upperpart of the earth’s atmosphere. They would not survive to sea level except for the relativistic MotionalEffects. Thetemperatures of the effect since their life time at rest is onlyabout materials hosting the y-ray emitting and absorbing 2 microseconds. nucleiin the above experiments need to be measured withprecision and kept closely equal to prevent Relativistic Dynamics.The designof particle the motional effects on time of the lattice vibra- acceleratorsand the analysis of high energy exper- tionsfrom masking the gravitational effect. imentsuses concepts of relativistic energy and Complicationsof solid state physicsand tempera- mmentumwhich are based squarely on the invariance ture measurementdo notallow a very accurate ofthe interval, equation (6) above. Thus, high measurement,but the temperature dependence of the energyphysics makes continuinguse of the Einstein- shiftin resonant frequency provides evidence for ianconcept of time. the difference between coordinate time and proper time. TheM6ssbauer technique has been used to demonstratethe effect of velocity on time in -Atomic Clocks Carried in Comercial Aircraft on Model 5061High Performance (Option 004) cesium Around the World Flights atomicclocks used were providedby the observatory. They were modifiedto improve their performance InOctober of 1971, J.C. Hafeleand R.E. underthe guidance of L.S. Cutler,38 who hadbeen Keating35 firstdemonstrated the relativistic ef- responsible for the original design at Hewlett- fects on time formacroscopic atomic clocks by Packard. We werekindly lent two hydrogen masers carryingan ensemble of four comercial cesium forthe ground clock set made by H. Peters by the beam clocks(Hewlett-Packard Model No. 5061) GoddardSpace FlightCenter,39 which also lent us belongingto the U.S. NavalObservatory around the the trailer usedin the experiments. Three rubidium worldon scheduled airline flights, first in the optically pumped frequ=?r>standards made by Efratom eastwarddirection, and six days later in the west- were included in each clock set .40 ward direction. The combinationof the surface velocity of theearth due to its rotation with the Theoretical Framework. Our experiments mea- velocity of the jet aircraft leads to the predic- suredthe difference in proper time recorded by tionof an asymmetry in the relativistic effects theaircraft clock set, T~,and theproper time forthe different circumnavigation senses. The recorded by theground clock set, T The prediction G' gravitationalpotential effect due to the altitude ofgeneral relativity is of the aircraft needsto be included. Thefollow- ingtable gives theirpublished values of the predicted effects:

Effect Westward Eastward T Potential 144 ? 14 ns 179 i 18 ns 22 T = (1 + @A/c2- VG/2c ) dt Velocity -184 ? 18 ns 96 +_ 10ns G 1 Net - 40 k 23ns 275 ? 21ns 0 Tripduration 65.4hrs. 80.3 hrs.

The uncertainties are from a lackof sufficiently detailed knowledge of thevelocity, altitude, and positionof the airplanes during the flights. 0

The ensembleof clocks were intercompared to 1 ns once an hour in order to identify any rate We usedshort pulses of laser light to carry out changesof individual clocks with respect to the thecomparison of clock readings between the ground average.Several such rate changeswere identified and theairplane as prescribed by Einstein,equa- and corrected for in arriving at themeasured re- tion above.The appropriate spacetime diagrac~ sults. The systematicerror in this procedure is (1) forthe laser pulse time comparison is shown below. givenas k30 ns.Corrections for temperature and pressurechanges were not made. Themeasured Ground valuesof the average time difference with respect to the stay-at-homeclocks at the U.S. NavalObser- vatoryare given as:

Eastward -59 ns Westward?273 ns

The comparisonwith the predictions seems to show anuncertainty ofabout 13% forthe westward direction, but much worse for the eastward direction. It is difficult to assign an uncertainty for the comparisonof the individual potential and velocity effects,but their existence is certainly demon- strated. z AtomicClocks Carried in an Aircraft on Local The inertialsystem in which the integral (41) i,- Flights with Radar Tracking and Laser Pulse Time tobe evaluated is centered on thefreely fallin:, Comparison earthand is non-rotatingwith respect to distant matter, as shown inthe following diagram. Participants. These experiments were conduct- ed36by the author and L.S. Cutler, R.A. Reisse, R.E. Williams, J.D. Rayner, C.A. Steggerda, J. & 8-latitude Mullendore, S. Davis, L. Smalland B. Duvall(all at theUniversity of Marylandexcept L.S. Cutler, who is at Hewlett-Packard)during the period from mvE=wrcos8 May, 1975through January, 1976 with the support of the U.S. Navy,37 especially the Time Services Divisionof the U.S. NavalObservatory and its Director, G.M.R. Winkler.The Hewlett-Packard

17 + The vectorvelocity v inthe inertial system is A a strip chart recorder for visual monitoring of given by clockphases and temperatures, a drynitrogen tank forthe pressure control system, and a non-environ- + +* -+ + mentallycontrolled traveling clock. This equipment v=A vA +wxr (42) is shown inFigure 13. Intercomparisonof the epochsof the zero-crossings of the 5 MHz clockout- puts was made every 200 seconds. The reflection of +* whosevA is thevelocity of the aircr3ft yith re- laser light pulses fromthe aircraft was accomplished by placing an optical corner reflector of spectto the surface of the earth and W x r is the surface velocity+of the rotating earth whoseangu- thetype eveloped for the lunar laser ranging ex- beside the forwardobserving window on larvelocity is W. Thefadius vestor to the loca- periment4' tion ofthe aircraft is r. When v is squaredto theaircraft as shown inFigure 14. A photomulti- insertin equation (41), one obtains plierequipped with neutral density filters and a 100 Angstromband pass filter was housed as shown in Figure 15 so that it couldbe pointed by hand *2 +* ++ + +2 v2 = v + 2v (wxr)+(wxr) (43) from inside the forward observing window towardthe A A A - lasertransmitter on theground. The epochof the received laser pulses on the plane was measuredby theevent timer inthe proper time ofthe plane and The underlined term in the above+e uation is just storedin the computer where it couldbe read out twicethe eastward component of v) multiplied by andcommunicated tothe ground by voiceradio link. theeastward surface velocity v = W r cos B, where 0 is thelatitude. It is this Eerm whichleads to GroundEquipment. On theground at the the asymmetry inthe around the world flights des- PatuxentNaval Air TestCenter, a trailer contained cribedabove, since it is positivefor eastward anidentical clock box (Figure 16); event timer and flights andnegative for westward flights. In our NOVA 2 minicomputerwith standard magnetic tape, localflights, its integral was toosmall to be disk,and tektronix graphics terminal for analyzing measured. and displayingthe data (Figure x);and two hydrogen masers (Figure 18). Figure 19 Shows theair- AirborneEquipment. A schematicdiagram of craftparked alongside the trailer for direct com- theexperiment is givenbelow. The aircraft was a parison by coaxialcable of the aircraft andground NavyP3C anti-submarinepatrol plane, capable of clock sets beforeand after flights. Between flightsof 15 to 16 hoursduration at altitudes up flightsin the absence of the aircraft, both clock to 35,000 feet.Figure 11 is a picture ofour air- boxesand the airborne electronics were housed in craft, P3C 912, inflight. On boardthe plane was thetrailer. On thefive separate fifteen hour anensemble of three Hewlett-Packard cesium clocks flights,one boxwas flown three times andthe other twice.Figure 20 shows Dr. Williamsand Dr. Reisse preparing to transfer a clockbox to the plane, intowhich it had to beinserted through the narrow hatch shown inFigure 21.The installation of the electronicsand clock box in the P3C aircrafttypi- cally required a dayand a half.

Laser Light Pulse Time Comparison.The laser transmittingand receiving equipment was locatedin the van at thecorner of the hangar in Figure 19. The beam directing optics is pictured in Figure 22 andillustrated schematically in the above diagram. Underneaththe laser was located a 7.5 inchtele- scope42which was usedwith a beam splitter both to detect the reflected laser light with a photomulti- pliertube and to track the plane with closed cir- cuittelevision. This equipment in the van is shown inFigure 23. The laser is a frequencydoubled neodymium YAG system utilizing a mode-locked oscillator with pulse extraction and subsequent amplification, emitting a pulse 10 times a secondwith energyof 0.5 millijoules andduration of 100 picoseconds.The aircraft was flownmainly at night with its landing lights on toenhance the contrast carefullypackaged to provide a very well controlled foracquiring and tracking it visually. The flights environmentalong with an environmentally controlled approximatedthe path in a clockwisesense shown in set of threeEfratom rubidium clocks, the entire following map. Thecone shows theacceptance collectionof clocks and environmental package being the angle for the laser light pulse to be reflected called a "clockbox." This is shown inFigure 12 backby the comer reflector. The time comparisons inposition on theaircraft. onboard were an Also were made on the near side of each circuit, with event timer, capableof measuring the epoch of an occasionalgaps due to cloud cover or equipment eventwith a precisionof 0.1 nanosecond, a NOVA 2 difficulties. The aircraft wasacquired optically minicomputerand associated LINC magnetictape unit,

18 shown in Figures 27 and 9. rPATUXENTNAVAL AIRTEST CENTER ClockPerformance. Typical tomic clock stabilities of 2 to 3 parts in 10'' foran averagir time ofone day were achievedwith commercial Hewlett-Packard5061 high performance standards by making several modifications to themand by maintaining a rigorouslycontrolled environment. A plotof the experimentally measured Allan variance U (2; T) forfive separate standards compared with thesixth is givenbelow. The modifications con- sisted of a proprietary change in the beam tube

Number of pmnts of somple 437106 216 51 23 12 5 Conf~aence 4% 6% 8% 12% 18% 26% 41% \ 0 = THEODOLITESTATION IO UlLES

SCALE

shortly before the laser time comparison by pointing in the direction communicated by theChesapeake Test Rangewhich tracked the aircraft continuously withradar. The laser beam had a divergenceof about0.5 milliradians, which illuminated about one-halfthe length of the aircraft at the slant rangeof about twelve miles. The requiredpreci- sion pointing was provided by Steve Davis working with coarse and fine Heath kit model airplane controllers setting elevation andazimuth rates forthe beam directingoptics. The controllers I and closed circuit TV display are shown inFigure 2040 4080 816016320 32640 65280 130560 -24, while Figure 25 displays the landing lights as Seconds seen on the TV screen. When the laser pulse was hittingthe corner reflector, the return flashes were seen on the screen and could also be seen by theeye if one stood next to the laser beam. At theplane, the laser light was verybright (but which is now standard on all HP5061 high perfor- considerablybelow eye damage levels), actually mance units;the addition of an additional inte- casting shadows inthe darkened interior of the grationin the quartz crystal control loop to plane. An inadequateview of the laser transmitter reducefrequency offset due to steps or ramps in andrunways as seenfrom the plane at twilight is thecrystal frequency, (now available as anoption shown inFigure 26. (This is oneframe from a fromHewlett-Packard); and the increase of the colormotion picture film. It canbe seen, along beam current by a factor of about twoby raising with other parts of the experiments, in the BBC TV theoven temperature (also available as anoption program,"Einstein's Universe," presented on public fromHewlett-Packard), which increases short term television as part of the Einstein Centennial acti- frequencystability at theexpense of tube life- vit ies) . time. A simpleblock diagram of the standard is givenbelow showing the extra integration and RadarTracking. An essentialpart of the ex- additional buffer amplification to aid in the periment was thecontinuous measurementof the air- intercomparisonof the clocks. The modifications craft altitude and velocity during flight by radars were carried out at Marylandwith the supervision at theChesapeake Test Range locatedabout two andactive participation of L.S. Cutler.Figure miles fromthe ground clock set. At intervals -29 shows hirm tuning up theensemble of clocks duringflights, the angular measurements of the before they were inserted into the clock boxes. radars were calibrated by optical theodolities. The radar data was used to compute the relativistic time integral,equation (411, with an accuracy considerably better than that of the atomic clock measurementsthemselves, so thatthe clock perfonn- anceitself determined the accuracy of the comparisonwith general relativity. TheChesapeake Test Rangeand a closeupof one of the antennas are

19 The isolation against vibration and shock was BLGCKDIAGRAM OF HP5061 CESIUMBEAM ATOMIC CLOCK achieved by mountingthe box on four pneumatic Barrymounts which gave a resonantfrequency of about 3 Hz. Almost critical damping was achieved &h I_ by usingexpansion cylinders following an adjusta- AMPLIFIER OSCILLATOR bleorifice, which led to an increase of isolation of 12 db peroctave. The characteristicfrequencies ofthe aircraft were around 80 Hz. Sway ofthe box in the aircraft was restrained by a cushioned re- tainer ring acting on a vertical post extended up- wardfrom the box.Strong flexible cables were fastened around the pneumatic isolaters to restrain the 1000 lb. box inthe event of an accident.

The clockbox lid carried the voltage regula- tionand pressure control equipment as well as the SYNTHESIZER hAMPLIFIER environmentalcontrol box forthe Efratom rubidium clocks,which can be seen on the left in Figure 33. Similarcontrol procedures were followedfor these CESIUM CESIUM OVEN BEAMTUBE CONTROLLER clocks,but they proved much more susceptible than thecesium standards to the shocks of landing and take-off,those events producing rate changes. For thisreason, the rubidium data is not very useful for relativity measurementsand will not be present- ClockPackaging for Environmental Control. edhere. Carefulenvironmental control was maintained to keep small anychanges intemperature, pressure, SignificantFeatures. Some ofthe significant magneticfields, or supply voltages. Isolation featuresof the experiments are listed below: fromvibrations and shocks was provided.These controlswere accomplished by mountingeach set *Ensemblesof Clocks on Ground and in Aircraft ofthree clocks in a clockbox, shown opened in Figure30. The objective was tocontrol the Clocks ineach ensemble intercompared environment so thatany changes would affect the among themselvesevery 200 seconds. clockstability by less than The clocks were mounted vertically in individual magnetic *CarefulEnvironmental Control shieldsof 60 mil thick MO-Permalloy. Afterthe magnetic lid was put on (SeeFigure 31), individual -Temperaturestability AT < 0.060'K (rms) clocks were degaussed. To remove heat from the -Pressurestability AP 1 Torr clocks,and to control their temperature, air was -Magneticshielding circulated by anindividual fan through each of -Vibrationand shock isolation themagnetic shields, entering at thetop through -Voltage regulation the hoses shown in Figures 31 and 32 after passing a heater controlled by feedbackfrom a distributed Effecton clock stability < arrayof thermistors within the magnetic shield. No needfor systematic corrections The air exited a shieldthrough holes at its bottom andflowed along the interior bottom of the pres- *Returnof Clocks for PostFlight Comparison sure controlled aluminum clockbox, losing heat to theoutside through conduction. Variable speed No rate changesobserved for cesium fanscontrolled the flow of external air overthe standards beyond statistical expectation bottom of theclock box, the rate beingcontrolled forstationary clocks. automatically by theexternal temperature. (We are indebtedto Dr. J.P.Richard of the University *RepeatedMeasurements ofMaryland for this and other advice concerning thetemperature control). The temperature at in- -Clock BOX 1: 3 flights dividualpoints in the clocks was keptconstant to -Clock BOX 2: 2 flights about 0.060'K. The temperatureof the air changed -5 Test flights of G? hoursduration each by about loo inflaring through a magneticshield. tostudy and improve performance of experiment. The clockbox was nearly hermetically sealed when the lid was attached and either dry nitrogen *Laser Light Pulse Time ComparisonDuring or dry air was fed to it from a Granville-Phillips Flights feedback controlled value to keep the pressure constantto less than 1 Torr at a value slightly -No DopplerEffect Complications above sea levelatmospheric pressure. To allow -Techniqueof value for future space ex- for possible decompression of the aircraft cabin perimentssince optical pulses are pressure at high altitudes, the clock box was made little affected by the ionosphereand very strong with walls of 4 inch thick aluminum. solarcorona. This also isolated the clocks from acousticnoise. -First realization of Einstein's 1905 prescription for comparing separated

20 developduring the flight for the gravitational and clockswith light pulses. velocityeffects separately and for the net effect. The plotted points with error bars 2. 0.3 are *FlyingClocks Experience ofMost of (2 ns) Ig thelaser light pulse comparisons. Time The directcomparison measurements of the 5 -No relaxationof stresses as occursin MHz clockphases before and after the flight are free fall. shown in the following plot along with the laser -Periodsof steady acceleration limited pulse comparisons which were made when the plane totake-off andlanding. was on theground as well asin the air. The solid -Plane'srotations made slowlyto avoid linesare the comparison of the "paper clocks," Coriolis effects on cesiumbeams.

ExperimentalResults. Although much detailed data exists fromthe five 15 hour flights, only a representativesampling can be given here, which is I- takenfrom the flight of November 22, 1975. Shown below is a plotof the predicted effect of gravi- 47.1 f 0.25ns tational potential and of velocity on the rate of 1 the aircraft clock set with respect to the ground clock set calculated from theradar tracking data.

AWC2 0 l r: r: I l I I I l 10 20 30 40 50 60 HOURS

that is theaverages of the three cesium clocks in eachclock set. The irregularform is due to the intrinsicclock time fluctuations. In thisplot, thedifference in rates between the clock sets established before the flight has been subtracted out. The actual rates are shown inthe following plotof the laser timecomparison.

3530 I I I% 25 _r I - -3Onslday -30ns/day v] I1 '=- The uppercurve is a plot f (4 - $,)/c2which is 0 I seento average about 10-l'. de stepsin this uS 20- I W T quantity are caused by the need of the aircraft to v) - +45ns/day 2 I p 15- I remain at 25,000 feet for 5 hourswhile burning a offfuel toenable it toclimb to 30,006 feetfor z - f another 5 hours,before being light enough to climb IO to 35,000feet for the final 5 hours. The lower curve is a plotVA*2/2c2,of thevelocity effect 5- due to motionof the plane with respect to the 1; f ground at theChesapeake Test Range. The oscilla- I I I l J tions are due to the effect ofwinds as the plane O Ib 20 30 40 50 60 circles. effectThethis av ofvalue rage is seen HOURS to be aboutbeto corresponding to an average speedof 138 mfs. The secondand thjrd terys of equation(43) are notplotteg sigcs VA* * (W r) x The gap in the preflight data was caused by the will integrateto zero and (W x r) will benearly needof the laser operator to sleep before the cancelled by a similar term for the groundclocks. flight. The effectof the steps in altitude on Thelower plots are the integrals of theupper the flying clock rates canbe seen by plotting the curvesover the 15 hourflight, showing the time laser comparisonsduring flight in anexpanded difference AT = T* - T~ as it was predictedto

21 scale as is donebelow. The only changethe clocks Flying Clock Y3 versusGround Paper Clock Flight of November 22,1975 6o r Steps In Clock Rote Produced by Stepsin Altltude

-40 l - 60 38.0 38.5 39.0 39.5 40.0 Fractional Days

I I I 25 30 35 40 HOURS there is some scatter. Below is plotted a histogram forthe ratio of the measured time difference to that calculated fromGeneral Relativity using the radardata. The predictionshad an uncertainty no experienced was thechange in gravitational potential.

It is alsoof interest that the flying clocks 0.987 f 0.011 continued to behave with respect to one another exactly the same during the flights as before and f0.016 after.This is illustrated by thefollowing plot 4- - ofthe time offlying clock 13 with respect to the averageof the three flying clocks. Similar data v) existsfor each clock on eachflight. When COP L 3- ow paredto the ground paper clock, however, flying e= W :2- 2: 2; I- PREDICTION S UNCERTAINTY m f0.005 0, 1 1 l I 1.06 1.04 1.00 0.96 0.92 (MEASURED EFFECT)/(PREDICTED EFFECT)

0 more than k 0.5%. Theformal standard deviation of -5 t - the mean was 0.011. To allowfor possible system- Flight atic efforts, we arecurrently estimating (conser- vatively) an uncertaintyof f 0.016.The result -15 is : I l I I l -20 38.0 38.5 39.0 39.5 40.0 Measured Effect = 0.987 ? 0.016 FRACTIONAL DAYS CalculatedEffect (General Relativity)

The measuredbehavior of macroscopic clocks in air- clock #3 showed a step as seenin the next plot. craft flights - a "human scale" type of situation - (Theblack marks fusing into a thick bar are re- exhibitsthe remarkable properties of Einsteinian corded when a datapoint is absent for the direct time withinthe accuracy of measurement of aboutl%! comparisonof the 5 MHz phases, as was thecase duringthe flight). The stepin rA - is, of AtomicClocks Carried in an Aircraft on Global course,the result of the relativisticTgffects Flights With Inertial Navigation and Radar Alti- duringthe flight. metry.

If one treats each cesium clockon each of Participants. The flights were conducted the five flights as an individualmeasurement, in June and July,1977 by the same group(from the University of Maryland and Hewlett-Packard) whichconducted the local flights described 43 abovewith similar equipment. The Air Force joined the Navy insupporting the experiments by

22 2 providing a C141 longrange transport aircraft from speedof the rotating earth. Vs/2 is the"centri- theWright Patterson Air ForceBase, assistance in fuga1potential, and Q is thegravitational poten- reconfiguringthe equipment, and ground support tial, bothof which change with latitude such that facilities at the Andrews Air ForceBase in Mary- thecombination has a constantvalue independent of landnear Washington, D.C. latitude,

Purpose. The purposeof the flights was to studyexperimentally the implications ofGeneral 9 - + = constant(44) Relativityfor the elapse of proper time at dif- erentlatitudes on thespinning earth, freely fall- ingtowards the sun as it moves in its orbit. alongthe ocean surface. From theearlier discus- Clear understandingof these implications is of sion of thetheory, it will berecalled that the greatpractical importance for worldwide time relationbetween a propertime increment AT and a keeping,and will bediscussed later. Clarifica- coordinate time increment At is tionof the concepts by means ofsimple experiments aidsin the development of physical intuition. 2 AT = (1 -!$I At (45) Null Change ofProper Time with Latitude. On + - c2 2c c2 the spinning earth, general relativity predicts a null effect on proper time as one moves a clock fromthe equator to the pole along the mean ocean for the weak gravity andslow velocities which ex- surface.This was discussedearlier in the sections ist atthe earth's surface. Thus, along a surface ontheory in relation to Einstein's discovery of ofconstant geopotential, the relation of proper theeffect of gravity on time. His 1905prediction time tocoordinate time is that a clock at the equator would runslow with respectto one at thepole ignores the influence of gravitational potential since he did not discover it until 1907. Ifthe earth were a homogeneous perfectsphere as shown, thegravitational potential wouldbe the same everywhereon the earth's and all standard clocks at mean sea level are predicted to run at the same rateindependent of latitude. 4- Surface velocity = o ot pole ExperimentalResults for Flight to Thule. To m check this null prediction, a clockbox containing ----c-- Surface velocity maximum threecesium standards was transported in an Air at equator Force C141 fromWashington, D.C. toThule Air Force Base inGreenland as shown in the polar photograph I of a globein Figure 34, this being the largest convenientlyaccessible latitude change in one hemisphere. The latitudeof Thule is 76' 32'and thatof Washington is 38' 49'.After a number of surfaceand the 1905 prediction wouldbe correct. local test flightswith the reconfigured equipment However, theearth has the shape, to first order, in the C141 aircraft, the flight to Thule was under- ofan oblate ellipsoid due to its spin, as shown takenon June 23, 1977, after several days of inexaggerated form in the following sketch. The problem-freecomparison with the ground clocks, as gravitationalpotential $I atthe pole is less a combinationof long test flight and global mea- pole' surement. The plane was kepton the ground at Thulefor four days and returned on June 27. Althoughthe radar altimeter failed about 2 hours before arrival at Thuleand had to be replaced by oneflown in on a regular Air Forceflight, the experiment was generallysuccessful. Using the #pole +eq inertial navigation data and radarand pressure altimeters to evaluate the relativistic integral, equation(41), and making direct electrical compar- isonsof the aircraft and ground clock sets before and after the flight as hadbeen done for the local flightsfrom the Patuxent Naval Air TestCenter, but with pre and postflight periods of several days,the following comparison was obtained.

Measured: T~ - T~ = 38 ns 5 5 ns thanthat of the equator, Q , sincethe pole is closerto the center of thee&rth. The surfaceof Calculated: T~ T~ = 35ns ns theoceans of the ear h is determined by the - i 5 "geopotential," @ - Vs/2,5 where V is the surface

23 The time differencemeasured agrees within errors receivethe pallet with its clockequipment. The withthat predicted for the flights to and from first transfer of the equipment(without its front Thule.There is noevidence for any anomalous insulatingpanel) from the garage to theplane is latitudeeffect. The "EinsieinError" of 1905 - shown inFigures 40 through 4, The installed not including the gravitational effects - would equipmentwith Len Cutlerstanding in front is seen havepredicted a time difference of an additional inFigure 45. During an actual flight, the equip- 56 nsper day, or a total of 224 nsfor the four ment is shown fromthe front in Figure 46and from daydwell time! Becausethe aircraft had to be therear in Fioure 47. Enough seats were installed usedfor other purposes starting August 1, it was to accommodate theeight University ofMaryland notpossible to repeat the Thule flight or to make peopleand fourteen Air Forcepersonnel who went on flights fromWashington to Panama to checkfurther eachflight. In addition to the crew foroperating thenull prediction. It was deemed more important theplane, there were techniciansto operate and touse the remaining time to transport the clocks maintainthe gasoline powered portable electrical toChrist Church, New Zealand. generators,portable air conditioners, and portable heatersneeded to power theplane andprovide tem- ReconfiguredEquipment for C141 Aircraft. peraturecontrol of its interiorduring dwell times Beforedescribing the purpose and results of the on theground at theremote sites and at Andrews northernto southern hemisphere flights, the recon- Air ForceBase before and after flights. The trans- figuredequipment and the ground base at the portationof this equipment, some of it indupli- Andrews Air ForceBase will be briefly discussed. cate,required the large storage capacity of the Fipure 35 shows a frontview of the equipment being aircraft. It was essentialin maintaining continu- assembled on analuminut4frame in the shop of the ous operationof the clocks in an adequate environ- Universityof Maryland. The clockbox, seen on ment in the interior of the plane at theremote the left, was rewiredto meet rigorous Air Force sites, and duringthe 12 hourlayovers in Hawaii requirements. It was alsomounted,on improved on Christ Church flights. pneumaticsupports at theheight of its center of mass toreduce the sway encounteredwith the former Two Carousel IV inertialnavigation systems, bottommounting. The minicomputer, event timer, a radar altimeter, and a pressurealtimeter were taperecorder, chart recorder, and otherelectron- installed on the aircraft to provide accurate ics weremounted inan Air Forcefurnished rack measurementsof latitude and longitude,velocity whichincluded some vibrationand shock isolation withrespect to the ground, and altitudeabove the betweenthe inner structure and the outer structure ground.This information was recordedautomatically which was bolted to the mainframe. in digital formevery 0.6 secondon magnetic tape recorders.In addition, there was provisionfor Figure 36 is a rear viewof the frame and manualreadout which was loggedevery 15 minutes. equipment. A specialregulated power supplycapa- This log was usedwith a Hewlett-Packard 97 calcu- bleof working from either 6OHz or 400Hz was con- lator to compute a runningintegral of the differ- structed to power theclocks and other equipment. encebetween the proper time on the aircraft and It included enough Sears Die Hard batteries in a theproper time at the Andrews Air Force Base as special vented container to operate the clocks for theflights proceeded. The recordingand readout at least 12 hoursin the event of failure of other equipment is seenin Figure 48. At Thule it was sources.This apparatus is seen on theleft, being possibleto place the aircraft in a hangar, shown workedon by technician Lyndon Small. inFigure 49.

The entire frame was surrounded by double wall The midnightsun was very high in the sky at plywood panelscontaining insulation and wasmount- Thule since we werethere only a few days after ed on a standard Air Force 7 foot by 9 footcargo thesumer solstice. Figure 50showing the C141 pallet.Figure 2 is a picture of thecomplete whichbrought our replacement radar altimeter was assembly in a prefabricated garage structure built takenjust before midnight. The relativelyshort at the Andrews Air Force Base to contain the equip- shadows cast by thesun at midnight are shown in ment betweenflights. The hoses on the back panel Figure 51. The23O.5 tilt of theearth's spin circulate temperature controlled air intoand out axis whichcauses this summer solstice on the21st of thelarge insulated enclosure. Two Sears window ofJune each year in the northern hemisphere made air conditionersprovide cooling. Heaters inthe possibleanother experiment which required flying flat plenumon the left were used for fine temper- the clock from the northern to the southern hemi- ature control which could be maintained to a few sphere. degrees.This enclosure solved one of the major problems -- the large variation with time of the temperature within the aircraft during flights, andon the ground. The mounting on thecargo palletallowed the equipment to be placed on the C141 or removedfrom it in about 10 minutes compared withabout one and a half days for the earlier ex- perimentswith the Navy P3C aircraft.Figure 38 shows the C141, garage, trailer housingthe ground clocks,and van containing the ground computer equipment.Figure 39 shows the tail assemblyof the C141 with the petal doors whichcan open to

24 Does theGravitational Potential of the Sun term inthe Taylor's Series expansion of C$ about AffectProper Time on the Freely Falling Earth? thecenter of the earth is S tracted away, leaving Thefollowing diagram .~ shows that at the time of mlythe second order terms." These terms produce the summer solsticethe North Pole and points in the tides, but the difference in $ whichthey yield acrossthe earth's diameter wouldproduce a rate differencein proper times ofonly 7x 10-17 or 0.62picoseconds per day. However, thelinear I term, if it affected phenomenaon earth, wouldpro- I v_r 23?5 at time of summer solstice duce a dayto night shift in clock rates of about 8 x orabout 75 nsper day. This question was studied carefully by ProfessorBanesh Hoffmann (authorof the biography of Einstein recommended inthe first section of thispaper4) in 1957.45 He predicted that no sucheffect wouldbe measured inthe reference frame of the earth, but called for experimentsto check the prediction when clocksof sufficientaccuracy became available. the northern hemisphere are closer to the sun on In 1976 theque$&ion was examinedagain by theaverage (due to the spin of the earth) than the Professor Roman Sexl who was seekingan explana- SouthPole and points in the southern hemisphere. tionfor an erroneous report of a dependenceof Sincethe earth is fallingfreely towards the sun atomicclock rates on latitude.47 He concluded as it moves in its yearlyorbit around the sun, thatthere should be a seasonaleffect caused by thenearly fixed direction of the spin axis affords the tilt inthe earth's spin axis, described by the theopportunity of conducting experiments in a equation freely falling laboratory -- the earth as Einstein's freelyfalling elevator. At thetime of the Summer Solstice,the northern hemisphere is the"floor" andthe southern hemisphere is the "ceiling," with dT1 dr2 - 14.8{sin 0 - sin 0 1 - thepositions reversed at theWinter Solstice. dt dt 2 1 (47) Recalling the earlier discussion about cos [ t - 21 June] ns/day Einstein'sPrinciple of Equivalence, one can ask: 365 is thegravitational field of the sun transformed away forexperiments on the freely falling earth? Inparticular, will clockson the "floor" run at where TI and '2 arethe proper times at latitudes the same rate as clockson the "ceiling" even 01and 02 (southernlatitudes being taken as nega- thoughthey are at differentdistances from the tive).This equation results from the incorrect sun?Here we are takingfor granted the effect of retentionof the linear term in the expansion of gravitational potential difference onclock rates thesun's potential as just discussed. It wouldbe as establishedby other experiments. The question correctfor observations conducted from a frameof canbe answered experimentally by transporting referenceattached to the sun, but is wrong for clocksfrom the northern to the southern hemisphere observationscarried out on the earth. Professor nearthe epoch of a solstice, letting themdwell Sexl now acknowledgeshis error.48 for a while,and then returning them for comparison withthe stay-at-home clocks. From thetheoretical ExperimentalResults for Flights to Christ pointof view, the Principle of Equivalence seems Church.Figure 52 showson a globetilted at 23O.5 toprovide a clearanswer: on thefreely falling thepath taken by our C141 in transporting the earth(Strictly, the earth-moonsystem, but we clogksto Christ Church, New Zealand(latittde ignorethis complication since its effects are -43 29') fromWashington, D.CI (latitude 38 48') small)the gravitational effects of the sun are and thedifferent average distances of these loca- tions from thesun. The first trip was made from notexperienced, to first order, just as in the freelyfalling Skylab in orbit about the earth the July 10 toJuly 17 and a secondtrip from July 23 astronautsexperienced no effects of the gravity toJuly 30. Threedays were required for the fieldof the earth, to first order. Mathematically, travelout and back, including %l2 hour stopovers this means thatin the plot of gravitational poten- in Hawaiieach way and a 2 hourstopover at the Travis Force Base in California on thewestward tial C$ as a functionof distance from the sun, as Air journey.This allowed a dwell time inChrist shown inthe sketch below, the slope, or linear Churchof fourdays. Figure 12 shows theaircraft onthe ground at theOperation Deep Freeze Antarctic supportbase in Christ Churchsurrounded by some of the portable electrical generating and heating equipment (it was winter in New Zealand) it had carried with it.

Thedata for the time differences rA - are displayedin the following table: r

25 MeasuredCalculatedAlleged Value(ns)Value (ns) Effectof Sun (ns)

Flight 1 115 f 8 129 5 5 80 f 5

Flight 2 131 2 8 118 f 5 70 f 5

The data is still beinganalyzed to correct the readingsof the radar altimeter overthe varying topographyof the continental U.S. to givealtitude above the ellipsoid rather than above the local topography,but the changes in the above numbers will notbe large. There is noevidence, with a detection sensitivity of about 10% when themeasured andcalculated effects are compared,of the alleged effectof the sun.

Hydrogen Maser Carried on SuborbitalRocket Flight WithDoppler Cancellation Tracking

InJune 1976, a hydrogenmaser was carried as payloadin a suborbital flight by a Scoutrocket launchedfrom the Wallops Test Center of NASA in an experimentdesigned and conducred by R.F.C. Inthis case, the gravitational potential differ- Vessot, M. Levineand others of the Harvard/Smith- encecauses the frequency of the probe maser to be sonianCenter for Astrophysi~s.~~ Thepurpose was shiftedto higher values than the reference masers to measurewith high accuracy by groundtracking onthe ground -- a violet shift rather than a red thelarge change in frequency of the maser caused shift, but it is still convenientto speak of the by thelarge change in gravitational potential as effectas "redshift." The valueof the gravitation- it ascendedto an altitude of about one and a half al shift as a functionof height above the earth earthradii above theearth's surface and fell is plottedbelow. The received microwave frequency backinto the Atlantic Ocean in a flight lasting justunder two hours. A sketchof the trajectory is givenbelow. The ground path of theflight is 7- 1 l I shown inthe following map. Ground trackingwith REDSHIFT vs RADIALDISTANCE FROM EARTHCENTER microwavefrequencies was carriedout from stations 6 97 x

GEOMETRY OF ACCELERATIONS, VELOCITYAND SIGNAL PROPAGATIONVECTORS 'l \ RANGE OF EXPERIMENTPERFORMANCE P/L 150-170 LBS SCOUT F

,' I \o; i-

EARTH SURFACE RADIALDISTANCE 1000 nml

will be strongly affected by theordinary Doppler effectwhich is just the rate ofchange of slant rangedivided by thespeed of light. For a typical at WallopsIsland, Bermuda andFlorida equipped withhydrogen masers. In terms of relativistic plannedtrajectory, the Dop ler shift in frequency couldbe as high as 2 as shown inthe follow- frequencychanges, it is readily shown thatthey x ingplot. Since the gravitational relativistic are expressible as theintegrand of equation effect wouldbe about 4 x 10-l' and theexpected stabfiity of thehydrogen maser was hoped to be fProbe - fGround = g = 'Probe - 'Ground %lo- , extraordinarymeasures had to be taken to f 2 Ground measureor cancel the Doppler shift. Also, the largeand variable effects of the earth's iono- 2 2 spherecausing phase shifts in the propagated 'Probe - 'Ground microwave signals had to beconsidered. 2CL

26 REDSHIFTBEAT DATA FROM QUICK-LOOK HIGH-SPEEDPRINTER

7 1 TT r ~~~~ #J------'-'""' #J------'-'""' ' ' ' ' ' ' ' ' ' A1 1 l

(andnot recovered!) being held by its makers, Bob Vessot(on the right) and Marty Levine. Figure 56 is a picture of therocket during launch. TIME IN 1000 SEC UNITS Carefulanalysis of the ground trackingdata todetermine the actual rocket trajectory and com- A veryingeneous arrangement of three micro- parisonof the measured frequency shift as a func- wave linksat different frequencies as shown in the tion of time with that predicted by generalrela- simplified block diagram below solved these prob- tivityhas yielded the following value50 for the lems. gravitationalfrequency shift (the velocity effects were assumedgiven)

_-Aff - {l+ (5 2 126) x lod6} % (49) C

This is the most accurate measurement of the relativisticeffects onfrequency. A plot of the residuals at theearly stage of the analysis is givenin Figure 57. r- I Other AtomicClock Measurements I I Mountain toValley Experiments. The first I suchmeasurement was made in 1975 in Italy between I Torinoand a cosmicray laboratory at Flateau Rosa I I 3250 m higher by L. Briatore and S. Leschiutta 51 usingone cesium beam clock at eachlocation. Com- parison was achieved by receiving the same TV signal at each site andby directcomparison before and after the 66day dwell time at Plateau Rosa. Althoughno stringent environmental control was It was possibleto achieve real time cancellation attempted,nor were systematic corrections made for so that the redshift was evidentduring the flight environmentalchanges, a 15%measurement was as shown by thefollowing quick look beat frequency achieved, agreeing with the general relativistic data. The breakin the data just before the end calculation within that uncertainty. ofthe flight is dueto tracking station problems and interruptedthe phase continuity. It couldnot The secondmeasurement was made in Japan in subsequentlybe recovered, so theremaining data is Juneand July, 1977 by S. Iijima and K. Fujiwara5' notuseful for analysis. Thecombination of poten- ofthe Tokyo AstronomicalObservatory. One Hewlett- tial and velocityeffects produced zero beats dur- Packard5061 High Performance standard was trans- ingboth ascent anddescent. The ascent zero beat portedfrom the Tokyo Observatory(altitude 58 m data is shown inFigure 54. The rotationand abovesea level) to the Norikura Corona Station nutation of the spinning payload can be clearly (altitude 2876 m abovesea level) on two successive distinguished.Figure 55 shows theenvironmentally occasionsand left to operate for one week. Before controlled hydrogen maser package which was flown and after those trips, one week comparisons were

27 made with a similar clock at the observatory. portableclock trips. Systematiccorrections were made forthe effect of 53 differentenvironmental conditions at the different NAVSTARjGlobal PositioningSystem sites onthe rate of the clock. They alsopaid closeattention to the placement of the clocks in This is a new navigationsystem under develop- the local magnetic field and took great pains to mentby theUnited States Department of Defense. keepenvironmental control during the 8 hour It is shown in artist's conception,together with transport time in a cushionedand air conditioned some factsabout it inFigures and 2. There van.Their results were will be 24 satellites placedin 12 hour period circular orbits, 8 ineach of 3 orbitalplanes in- clined at 63' tothe equator and equally spaced Measured Effect around it. Eachof thesesatellites will carry a = 0.94 ? 0.05, CalculatedEffect (50) verystable atomic clock (with several spares) and will transmit a pseudo-random noise code with a bit repetitionfrequency controlled by theatomic a verification at the5% level. clock.Information about the orbit of the satel- Theseexperiments measured purely the effect lite is alsotransmitted. User equipment will re- ceive signals from four or more GPS satellites ofgravitational potential difference. simultaneously,or sequentially, locking on to the transmitted code by shifting a local clock which Comparison of AbsoluteFrequency Determina- steps the samepseudo-random noisecode in the re- tions.Since the early 1970's, theNational Bureauof Standards in Boulder, Colorado, at an ceiver.Large scale integrated solid state elec- troniccircuits in the receiver package can then altitudeof about 6000 feetabove sea level,has calculatethe position, velocity, and time for any been including the gravitational effect A4/c2 'L user. 2 x inthe determination of. theabsolute cesiumfrequency with its laboratory beam tubes. The stable atomic clocks in orbit are the Otherstandards laboratories are at much lower heart of thesystem. In orderfor all ofthem to altitudes so the effect is notyet significant i.n remain synchronized with each other and with the terms ofachievable accuracies for them.However, groundclocks at the U.S. NavalObservatory which theinternational definition of the second is sets timeworldwide for the Defense Department, basedon the value of the cesium ground state the effects of general relativity mustbe included. hyperfinetransition sea level, so thegravita- When placed in such an orbit, a standardclock will tional shift of1.09 10;16=meter must be x runfast with respect to an identical one on the includedin any absolute measurement. Inclusion ground by 44,000nanoseconds per day! This effect of the effect in the NBS measurementsdoes result was first measuredwith the NTS-2 satellite carry- in smaller differencesin current international ing a cesiumatomic clock.54 The clocks must be comparisons. adjustedto run slow by that amount beforebeing placed in orbit in order to keep in synchroniza- tionwith atomic clocks on the earth's surface. Practical Applications Furthermore,periodic change in distance from the center of the earth for a satellite in a slightly elliptic orbit can lead to significant effects. GlobalTimekeeping Foran eccentricity of 0.005, thepeak to peak time difference will be 24 nanoseconds.This translates At thelevel of 0.1 microsecond,the relativ- into a rangeuncertainty of 24 feetwhich is very istic effects of clock transport by aircraft are significant in a systemwhose present design goal quite significant. ' Forexample, in the global is meters,and must be included in the system measurementsinvolving trips to Christ Church, New 10 operation. Zealandfrom Washington, D.C. andback, the relativistic time differenceproduced was 2.120 nano- The factthat standard clock rates are con- seconds. It is interestingto give a breakdownof stant at mean sea level on the ellipsoidal surface the calculated relativistic effect for each leg: of thespinning earth as discussed earlier allows theestablishment of a coordinate time for the Washington to California: +29 ns GlobalPositioning System which can be made the same asUniversal Timeon the surface of the earth. Californiato Hawaii : +31 ns Thestandard atomic clocks in orbit will keepthis GPS time when they are offset by the ~44,000 nslday Hawaii to New Zealand : +52 ns E* l discussedabove and corrected for the relativistic effectsof the elliptic orbit. Stationary standard New Zealandto Hawaii : +l6 ns W-tE clockson the ground must have their rates compen- } sated,depending on their distance above or below Hawaii to Washington : - 6 ns the mean ocean surface ellipsoid by * 1.09 x per meter in order to keep GPS coordinate time. The asymmetrybetween EN and W+E is veryapparent. It is clearthat even for short flights, the ef- Significance fects are importantat the ten's of nanoseconds level. The U.S. NavalObservatory is now usingan Thetwo applicationsdiscussed briefly above algorithm to estimate these effects for its trans- are among thefirst non-scientific uses of Einstein-

28 ian Time. Thatthe remarkable behavior of clocks c 2 c2c2 as predicted byGeneral Relativity is now required X= -(k -1)T 2 T-T)= -(k2 tobe included in practical applications is anin- tellectual milestone, made possible by theextra- andthe time of this reception event by B accord- ordinary stability of modern atomicclocks. ing to A is

t= - (T + k 2 T) = -1 (k2 + 1) T 2

2 2 The velocity v = x/t = c (k - l)/(k + 1)and Referencesand Notes theresult in the text followsby solving for k.

7.The distancescorresponding to the units on the 1. Quoted inHilbert, by ConstanceReid. Published time andspace axes are determined by plotting by Springer-Verlag: New York,Heidelberg, Berlin, branches ofthe rectangular hyperbolae 1970,page 105. t2-x2=,1 2.Martin Klein, "Einstein and the Academic Estab- lishment,"inEinstein, 4 Centenary Volume, withrespect tothe light cone as shown inthe edited by A.P. French,Harvard University following diagram: Press,Cambridge, Massachusetts, 1979, page 209.(Figure 6 is takenfrom this essay)

3. AlbertEinstein, "On Education"in Out of My Later Years, New York Philosophical Library, 1950.Reprinted in the commemorative volume citedin reference 2, page 315.

4. BaneshHoffmann, AlbertEinstein, Creator and Rebel. The VikingPress, New York,1972. Paperbackedition, New AmericanLibrary, New York,London, and Scarborough, Ontario, 1973. / 5. Hermann Bondi,Relativity and Cormnon Sense, / 4 / \ New Approach Einstein, Anchor Book Science StudySeries, Doubleday and Company, Inc., GardenCity, New York,1964. Intersectionof the time andspace axes foran 6. Consider6. thefollowing spacetime diagram inertialin observer yields thecalibration points. whichobserver B is moving with constant velocity v withrespect observerto A. 8. This is shown veryeasily with the"k-calculus" and thefollowing diagram

The spatialaxes have been suppressed. It is When B is at the same position as A, they set clear fromequations (1) and (2) inthe text theiridentical clocks to read 0. At time T that later A emits a lightpulse which is received by B at time kT and imediately transmitted tl = t - x/c tll = t' - x'/c back to A who receives it at time k(kT) = k2T sincethe Doppler stretching has operated twice By equations (1) and (Z), theposition of B as t3 = t + x/c t31 = t' + x'/c determined by A when B receives and reflects thepulse is

29 It is alsoclear from thedefinition ofthe conviction,could be only a differencein Dopplerfactor k, that thechoice of reference point. Judged fromthe magnet there certainly were no tl' = ktl electricfields; judged fromthe conducting circuitthere certainly was one.The existenceof an electric field was there- t = kt3' fore a relativeone, depending on the state 3 ofmotion of the coordinate system being used,and a kindof objective reality could These two equations may be written as begranted only to the electric and magnetic fieldtogether, quite apart from the state ofrelative motion of the observer or the coordinatesystem. The phenomenon ofthe electromagneticinduction forced me topost- t + x/c = k (t' x'/c) + ulatethe (special) relativity principle." Multiplyingthese equations together and multi- 10. P.G. Roll, R. Krotkov,and R.H. Dicke, "The plyingthe result by c2,one has the result Equivalenceof Inertial and Passive Gravitation- stated as equation(4) in the text. If one al Mass," Ann. Phys(U.S.A.) 442-517 (1964). solvesthis pair of simultaneous equations for s, t' and x'in terms of t andx, the Lorentz V.B. Braginskyand V.I. Panov,"Verification of transformation is obtained. theEquivalence of Inertial and Gravitational Mass," & 873-879 (1971). 9. New York Times, March 28,1972; page 32.The a.Eksp. x.G. a, English translation in Physics - firstpart of this excerpt is alsovery illumin- e. JETP Lett. 280-283 (1972). ating, so we reproduce it here: B, 11. C.F. Gauss,"Disquitiones Generales circa "Inthe development of special rela- SuperficiesCurvas," Gijttingen, 1827. There tivitytheory, a thought not pre- - hasjust appeared-a modern translation of viouslymentioned concerningFaraday's - "GeneralInvestigations of Curved Surfaces" in workon electromagnetic induction played Astgrisque62: "150 YearsAfter Gauss," by P. for me a leadingrole. Dombrowski, publishedby the Soci6t6 Math& Matiquede France, 1979. Accordingto Faraday, when a magnet is inrelative motion with respect to a 12. C.W. Misner, K.S. Thorne,and J.A. Wheeler, conductingcircuit, an electric current Gravitation, W.H. Freeman and Company, San is inducedin the latter. It is all Francisco,1973. Coverdrawing and page 4. the same whetherthe magnet moves or theconductor; only the relative mo- 13.Bertrand Russell, The ABC ofRelativity, Third tioncounts, according to the Maxwell- RevisedEdition, New York, New American Library Lorentztheory. However, thetheoret- MentorBook, 1959, page 80. (Original edition, icalinterpretation of the phenomenon 1925). inthese two cases is quitedifferent: 14. J. Evershed,Bulletin of the Kodaikanal Observ- If it is the magnet that moves, there atory, 36 (1914). exists in space a magneticfield that changeswith time and which, according 15. W. Pauli,Theory of Relativity. Pergamon Press; to Maxwell, generatesclosed lines of New York,London, Paris, LosAngeles. 1958, electricforce that is, a physically -- Page153. real electricfield; this electric field sets in motionmovable electric masses 16. J. Brault,Bulletin ofthe American Physical (that is, electrons)within the conduccor. Society, 8, page28 (1963). However, ifthe magnet is at rest and 17. F. Roddier,Annals of Astrophysics, 3, page theconducting circuit moves,no elec- 463(1965). tric field is generated;the current arisesin the conductor because the 18. J.L. Snider,Physical Review Letters,28, page electric bodies being carried along with 853(1972). theconductor experience an electro- motiveforce, as establishedhypotheti- 19.J.L. Greenstein, J.B. Oke, and H.L. Shipman, cally byLorentz, on account of their AstrophysicalJournal, page563 (1971). (mechanicallyenforced) motion relative 169, to themagnetic field. J.L. Greensteinand V. Trimble,Astrophysical Journal, p. 283 (1967). The thoughtthat one is dealinghere 149, with two fundamentallydifferent cases 20. A discussionof the problems involved is given was,for me, unbearable. difference The by S. Weinberg,Gravitation Cosmoloe;y, John betweenthese two casescould not be a 4 Wileyand Sons, Inc., New York,London, Sydney, realdifference, but rather, in my Toronto.1972. Pages 79ff.

30 21. H.E. Ives and G.R. Stilwell,"An Experimental 34. B. Rossi and D.B.Hall, "Variation of the Rate Studv of the Rate of a Moving Atomic Clock," of Mesotrons with Momentum," Physical Review, (I ad 11) Journal of the Optical Society of -59, page 223 (1941). America, 8, p. 215 (1938); 3, page 369 (1941). 35. J.C. Hafele and R.E. Keating, Science,177, page 22. G. Otting, Physikalische Zeitschrift,40, page 166 and page 168 (1972). 681 (1939). 36. In addition to the main participants listed in 23. H.I. Mandelberg and L. Witten, Journal of the the text, the following people participated Optical Society of America,2, page 529 from the University of Maryland: J.P. Richard (1962). and D.G. Currie advised on some technical ques- tions; F. Meraldi mounted the corner reflectors; 24. J.J. Snyder and J.L.Hall, Laser Spectroscopy, and J.J. Giganti and J. Mathews did some elec- Proceedings of the Second International Confer- tronic design and construction. ence, 23-27 June, 1975,K&g&ve, France, Springer-Verlag: Berlin, Heidelberg,New York, A detailed account of the measurements is con- 1975. Page 6. tained in two University of Maryland Ph.D. dis- sertations: 25. S. N. Bagayev and V.P. Chebotayev, Pis 'ma Zh. Eksp. i Teor. Fiz.,16, page 614 (1972). R. E. Williams, "A Direct Measurement of the Relativistic Effectsof Gravitational Potential on the Rates of Atomic Clocks Flown in an Air- 26. R.V. Pound and G.A. Rebka, Physical Review Letters, 2, page 439 (1959); 6, page 337 craft," (May, 1976). (1960). R. A. Reisse, "The Effect of Gravitational Potential on Atomic Clocks as Observed with a 27 I R.V. Pound and J.L. Snider, Physical Review Laser Pulse Time Transfer System," (May, 1976). Letters, 13, page 539 (1964); Physical Review 13, 140, page 788 (1965). See also R.V. Pound, The work has also been describedin talks at "Terrestrial Measurementsof the Gravitational Red Shift," in Albert Einstein's Theory of meetings and symposia, including: Precise Time General Relativity, edited byG. Tauber, Crown and Time Interval Meeting, Goddard Space Flight Center, December, 1976; 30th Frequency Control Publishers, Inc., New York, 1979. Pages 132ff. Symposium, Atlantic City, June, 1976 (During Round Table Discussion on Remote Time Compari- 28. H.J. Hay, J.P. Schiffer, T.E. Cranshaw, and son); Second Symposiumon Frequency Standards P.A. Egelstaff, "Measurement of the Red Shift and Metrology, Copper Mountain, Colorado, July, in an Accelerated System Using Wssbauer the 1976; Meeting of Commission 31 (Time) at the Effect in Fe," Physical Review Letters,4, XVI General Assembly of the International Astro- page 165 (1960). nomical Union, Grenoble, France, August, 1976; Meeting on Experimental Gravitation, Sponsored 29 W. Kiindig, "Measurement of the Transverse by the Accademia Nazionale dei Lincei, Pavia, Doppler Effect in an Accelerated System," Italy, September,1976; Symposium on Time and Physical Review,129, page 2371 (1963). Frequency at the 19th General Assembly of the International Union of Radio Science, Helsinki, 30. K.C. Turner and H.A. Hill, "New Experimental Finland, August, 1978. Limit on Velocity Dependent Interactions of Clocks and Distant Matter," Physical ReviewB, 37. The support of theU.S. Navy has come from many page 134 (1964). organizations in addition to theU.S. Naval Ob- servatory, includingits Directors Kai Strand 31. J.B. Thomas, "Reformulation of the Relativistic Conversion Between Coordinate Time and Atomic and Gart Westerhout. These include: Time,'' Astronomical Journal, 80, No. 5, p. 405 The Naval Materiel Command (1975) . James Probus, Director of Navy Laboratories Norris Keeler, Directorof Navy Technology 32. A.J. Greenberg, D.S. Ayres, A.M. Conunach, R.W. The Office of Naval Research Kenny, D.O. Cadwell, V.B. Elings, W.P. Hesse, John Dardis, Project Monitor and K.J. Morrison, "Charged Pion Lifetime and Doran Padgett, Project Monitor a Limit on a Fundamental Length," Physical William Condell, Physics Branch Chief Review Letters, page 1267 (1969). 3, Fred Quelle, Boston Office The Naval Air Development Center 33. F.J.M. Farley, J. Bailey andE. Picasso, "Ex- Kenneth Lobb, Technical Director Theory perimental Verificationsof the Special RichardRonald Vaughn Sheklin)Navigation Laboratory of Relativity,'' Nature, 217, page17 (1968). Patuxent Naval Air Test Center Robert Merritts, Project Engineer (He worked night and day along with the principal participants and contributed much to the success of the experiments). Pilots, Flight Engineers, Crew Chiefs, and Airmen for P3C-912.

31 FrankDesrosier, Jerome Mass6, Ernest Grossen- 38.The modifications were carried out at Maryland bacher, Wade Hay, Ben Scesa, Dan Koch, Karl with R. Hyattand Bourdetof Hewlett-Packard J. Harzerand Edward Gorsky. assisting L.S. Cutlerand the Maryland group. 39. Frequentassistance in maintenance was provided 45. B. Hoffmann, "Noon - Midnight Red Shift," by D. Kaufman and J. Soucyof the Goddard Space Physical Review, 121, page 337 (1961). FlightCenter. 46. R.U. Sexl,"Seasonal Differences Between Clock 40. We areindebted to Ernst Jechert and Hans Rates," PhysicsLetters, e,page 65 (1976). Baduraof Efratom for the loan of these standards. 47. W.H. Cannon and O.G. Jensen,"Terrestrial Time- keepingand General Relativity: A New Discov- 41. The developmentof this experiment is described ery,"Science, 188, page317 (1975). The errors by C.O. AlleyinAdventures Experimental in this paper have been pointed out in many Physics,Alpha, 1972. Edited by B. Maglich. letters in a subsequentissue of Science: Themajor scientific result of thelunar laser "Accelerationand Clocks," Science, 191, pages rangingexperiment is a test ofthe Principle 489-491(1976). The authorshave retracted of Equivalencefor massive bodies (Earth and theirclaims. Moon bothfalling to the sun): J.G. Williams, R.H. Dicke, P.L. Bender, C.O. Alley, W.E. 48. R.U. Sexl,private communication, August, 1977. Carter, D.G. Currie, D.H. Eckhardt, J.E. Faller, W.M. Kaula, J.D. Mulholland, H.H. Plotkin, S.K. 49. R.F.C. Vessotand M.W. Levine,Gravitazione Poultney, P.J. Shelus, E.C. Silverberg, W.S. Sperimentale,Accademia Nazionale dei Lincei, Sinclair, M.A. Slade,and D.T. Wilkinson, Rome, page371 (1977). Physical Review Letters, 36,page 551 (1976). 59. R.F.C. Vessot,presented at SecondMarcel 42. We areindebted to Dr. Frank Hoge of the Grossmann Meeting on RecentDevelopments in WallopsCenter of NASA forthe loan of this GeneralRelativity, Trieste, Italy, July, 1979. telescope. 51. L. Briatoreand S. Leschiutta,"Evidence for 43. The Air Forceorganizations providing support the Earth Gravitational Shift bvDirect Atomic- included : Time-ScaleComparison," I1 Nuovo Cimento, 3% The Air ForceSystems Command No. 2 (1977). Maj. Gen. G. Hendricks,Director of Labora- tories 52. S. Iijima and K. Fujiwara, "An Experimentfor Dr. BernardKulp, Chief Scientist thePotential Blue Shift at the Norikura Corona The Air ForceOffice of ScientificResearch Station," Annals of the Tokyo Astronomical e- MajorRichard Gullickson, Project Monitor servatory,Second Series, Volume XVII, Number Col. R. Detwiler,Physics Branch Chief Z, (1978). 4950th Test Wing, WrightPatterson Air Force 53.The NAVSTAR/Global PositioningSystem is fully Base Lt.Steve Stratton, Test Director (He described by seventeen articles in the GPS worked closelywith the major participants, specialissue of Navigation,Journal of the contributing much tothe success of the Institute of Navigation, Vol. 25, No. 2, Summer, measurements). 1978. Col.William Odgers. Comanner 54. T. McCaskill, J. White, S. Stebbins,and J. InstrumentationBranch Buisson, "NTS-2 FrequencyStability Results,'' ModificationCenter Proceedingsof the 32nd FrequencyControl Sym- Pilots,Navigators, Flight Engineer, Load- posium,1978. masters, Crew Chiefs,and Airmen forc141 -- 779. 44. The entire Mechanical DevelopmentDesign group andmachine shop personnel of the Department ofPhysics and Astronomy of the University of Marylandperformed in anoutstanding manner to accomplishthe reconfiguration of the equipment tovery exacting Air Forcerequirements in the short time availablebetween the author- ization ofthe project in early April and the beginningof the experiments in late May. The following people deserve special recognition:

1 ,B;Lher.tLinstein..in his...study. in Berlin,

32 .. i . ?

,2. Herblock drawing in the Washington Post after 3. The earliest known picture of Einstein F age around Einstein%death in 1955. 5 years,

4,. Einstein in elementaryschool in Munich atthe age 5. Einstein at the age of 14, of l0 (Secondfrom right, first row).

6. The classroom of Dr. JostWinteler in Aarau. 7. Einsteinas a student at the ETH in Zurich, Einstein at age 16 is at right. -

8, Einstein at hi? desk in the Swiss Patent office in_ 9: Einsteinin a playful mood at the CaliforniaLnsti- Bern at age 26, tute of Technology in the early 1930%. 33 11, Navy P3C Orion Aircraft 912 used inthe experiments,

12,. Clock Box installed on aircraft. 13.Electronic racks installed on aircraft.

14. ODtical cornerreflector on theaircraft of the type 15. Housing of photo-multiplierfor detection of laser uked for the Apollo Lunar. Laser Ranging Retro-Reflec-7-Tght pulses on theaircraft, tors,

17. Ground computer system,event timer Ind strip Box in 16. Clock trailer on ground. chartmonitoring displays in traile (R.E. Williams, left and R.A. Reisse), 34 18. Two hydrogen masers made byHarry Peters on loan 19. Aircraft onground near trailer containing fromthe Goddard Space FlightCenter. atomicclocks and van containinglaser equipr men t .

20. Clock Box being removed from trailer. 21. Narrow hatch of aircraft.

22. Laser Beam directing and receiving optics. 23. Laserequipment and receivingoptics in van.

Landing lights of plane on TV display during 24. Closed circuit TV display with coarse and fine 25. joysticks for aircraft tracking. tracking. 35 27. Chesapeake Test Range.

28. Ground trackingantenna at the Chesapeake Test 29, L.S. Cutleradjusting ensemble of modified Ranae. Hewlett-Packard 5061A atomicclocks.

31.Clock inserted in its magnetic shield,. 30. Interior of Clock Box.

32. Air flow hoses for controllingtemperatures and -33. .Lid carrying Efratom rubidium atomic clocks removing heat from clocks. and voltage and pressure regulation equipment, 36 34\ Polar photograph of globe showing distances of 35. Airborne equipmentbeing reconfiguredfor C141 Washtngton and Tfiulefrom the Earth's spin axisb. cargo pallet(Front View).

36. Airborne equipmentbein reconfiguredfor C14 1 37. Airborne equipment on cargo pallet housed in cargo pal let (Back Viewy (Technician Lyndon Smal 1 pre-fabricatedgarage of Andrews Air Force at left). Base.

38, Air Force C141 Starlifter Aircraft 779 at 39. Tail of C341 with petal doors throughzhich Andrews Air force Base next to garage, trailer 3 equipment was loaded, and van. w*e,m--*

- - 40,Preparing to transfer equipment from garage. 41,Front lift carrying pal let to aircraft,

37 42! Petal door open receiveto pallet: 43. Matching of palletaircraftto roller tracks.

44: ~olltngpallet to forward part of aircraft, 45, Len Cutlerbeside installed pallet on aircraft.

46. Clock Box AsseTbly during flight. (Seen from 47. Clock Box Assembly during flight, (Seen from rear nf alanel. front of plane),

48, Recording and readout equipment forinertial 49. Preparing to placeaircraft in hangar at the navigationunits and altimeters, Base,Force Air Thule 38 50. A C141 at Thule just before midnight onJune 25. 51. Midnight shadows cast by sun atThule on 25.

52. Globe tilted at 23$5 showing relation between 53. C141 779 on ground atChrist Church surrounded Washington and Christ Church at time of SUmmer bysupport equipment. solstice (Sun to right).

~. ,*- 54. Zerobeat during ascent of hydrogen maseron 55. Environmentally packagedhydrogen maser ,to be rocketprobe, carried by Scout rocket beinq held by R, 'F, C,, Vessot (right) and M. Levine. REDSHIFT FREQUENCY RESIDUALS AND GRAVITATIONALPOTENTIAL VARIATION VS TIME

LXPZRlYEhT TIYE .HR/MNIGMT JUNE IS. l4?6

-57. Residuals during an earlystage of theanalysis 58. Artist's drawing of NAVSTAR/Global Positioning of the hydrogenmaser rocket probe data,. System,

59. Major segments of the NAVSTAR system,

39A