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Relativity and Clocks

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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 in the 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 ex- perience on the earth, the primary curvature is It is of particularsignificance that the ex- thatof &, notspace. A body falls,according traordinary stability ofmodern atomicclocks has to Einstein's view, not because of the Newtonian recentlyallowed the experimental Study and accur- forcepulling it tothe earth, but because of the ate measurement of these basic 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 synchronization using 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 the Herblock 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 from the 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 clock synchronization and navigational systems will us by 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 in elementary 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 the production of scientific results be- highschool dropout because of dissatisfaction causeof his concern with the corrupting influence with the 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 the Patent 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 introducing the 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 Einstein began 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 the tensor 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 ized in the subject and was a member of the faculty ofMaxwell's Theory of the electromagnetic field, ofmathematics at the same ETH in Zurich when which was notthen taught at the ETH). He passed Einstein was a member of the physics faculty there the few required examinations only with the help from1912 to 1914.Figure 9 shows Einsteinin a of his friend, 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 years of 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 Einstein could not obtain an academic position or clear way. Some of theremarks in the next sec- a permanentjob of any sort for about a yearand tions of this talk follow the approach ofHoffmann.
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