IL NUOVO CIMENTO

VOL. 37 B, N. 2

11 Febbraio 1977

Evidence for the Earth Gravitational Shift by Direct Atomic-Time-Scale Comparison ('). •.

BRIATORE

l s t i t ~ t o d i F i s i e a Generale dell' U n i v e r s i ~ - T o r i n o L a b o r a t o r i o d i C o s m o g e o ] i s i c a del C N R - T o r i n o

S. LESCm~TTA l s t i t u t o E l e t t r o t e c n i e o ~ a z i o n a l e ~ Galileo F e r r a r i s ~ - T o r i n o

(rieevuto il 14 Luglio 1976)

Summary. - - On the basis of the height difference between the CNR cosmic-ray laboratory at Plateau Rosa, 3500 m, and Turin, 250 m above s.l., a direct measurement of the terrestrial gravitational shift has been made b y the comparison of the time scales of two cesium beam atomic frequency standards of the Istituto Elettrotecnico Nazionale ~ Galileo Ferraris ~. The principle of equivalence predicts the effect A t / t = - - A U/o 2 = = 3.54.10 -1~, corresponding to the gain of the standard at m o u n t a i n altitudes &~/t = 30.6 ns/d. The results A t / t = (33.84-6.8) ns]d and A t / t = = ( 3 6 . 5 i 5 . 8 ) n s / d , derived with two independent operating criteria, have been obtained from 1584 h of actual measurement, with reference to an atomic time scale whose linearity was continuously and carefully tested. The results are discussed in terms of the current gravitational theories and in view of future experimental researches, which will be permitted by the advancements of the metrology of time.

:l.

-

Introduction.

W e a l r e a d y p o i n t e d o u t t h a t t h e r e c e n t a d v a n c e m e n t s of t h e m e t r o l o g y of t i m e , b o t h as p h y s i c a l c h a r a c t e r i s t i c s a n d i m p r o v e d t e c h n o l o g i c a l p e r f o r m a n c e s of t h e s t a n d a r d s , p e r m i t , a t l e a s t i n t h e l i m i t s of t h e m e a s u r e m e n t (*) To speed up publication, the authors of this paper have agreed to not receive the proofs the correction. 219

220

L. B R I A T O ~ E

and

s. L E S C H I U T T A

precision, direct verifications of the g r a v i t a t i o n a l terrestrial shift, discussing t h e effects of E a r t h ' s r o t a t i o n a n d flattening b y the comparison between i n d e p e n d e n t local a t o m i c t i m e scales (,). N o w we present the results of our m e a s u r e m e n t s of t h e a l t i t u d e effect carried out on the basis of t h e height difference between t h e CNR cosmic-ray l a b o r a t o r y at P l a t e a u Rosa, 3500 m, a n d Turin, 250 m a b o v e s.l., for which t h e equivalence principle predicts the relative t i m e v a r i a t i o n -- A U / e z ~ At]t = 3.54.10 -18, corresponding to t h e gain Atfl = 30.6 ns/d of t h e clock a t m o u n t a i n altitudes. The m e a s u r e m e n t s h a v e been p e r f o r m e d b y t a k i n g u n d e r careful scrutiny the comparison between t h e proper t i m e scales of t w o cesium b e a m atomic f r e q u e n c y s t a n d a r d s of t h e I s t i t u t o Electrotecnico Nazionale (, Galileo Ferraris ~, Turin, n a m e l y I E N 4, constituting the reference scale in Turin, a n d I E I ~ 6, o p e r a t i n g as the t e s t s t a n d a r d a t P l a t e a u Rosa, for a n overall altitude actual m e a s u r e m e n t of 1584 h. After the experiment, the possibility of a f r e q u e n c y v a r i a t i o n due to m e c h a n ical stresses, not negligible a priori as a consequence of the e x t e r n a l - p r e s s u r e v a r i a t i o n on some delicate p a r t of the i n s t r u m e n t , was also checked in a special b a r o m e t r i c c h a m b e r . The ]inearity of the reference scale k e p t in Turin and its confidence level h a v e t h e n been a n a l y s e d with reference to the I n t e r national Atomic Time scale (TAI), as k e p t b y the B u r e a u I n t e r n a t i o n a l de l ' H e u r e ( B I H ) , Paris. U n f o r t u n a t e l y , m a n y causes b e y o n d our control, as well as m a n y o p e r a t i n g procedures of the I E N t i m e m e t r o l o g y i n t e r n a t i o n a l links (for instance, the flying clock comparisons necessary in t h a t period in R o m e , Paris, Prague), forced us to insert this e x p e r i m e n t a m o n g various activities, imposing a dilatation of the m e a s u r e m e n t s over a r a t h e r long period. Moreover, one has to r e m a r k t h a t for the first t i m e such a direct comparison has b e e n realized over long periods, b y working with p a r t i c u l a r technical procedures and, in t h e ease of IE:N 6, b y operating in a hostile e n v i r o n m e n t b o t h for persons and i n s t r u m e n t s . :By the way, it can be observed t h a t the cesium b e a m s t a n d a r d s are less delicate t h a n expected, which is interesting if we look at the stresses of a possible space-borne use of t h e s e devices. The results so far o b t a i n e d will be discussed in t e r m s of the recent g r a v itational theories. I n this sense the present work, which is precisely a t e s t of the strong equivalence principle, e v e n if limited to a w e a k field as the terrestrial one, well inserts itself in t h e renewed activities for t e s t i n g the c u r r e n t g r a v itational theories. This m e a s u r e m e n t in p a r t i c u l a r can be r e g a r d e d as a first step t o w a r d m o r e significant e x p e r i m e n t s on the E a r t h a n d its surroundings, in the p l a n e t a r y s y s t e m a n d in the stronger field n e a r t h e Sun, u p to distances of t h e order R - - ~ ( 5 + 1 0 ) R o , p e r f o r m e d with similar technical procedures, though employing different f r e q u e n c y s t a n d a r d s or, better, m o r e s t a n d a r d s

(1) L. BRIATORE and S. L~SCHIU~TA: Lett. Nuovo Cimento, 15, 203 (1976), and a letter in press.

: E V I D E N C E F O R TH:E E A R T H G R A V I T A T I O N A L S t t I F T :ETC.

221

b a s e d u p o n various basic processes. The reason for this lies chiefly in the fact t h a t t h e r e is no c o n c e p t u a l a r g u m e n t , as well as no theoretical support, to t h i n k t h a t various t y p e s of f u n d a m e n t a l interactions m a y h a v e the same response to the same g r a v i t a t i o n a l field. We shall r e t u r n to this point later on, m e r e l y recalling here t h a t all t h e following considerations r e g a r d n o t h i n g else b u t the hyperfine structure level interactions of cesium atoms, n a m e l y a t y p i c a l low-energy electromagnetic interaction. The technical side of t h e e x p e r i m e n t is described in sect. 2; in sect. 3 the d a t a g a t h e r e d are discussed, a n d finally in sect. 4 some conclusions are presented.

2. - E x p e r i m e n t a l apparatus.

2"1. T h e e x p e r i m e n t a l method. - The e x p e r i m e n t a l a p p a r a t u s consisted of two identical sets of i n s t r u m e n t s , one assembled for P l a t e a u l~osa, t h e other pre-existing in Turin as a p a r t of the IE57 L a b o r a t o r y for F r e q u e n c y a n d T i m e metrology. The two groups of i n s t r u m e n t a t i o n are o p e r a t e d a u t o m a t i c a l l y , in the sense t h a t once a d a y the m e a s u r i n g e q u i p m e n t s are a c t i v a t e d , the measu r e m e n t s are p e r f o r m e d a n d a p r i n t - o u t is produced. As a c o m m o n t i m i n g m a r k used in the two locations, two kinds of pulses were considered~ t h e V H F television synchronization pulses a n d t h e emissions of a L o r a n - C chain, the latter being a hyperbolic navigation system. On these two kinds of pulses are b a s e d t h e m o s t precise t i m e c o m p a r i s o n m e t h o d s available t o d a y up to distances of t h e order of one t h o u s a n d kilometers. The t y p i c a l errors r a n g e b e t w e e n 20 a n d 200 ns, depending on the e x p e r i m e n t a l conditions; these figures are well d o c u m e n t e d in the l i t e r a t u r e (3). A p r e l i m i n a r y field s t r e n g t h m e a s u r e m e n t at P l a t e a u l~osa showed t h a t the b e t t e r Loran-C reception is t h a t of t h e E s t a r t i t station, Spain, whose emission at 100 K H z is p r e s e n t with a n electric field of 1.6 m V / m , t h o u g h with a w e a k superimposed interference. H o w e v e r , during t h e whole e x p e r i m e n t , t h e television V t t F pulses, e m i t t e d b y the :gt. E r e m o station, Turin, were m a i n l y used, so t h a t we shall describe only this p a r t of t h e a p p a r a t u s , the other h a v i n g b e e n in function sometimes just for overall checks, conceptually p e r f o r m e d in e x a c t l y the s a m e m a n n e r as the V t t F ones. The two t i m e comparison systems arc b a s e d on t h e d e t e r m i n a t i o n of t h e local arrival t i m e of a same pulse e m i t t e d f r o m a t r a n s m i t t i n g station. Provided the delays of p r o p a g a t i o n are known, t h e difference of the two times of arrival gives directly the t i m e difference b e t w e e n t h e two local clocks. I n our e x p e r i m e n t , as we shall see later, it is sufficient t h a t these delays r e m a i n con-

(3) G. ROV:E~A: Alta lXvequenza, 41, 822 (1972).

9.~

L. BRIATOR]~

and

s . LESOH~UTTA

s t a n t in time. This l a t t e r condition is f~lfilIed because line-of-sight or g r o u n d w a v e p r o p a g a t i o n s are considered whose dependence on a t m o s p h e r i c conditions can be in our case disregarded. 2"2. Per]ordnance and calibration o] the apparatus. - As a c o m m o n t i m i n g m a r k , one of the synchronization pulses of the T V emissions was a d o p t e d . Two series of pulses are used in each television signal to provide the so-called <(line ~ a n d ~(frame ~ synchronizations; a television n e t w o r k can be indeed considered as a high-precision t i m i n g system, in which, at times, some millions of receiving devices are m u t u a l l y synchronized with a precision b e t t e r t h a n 1 ~s, if we exclude the p r o p a g a t i o n delays b e t w e e n t h e various locations. This technique, first p r o p o s e d in Czechoslovakia (3), has found wide use for t i m e a n d f r e q u e n c y comparison. Since t h e m e t h o d is b a s e d on t h e t i m e differences r e a d in two or m o r e locations, no special r e q u i r e m e n t s are to be provided for t h e pulse. The f r e q u e n c y of the T V pulse generator, in fact, is n o t a s t a n d a r d a n d t h e UTC t i m e of generation of the pulse does not m a t t e r , p r o v i d e d t h a t the v e r y s a m e pulse is used b y all of the i n t e r c o m p a r i n g laboratories. To identify w i t h o u t a m b i g u i t y t h e w a n t e d signal, it is sufficient t h a t t h e difference between the clocks, before the m e a s u r e m e n t , be less t h a n a b o u t 10 ms, if as a t i m i n g m a r k one of t h e f r a m e synchronization pulses is chosen. The repetition r a t e of these pulses is 20 ms in E u r o p e a n d 16.667 m s in t h e USA. The a b o v e - m e n t i o n e d condition, t h a t t h e error between t h e clocks be less t h a n 10 ms, is easily achieved with o t h e r t i m i n g m6thods, such as t h e use of MF or H F s t a n d a r d t i m e emissions. I n our case (fig. 1) t h e c o m p a r i s o n s y s t e m s were a c t i v a t e d b y t h e clock-

L oro.n -C receiver

IEN 6

time

cesium beam st cLnclarc~

I

Y

master clock

switching

Ioo,oo,.

oro r m ,, t I

l

interval counter

orioter L

I

Tv

receiver

rI

identifier

I

Fig. 1. - Block diagram of the electronics of the apparatus at Plateau Rosa.

(s) j. TOLMAN, V. PTA~EK, A. SOU~.K and R. STECHER: IEEE Trans., IM 19, 247 (1967).

EVID]~NC]9 FOR T H E F,ARTH G R A V I T A T I O N A L S H I F T :ETC.

~9.~

p r o g r a m m e r , at t h e s a m e local time, for a period of two minutes. Since t h e counter is s t a r t e d b y t h e signal of t h e (~second ~) given b y the local clock a n d is s t o p p e d b y t h e first f r a m e pulse arriving at t h a t location a f t e r t h e beginning of t h e local second, 120 differences are printed. The resolution of t h e reading counters used in T u r i n a n d a t P l a t e a u R o s a were 0.1 ns a n d 10 ns, respectively. Again w i t h reference t o fig. 1, ~he video signal received b y a commerciM set is routed to a synchrodecoder (4), in which t h e chosen pulse is detected, a n d sent to t h e stop channel of t h e counter. The delays introduced b y t h e receiverdecoder s y s t e m are of t h e order of 50 ~s, with a fluctuation (la) of 100 ns. clock A

TVpuLse

origin

TV pu~se

arrival

OA

Location A time

r,

, |

! !

clock B

I~TV pulse

rigin

I

~TVpuLse j _1a rri va l _1

-r

il

location B time -----

Fig. 2. - Quantities involved in the measurement of T o. One set of 120 daily data was taken for each of the two locations. Moreover, direct measurements of Te were taken at the beginning and the end of the mountain altitude operation.

T h e quantities involved in t h e m e a s u r e m e n t are given in fig. 2. The t i m e difference b e t w e e n t h e two clocks To is given b y

(1)

To= T ~ - / ) ~ + Z ~ -

Ze+ De,

where Ta a n d Te are t h e readings in t h e locations A a n d B, D~ a n d De t h e i n s t r u m e n t a t i o n delays a n d Te~e----Tp~--TpB is t h e p r o p a g a t i o n delay of t h e T V signal b e t w e e n t h e two laboratories or t h e difference in p r o p a g a t i o n if p a r t of t h e p a t h is c o m m o n ; t h e positive sign holds if t h e signal arrives a t the location B before t h a n at A. I f t h e r a t e difference b e t w e e n t h e clocks is of concern, it is sufficient to r e p e a t the m e a s u r e m e n t of To periodically. Giving To in ns a n d t a k i n g t h e reading at the i n t e r v a l of one day, we h a v e

(~)

•

= (To1- ro,)/8.6~.1o18,

(4) A. RACCI~T: A l t a .F~'equenza, 39, 741 (1970).

224

L. B R I A T O R E

and

s.

LESCHIUTTA

where the suffixes 1 a n d 2 refer to measurements performed in consecutive days. Finally if, as in our case, it can be verified t h a t the i n s t r u m e n t a t i o n a n d propagation delays are sufficiently constant, eq. (2) reduces to

(3)

Av/v = (T,.~ + T ~ , - - T~a-- T,,)/8.64"1013 ,

i.e. the difference in rate is obtained b y using only the readings. As seen, the values of the instrumentation and propagation delays are not needed; nevertheless, the instrumentation delay and its variance were measured and their contribution to the error is estimated to be 30 ns ( l a value) for one set of data, i.e. for the 120 readings. Also the q u a n t i t y T p a . W a S measured b y using a portable atomic clock; on the day April 18, 1975, before the period in which the clock I E ~ 6 was to be k e p t at P l a t e a u Rosa, the following results were obtained:

UTC (IEN) -- I E N 6 = 34.59 ~s,

TpB-- Tea = 284.64 ~zs

and, consequently, Ta -- D a - - T~ + / ) 8 = 319.23 9 s .

After performing some preliminary trials to test the reliability of the measuring system u n d e r severe e n v i r o n m e n t a l conditions, the set-up has been checked b y inserting at P l a t e a u Rosa, in the place of the atomic clock I E N 6, a quartzcrystal oscillator Sulzer S 79, which operated, in two separate periods, for 45 d. n o significant physical result was t h e n measured, b y merely observing with high precision the drift a n d the absolute difference between the oscillator and the UTC reference scale in Turin; the procedure p e r m i t t e d to optimize the performance of the system particularly with regard to the reception efficiency even in the worst atmospheric conditions. A f u r t h e r inspection, aiming at adopting some final protective devices, has been successively performed b y inserting for a 20 d check period a F R T rubidium f r e q u e n c y standard. Then the proper measurement runs were initiated with I E N 6.

3. - D a t a a n a l y s i s and results.

The measurements were carried out over a 66 d period, from April 19 to J u n e 24, 1975. The daily difference of the quantities IE:N 6 -- T V at P l a t e a u Rosa and UTC (IEN 4 ) - TV in Turin, added over the whole period, gives a t o t a l increment ATo = (3259 + 50) ns, and the least-square fitting of the daily measurements gives for the difference in rates At/t ~ (47.9 • 3.7)ns/d.

EVIDENCE

FOR THE EARTH GRAVITATIONAL SHIFT ETC.

225

Moreover, a f t e r a technical delay of two days, I E I ~ 6 has been t r a n s p o r t e d on J u n e 26, 1975, in Turin, where i m m e d i a t e l y at t h e arrival the direct lect u r e of its intrinsic t i m e has been made. The result To----UTC (IEI~ 4 ) - -- I E N 6 = 31.149 ~s, c o m p a r e d with t h e previous reading T. ----34.590 ~s on April 18, gives AT. = 3441 ns over 68 days, or At/t = 50.6 us/d, in r a t h e r good a g r e e m e n t with t h e first i n d e p e n d e n t result. UTC (Bm) 2.2

I r163 UTC (IEN) reference

ar~vance

47.9 :t1:~,7 -

"'.1

~

Turin

operation at PLoLteo.u Rosa

I

~

Turin

Fig. 3. - Schematic drawing of the least-square-fitted relative behaviours of IEN 6, UTC (IEN) and UTC (BIH) for the periods concerned. The slopes are referred to UTC (IEN) and are given in ns/d.

NOW these quantities are to be c o m p a r e d with the difference in rates I E N 6 - - I E N 4, in Turin, before a n d a f t e r the d i s p l a c e m e n t of t h e t e s t clock a t P l a t e a u Rosa (fig. 3). The d a t a concerned are n o t y e t completely rigorous a n d univocal, since the weak, inevitable variations of the f r e q u e n c y of each s t a n d a r d cause the slope o b t a i n e d with t h e least-square fittings to v a r y weakly with the period chosen for the calculations. We decided at last to calculate these slopes o v e r periods of a b o u t 20 d, considering t h e following two simple r e m a r k s : i) the sum of the two periods before a n d a f t e r the m e a s u r e m e n t is of t h e s a m e order as the duration of the m e a s u r e m e n t proper, ii) these periods do not significantly differ f o r m t h e m e a n period indicated in t h e literature, on the basis of a long experience, in which the f r e q u e n c y of a cesium b e a m s t a n d a r d can be a s s u m e d to b e stable (5). I n this w a y we o b t a i n e d the values Atfl = ---- (15.3 4- 4.1) ns/d a n d At/t = (12.9 ! 4.6) ns/d for t h e 20 d periods preceding a n d following t h e m o u n t a i n operations, respectively. Since t h e y do not n o t a b l y differ, t a k i n g into account t h a t their difference corresponds to the relative f r e q u e n c y v a r i a t i o n Av/r.-~ 3-10 -14, a b o u t 1/10 of the concerned effect, we can simply refer to their m e a n value a n d assert t h a t , during t h e e x p e r i m e n t , I E I ~ 6

(s) J. E. LAVERY: -PRO0. P T T I , 4, 168 (I972). 15 -

II Nuovo Cimento B.

~

L. B R I A T O R E a n ~

S. L E S C H I U T T A

k e p t with respect to I E N 4 the m e a n s y s t e m a t i c gain, w i t h o u t e x t e r n a l effects, At/t = (14.1 • 5.2) ns/d. Then, as a first conclusion, we can say t h a t t h e difference in rates b e t w e e n t h e two s t a n d a r d s due to the g r a v i t a t i o n a l shift is included, b y t h e two i n d e p e n d e n t m e a s u r e m e n t criteria, between the m i n i m u m At/t = (33.8 =h 6.4) ns/d a n d the m a x i m u m At/t -~ (36.5 =~ 5.2) ns/d. There remains to discuss the confidence of the reference scale in Turin, which, up to now, has been a s s u m e d as absolutely uniform. The n o t a t i o n UTC ( I E N ) stands for universal co-ordinated t i m e as k e p t b y t h e I E E , and, in t h e period considered, UTC (IEN) was r e p r e s e n t e d b y the readings of the a t o m i c clock I E N 4. This s t a n d a r d is used for all t h e f r e q u e n c y a n d t i m e comparisons p e r f o r m e d in t h e l a b o r a t o r y and, in particular, with the B I H . The B I H p u b l i s h e s a m o n t h l y bulletin with t h e values of the differences UTC ( l E E ) - -- UTC ( B I t t ) for the d a y s whose J u l i a n n u m b e r ends with zero, t h a t is a value e v e r y decade. These figures are o b t a i n e d via Loran-C m e a s u r e m e n t s a n d are given with an u n c e r t a i n t y of 0.1 ~s. According to the procedures a d o p t e d b y the I E N , the r a t e s of the clocks are untouched, a n d consequently UTC (IEN) represents the best a p p r o x i m a t i o n of t h e definition of the S I second, available in Turin, a n d a n u m b e r of criteria is a d o p t e d in order to ensure, as far as possible, the u n i f o r m i t y of its rate. F o r the kind of analysis here p e r f o r m e d , since variations in rates are sought, t h e t r u e value of the UTC (IEN) r a t e does not m a t t e r , p r o v i d e d it r e m a i n s c o n s t a n t during t h e e x p e r i m e n t . This r a t e a n d its v a r i a t i o n can be o b t a i n e d b y m e a n s of the afore-said bulletins of the B I H ; for t h e period of interest, t h e result is UTC ( l E E ) - - U T C ( B I t t ) ----2.2 ns/d, a n d consequently the u n i f o r m i t y of t h e r a t e of the a d o p t e d reference is verified to be within 3 . 1 0 -14 . N o w let us t u r n to t h e afore-said b a r o m e t r i c check on the a p p a r a t u s . L e t Q1 a n d Qo, respectively, be t h e line a n d c a v i t y Q of the i n s t r u m e n t , a n d let us write Q ~-v0/8~o for the ratio of their o p e r a t i n g f r e q u e n c y to the intrinsic frequency width. I f a frequency shift Av~ due to e x t e r n a l causes a p p e a r s in the cavity, the v a r i a t i o n A~ of the e m i t t e d frequency could be estimated, at least in principle, as A~----(Qo/Q~)A~,~ for an active s t a n d a r d , a n d as Av = (Qr for a passive one (~). But, while in the first case t h e order of m a g n i t u d e of A ~ a n d its sign can be argued, in the second, which is t h a t concerned, it is m u c h more difficult. I t m u s t be observed t h a t , for a commercial passive standard, Q o ~ 104, Q ~ lO 8, t h e n Av ~ 10-~~ I n the p r e s e n t case it r e m a i n s to p r o v e t h a t Av~< 10 -8 H z due to possible pressure effects, in order to obtain a v a r i a t i o n Av g 10 -~3 ttz. To appreciate these figures, t h e f r e q u e n c y assigned to the hyperfine line used in cesium b e n m s t a n d a r d s is of 9192631770 Hz. To ensure t h e condition necessary in the m e a s u r e m e n t , the s t a n d a r d was placed in a special b a r o m e t r i c c h a m b e r in T u r i n a n d t h e r e m a i n t a i n e d in

(6)

H. H~LLWIG: s

6, 118 (1970).

~VIDENC~

F O R TH]5 E A R T H G R A V I T A T I O N A L S H I F T :ETC.

227

c u r r e n t o p e r a t i o n a t t h e m e a n pressure of P l a t e a u Rosa, 660 g]cm ~ of residual a t m o s p h e r e . These m e a s u r e m e n t s were performed, since no sufficient d a t a are available in t h e open literature on the b e h a v i o u r a t pressures corresponding to elevations of a few kilometers~ while some i n f o r m a t i o n is available for v e r y low pressures. On the s a m e occasion~ in order to be able to discriminate a m o n g t h e various sources of f r e q u e n c y instabilities due to pressure variations~ barometric tests were p e r f o r m e d on different devices~ since a cesium b e a m s t a n d a r d is composed, at least~ of a quartz c r y s t a l oscillator, an a t o m i c referent% a synthetizer, an electronic s e r v o s y s t e m a n d a n u m b e r of power supplies. The t h r e e last c o m p o n e n t s do n o t exhibit m a r k e d dependence on pressure; the v e r y slow effects can be t r a c e d to different h e a t t r a n s f e r characteristics. The quartz c r y s t a l s t a n d a r d s h a v e shown m a r k e d f r e q u e n c y variations during the changes in pressure, but, when the pressure was k e p t constant, t h e characteristic r a t e of each individual device was recovered. F o r r u b i d i u m gas cells a n d cesium b e a m s t a n d a r d s the s a m e b e h a v i o u r was observed, i.e. the transitions are sensed, while the r a t e existing before the pressure variations is usually recovered in a few hours a f t e r the v a r i a t i o n itself. The m a x i m u m difference in r a t e observed as a consequence of the pressure v a r i a t i o n corresponding to t h e elevation of 3250 m for cesium s t a n d a r d s is 2 ns/d. But, during the whole period of m o u n t a i n operations, t h e e n v i r o n m e n t a l conditions h a v e b e e n continuously m e a s u r e d , t h u s showing t h a t the m a x i m u m v a r i a t i o n s in pressure a n d t e m p e r a t u r e were comprised within ~p = ~ 10 m m H g a n d a T = ~= 6 ~ then, surely~ no significant error has b e e n i n t r o d u c e d b y the e n v i r o n m e n t a l conditions. I n conclu~ion~ the results previously quoted are to be considered as the definitive ones. I f we t a k e into account t h e m a x i m u m possible error which could h a v e been i n t r o d u c e d b y the reference scale in Turin, t h e y are set in t h e final f o r m

(At~t)1-~ (33.8 ~- 6.8) n s / d , (At/t)~ ---- (36.5 • 5.8) n s / d , where t h e suffixes 1 a n d 2 refer to t h e m e a s u r e m e n t s p e r f o r m e d as given b y eq. (3) a n d b y direct readings of the p r o p e r atomic t i m e of I E l q 6, respectively. The uncertainties given in b o t h cases chiefly reflect t h e errors m a d e in t h e e s t i m a t i o n of t h e rates befor% during a n d a f t e r t h e e x p e r i m e n t ; in t h e first a p p r o a c h , some contributions are e x p e c t e d f r o m t h e measuremen~ s y s t e m , while, in t h e second, t h e effects of t h e resolution of 0.1 ns of t h e counter used a n d those of the s h o r t - t e r m fluctuations of t h e clocks can be disregarded. These d a t a are to be c o m p a r e d w i t h t h e theoretical value At/t----gable2= 30.6 ns/d, if we t a k e into a c c o u n t t h a t the m e a s u r e m e n t s are practically a t the limits of t h e a c t u a l s t a t e of t h e art.

228

L. BRIATORE and s. LESCHIUTTA

4. - D i s c u s s i o n a n d c o n c l u s i o n s .

Since the early formulation of the general t h e o r y of relativity, EINSTEIN pointed up the possibility of its experimental verification (7), based on three effects: the deflection of light rays travelling near a b o d y of large mass, the precession of the perihelion of planets because of the slow m o v e m e n t of the orbit within its plane a n d the gravitational red-shift of spectral lines (beside other effects found later}. The t h e o r y h a d a striking success; the minute deviations from the classical laws of motion of the planets have been verified with the accuracy of a few percent (8); the measured deflection of light rays in the Sun field agrees with the t h e o r y within experimental errors of (15 --20) % (9) ; finally, the gravitational red-shift of spectral lines has been verified since the 20's for the Sun (lo), for Sirius B (~1) and other stars (1~) up to 5 % of error. Moreover, there are on a terrestrial scale the elegant experiment of P o u n d a n d R e b k a (13), carried out with an accuracy of 1 % of the predicted small fractional frequency shift, the flying-clock measurements of ttafele and K e a t i n g (14) a n d the present work. Once more, in conclusion, one can say t h a t on both terrestrial a n d astronomical scales there are no experimental data against the general-relativity

(7) A. EINSTEIN: Jahrb. Radioakt. n. Elektronik, 4, 441 (1907); Ann. d. Phys., 35, 898 (1911); S . B . Preuss. Akad. Wiss., 831 (1915); Ann. Phys. Lpz., 49, 760 (1916). (s) J. LENS]~ and H. THIRRING: Phys. Zeits., 19, 156 (1918); G. M. CLEMENC]~:Rev. Mod. Phys., 19, 361 (1947); Astron. Papers, 13-5, 367 (1964); J. J. GILVARY:Publ. Astron. Soe. Paci]ic, 65, 173 (1953); Phys. Rev., 89, 1046 (1953); Nature, 183, 666 (1959); L. LA PAz: Publ. Astron. Soe. Paci/ic, 66, 13 (1954); M. F. SUBBOTIN:Astron. ~urn., 33, 251 (1956); V. L. GINZBURG: 2Urn. Eksp. Teor. Fiz., 30, 213 (1956); Usp. Piz. Nank, 59, 11 (1956); 63, 119 (1957); Fortschr. Phys., 5, 16 (1957); W.A. BlCUMBERG: Bull. Inst. Teor. Astr., 6-10, 733 (1958); N. S. KALITZII~:NUOVO Cimento, 9, 365 (1958). (9) J. SOLDNER: Ann. Phys. Lpz., 65, 593 (1921); S. I. VAVILOV:Experimental Bases o] the Theory o] Relativity (Moscow, 1928); G. VAN BIESBROECK: Astron. Journ., 55, 49 (1950); 58, 57 (1953); P. P. PAlCENAGO: in Stellar Astronomy (Moscow, 1954); A. A. MIHAILOV: Astron. ~urn., 33, 912 (1956); G. W. SKROTZKY:Dokl. Akad. Nauk, 114, 73 (1957); H. V. KLAUBER: Vistas in Astronomy, 3, 147 (1960). (lo) A. PEROT: Compt. Rend., 171, 229 (1920); L. GR]~B~.: Phys. Zeits, 21, 662 (1920); Zeits. Phys., 4, 105 (1921); C.E. ST. JOHN: Astrophys. Journ., 67, 93 (1928); E. FREUNDLICH: Phys. Zeits., 16, 115 (1915); 20, 561 (1919); H. voN SE]~LIG]~R:Astr. Naehr., 202, 83 (1916); J. W. Bt~AUZT: Thesis (Princeton University, N.J., 1962; unpublished); Z. E. BLAMONTand F. RODDI]~R: Phys. Rev. Lctt., 7, 437 (1961); F. RODDIER: Ann. Astrophys., 28, 463 (1965); J. L. SNn)ER: Phys. Rev. Lett., 28, 853 (1972). (11) W. S. ADAMS: The Observatory, 48; Proc. Amer. Acad. Sei. (1925). (1~) Publ. Astron. Soe. Paci]ic, 33 (1937); V. G. FESSENKOV: Trans. Intern. Astron. Un., 8, 681 (1952). (13) R. V. POUND and G. A. REBKA jr.: Phys. Rev. Zett., 4, 337 (1960); R. V. POUND and J. L. SNIDER: Phys. Rev. Lett., 13, 539 (1964); Phys. Rev., 140, B 788 (1965). (14) j. C. HAFELE and R. E. KEATING: Science, 177, 166 (1972).

EVIDENCE

FOR THE

E A R T H G R A V I T A T I O N A L S H I F T F, TC.

229

theory. :Nevertheless, there is n o t even the possibility of a choice between the recent theories, metric and nonmetric, accepting or violating the equivalence principle. The principle often called of strong equivalence, b y which EII~STEII~ describe4 space-time in general relativity by a c o n t i n u u m in which the special t h e o r y locally holds, postulates t h a t all local, freely falling, n o n r o t a t i n g reference frames are equivalent for the performance of all physical experiments. The weak principle of equivalence describes only the proportionality between gravitational and inertial mass; it has been tested first b y the E6tv6s balance experiment (~), t h e n with a refined procedure b y ROLL a n d co-workers (16), a n d recently up to one p a r t in 10 ~ b y BI~AGII~SKYa n d PAYor (~7). B u t t h e r e is also a semi-strong equivalence principle, which can also be applied to general relativity, allowing a description of the Universe in which the so-called physical constants m a y v a r y at different times a n d in different positions. Gravitational-red-shift measurements can test nonmetric theories, particularly b y the comparison of the red-shift of different clocks at the same location in a gravitational field, provided t h e y are sensitive to second-order effects, looking for terms in (AU/c:) 2. I n fact, every metric t h e o r y which has the correct :Newtonian limit predicts the correct first-order red-shift, while some nonmetric theories predict a wrong first-order red-shift, even if t h e y can have correct :Newtonian limit. F u r t h e r m o r e , there are arguments indicating th~,t in the latter case every t h e o r y necessarily predicts a gra~dtational red shift depending on the nature of the clocks whose red-shift is being measured (~); conversely, the red-shift shows to be universal, independent of the natm-e of the clock, if a n d only if the gravitation is described b y a metric t h e o r y (~9). Direct experimental tests of these questions have been up to now difficult

(is) R. V. E6TV~)S, D. PEKAR and E. FEKETE: Ann. d. Phys., 68, 11 (1922). (16) p. Cx. ROLL, R. KROTKOVand R. H. DICKE: Ann. o]. Phys., 26, 442 (1964). (17) V. ]3. BRAGINSKYand V. I. PANOV: ~urn. Eksp. Teor. Fiz., 61, 875 (1971). (is) L. I. SCHIFF: Amer. Journ. Phys., 28, 340 (1960); A. SCHILD:in Evidence ]or Gravitational Theories, edited by C. MOLL]~R (New York, N.Y., 1962); R. H. DICK~: in Relativity, Groups and Topology (Now York, N. Y., 1963) ; H. Y. CHIu and W. F. HO~'~MA~N, editors, and R. H. DICK]~:in Gravitation and Relativity (New York, N. Y., 1964); K. S. THORNE and C. M. WILL: Astrophys. Journ., 163, 611 (1971); S. WEINgERG: Gravitation and Cosmology: Principles and Applications o] the General Theory o] Relativity (New York, N.Y., 1972). (19) For details see D. R. BRILL and J. WHEELER: Rev. Mod. Phys., 29, 465 (1957); L. I. SCHIFF: Amer. Journ. Phys., 28, 340 (1960); R. H. DICK]Z: Amer. Journ. Phys., 28, 344 (]960); J. N. BAHCALLand M. SCHMIDT: Phys. Rev. Lett., 18, 1294 {1967); K. S. THORI~E, C. M. WILL and W. T. NI: Theoretical Framework ]or Testing Relativistic Gravity (Pasadena, Cal., 1971); K. S. THORNE, D. L. LEE and A. P. LIGHTMAN: Phys. Rev. D, 7, 3563 (1973); A. P. LIGHTMAN and D. L. LEE: Phys. Rev. D, 8, 364 (1973); C. W. MISNER, K. S. THORNE and J. A. WHEELER: Gravitation (S. Francisco, Cat., 1973).

~0

L. BRIATORE

a n d s. L E S G H I U T T A

to perform and impossible for the second-order effect. ~Towadays, the situation is changing; the technology of space exploration a n d the great advances in time metrology permit high-precision measurements in locations in which red-shift effects reach vahtes suitable for observation. I t is sufficient to t h i n k of hydrogen-maser oscillators~ which allow comparison of frequency stability to better t h a n one p a r t in 10~4~ p r o b a b l y one p a r t in 10 ~5 in the near future, b y which interesting results can be obtained also on the E a r t h , in view of a global terrestrial timekeeping of b o t h f u n d a m e n t a l a n d practical value. B u t the most significant results will come from the space flight measurements in preparation. The Smithsonian Astrophysical Observatory has proposed to the N A S A an experiment to measure the effect of the E a r t h field on the rate of a hydrogen-maser oscillator system with an accuracy of 2.10-5~ b y a geocentric orbital flight of 3.5 I~ up to 18~ 350 km. A F r e n c h group is working on a satellite carrying clocks on an extremely excentric orbit; a E u r o p e a n collaboration group is working out the preliminary feasibility s t u d y of an interp l a n e t a r y vehicle carrying different clocks on a t r a j e c t o r y reaching J u p i t e r a n d then inserting in a solar orbit with the perihelion at a b o u t 4R o. No d o u b t t h a t next years will bring contributions to our knowledge of gravitation, a still mysterious f u n d a m e n t a l interaction. We hope t h a t experiments like t h a t described in this paper with t h e foreseable technical improvements in the stability of future frequency standards will give significant answers also on the E a r t h . $$$

The authors gratefully acknowledge the constant advice a n d useful suggestions of Profs. C. CASTAGNOL~ a n d A. FE•RO MXLONE. Thanks are due to Dr. P . G . GATZ,TANO a n d Mr. A. RO)~ERO for the P l a t e a u Rosa operation a n d to Mr. E. ANGEZOTTI for the measurements in Turin.

9

RIASSUNT0

0perando sul dislivello fra il laboratorio di fisica cosmica del CNR di Plateau Rosa, 3500 m, e Torino, 250 m s.m., si ~ ottcnuta la misurazionc diretta dello spostamento gravitazionale terrestre dal confronto delle scale temporali di due campioni atomici di frequenza al cesio dell'Istituto Elettroteonico Nazionale r Galileo Ferraris ~. I1 principio di equivalenza prevede t'effe~o At/t ~ - A U / c ~ - ~ 3.54-10 -I3, corrispond(~nte ali'auticipo At/t : 30.6 ns/d dcl campione in qtlo~a. Da 1584 h di misura effettiva e con due metodi operativi indipendenti sono stati ottenuti i risultati At]t= (33.8~=6.8)ns/d c A t [ t = : (36.5• ns/d, con riferimento a una scala di tempo atomico continuamente controllata. Si discutono i risultati nel contesto dellc attuali teorie della gravitazionc e in vista di futuri avaazamenti deLla metrologia del tempo.

]~VIDENC]~ FOR THE EARTH GRAVITATIONAL SHIFT ETC.

231

IIO~TBep}K,~eHHe 3eMHOrO r p a B w r a u n o H H o r o c ~ s n r a C IIOMOIE[IbIO npstM0rO cpaBHeHm~ MaCttlTa60B aTOMHI,IX BpeMeH.

Pe3mMe ( * ) . - Ha OSHOBe BbICOTItO~ pa3HOCTI~ M e ~ y na6opaTopHflMH KOCMHqCCKHX Hy~e~ HatmOHaHbHOrO I~eHTpa I/ICCHC~OBamtI~ Ha IIHaTO Po3a, 3500 M, r I B TypnHe, 250 M Ha~ ypOBHCM MOpg, 6blHO rtpoBe~eHo rtpnMoe n3MepcHne 3eMHoro rpaBnTaUI4OnHOrO C~BHra, IIOCpC~CTBOM c p a B H e n n ~ BpcMeHHI~IX IHKaJI ~ByX CTaH~apTOB ~IaCTOT aTOMOB

ue3~ut HatmoHazmHoro I/IHCTHTyTa~)HeKTpOHtIKH<>. IIp~nunn arBnaaHerrrnocTn rrpe~xcraabtaaeT Bennqi~Hy At/t~ --AU/e~'= 3.54.10 -la, COOTBeTCTByIO~ npHpameHmo CTaH~apTa Ha BI~ICOTaX At/t~ 30.6 ns/d. C noMombro ~syx He3aBl~Cmar~ix xpnTepneB B Teqerme 1584 ~ naMepeHnl~ nOHyqeHbI cyte~ymmHe pe3y~rbTaTT,I At/t= (33.8d:6.8) ns/d rI At/t~ (36.5 :k5.8) ns/d. IIoHyqerim,te pe3yHbTaTbI o6cy:acdlaIoTc~t B TepMm~ax cy~eCTBy~OmHXrpaB~TaImOHrrblX Teoprrfi ~ n CBH3HC 6y]lynIHMr~ 3KcnepHMeHTanb~IM~ HOHCKaM~i,KOTOp]bIe 6ygyT CIIOCO~CTBOBaTbnporpeccy MeTpOJ~OrHH BpeMergA. (*)

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