Macroscopic Rotors and Gravitational Effects

-Astronomical bodies have, i n the pas t , provided e s s e n t i a l l y t h e only macroscopic b a s i s f o r s t u d i e s of g r a v i t a t i o n by means of r o t a t i o n s . Now new technology provides the p o s s i b i l i t y t h a t laboratory r o t o r s may be made more p r e c i s e than astronomical ones. This a r t i c l e surveys t h e proper t i es of some of both types of r o t o r s and describes several laboratory experiments f o r t e s t s of General Re la t iv i ty . Introduction.-Except f o r astronomical bodies, we seldom think of p rec i s ion r o t o r s as too ls f o r studying grav i ta t ion . Three exceptions can be mentioned. 1 ) The Hughes-Drever experimentslr2 with p a r t i c l e s a s p rec i s ion r o t o r s took advantage of the priviledged s t a t u s of these r o t o r s a s n o n i n e r t i a l frames i n order t o t e s t f o r the poss ib le a n i s o t r o ~ y of space. 3,4 2) The Stanford Rela t iv i ty Gyroscope w i l l provide a t e s t of General R e l a t i v i t y predict ions of spin-orbi t and spin-spin coupling of the gyro t o the e a r t h ' s r o t a t i o n i n a s a t e l l i t e orbi t .5 Here the gyroscopic p roper t i es , not pure r o t a t i o n , a r e what is of i n t e r e s t . 3) ~ r e m e r e ~ 6 used the decay of a spinning r o t o r i n an experiment aimed a t t e s t i n g what i s now known t o be an inva l id theory7 of g r a v i t a t i o n a l rad ia t ion . This l a s t t e s t i s c l o s e s t i n experimental method t o those t o be discussed here, although these w i l l have rad ica l ly d i f f e r e n t ob jec t ives from t h a t one. The object ives of concern h e r e a r e , ins tead , mostly r e l a t e d t o a s e r i e s of Machian concepts which reach beyond Eins te in ' s General Re la t iv i ty . This includes t e s t s f o r changes i n t h e Newtonian g r a v i t a t i o n a l number, G, and the r e l a t e d question of spontaneous, cosmological matter creat ion. We a l s o w i l l d iscuss a t e s t f o r non-metric r e l a t i v i t y . The temporal and s p a t i a l sca les of these '%lachian" phenomena a r e huge, and Earthbound schemes must use u l t r a p rec i s ion t o cope with the narrow spans ava i l able t o us l o c a l l y . The f i r s t two p a r t s of t h i s a r t i c l e w i l l consider such a question, and discuss i n what ways i t makes any sense t o compete i n the ' l abora tory aga ins t t h e reaches of astronomy. In succeeding s e c t i o n s we w i l l descr ibe th ree experiments which use prec i s ion laboratory r o t o r s t o measure g r a v i t a t i o n a l effects--two of them i n progress. Astronomical and Laboratory R o t o r s . ~ i c k e ~ , and subsequently ~ u l l e r ~ , have used ancient observations of ec l ipses , e t c . to provide a long temporal base l ine f o r measuring the t i d a l d e f i c i t i n the secu la r decay of the lunar o r b i t a l motion a s a possible means of est imating 6. Prec i s ion of t h e e a r t h ' s r o t a t i o n a l and o r b i t a l motion is of much concern i n the time-keeping asDects of such ca lcu la t ions . Van ~1andern lO has used lunar occu l ta t ions is combination with atomic-clock timing of t h e secu la r decay of the lunar o r b i t f o r t h e same reason. This does not involve considerat ions of p rec i s ion of r o t a t i o n a l m o t i o n , bu t i t does i n d i c a t e the d i r e c t i o n i n which modern s tud ies of such e f f e c t s a r e going. A p a r t i c u l a r example is t h e way t h e prec i s ion of t h e atomic clock makes up f o r t h e s h o r t temporal basel ine ava i lab le i n t h e time span s ince i t s invent ion and use. In add i t ion , these Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981849 C8-430 JOURNAL DE PHYSIQUE experiments exp lo i t the new way of considering ~ i r a c ' s l ~ ideas about changing G . In p a r t i c u l a r , h i s use of two metr ics , atomic and cosmological, make comparison of the clock time and lunar o r b i t time (corrected f o r t i d a l e f f e c t s ) a d i r e c t t e s t of t h i s version of predict ions f o r changing G. Reference 13 l i s ts a number of o ther such t e s t s , t h e b a s i s of which w i l l be discussed i n the following sec t ion . Although even galaxy c lus te rs14 have been involved i n considerat ions of 6, we w i l l use the e a r t h a s a more tang ib le p rec i s ion spher ica l r o t o r f o r comparison with a laboratory r o t o r (of 5 cm rad ius ) . Table I l i s ts some of the per t inen t mechanical p roper t i es of these two ro tors . Table I. Mechanical p roper t i es of astronomical and laboratory r o t o r s of i n t e r e s t . Property Earth Laboratory Rotor Radius (cm) 6.4 x lo8 5 Density (gmlcmL) 5.5 8 Surrounding atmosphere* a ) Gas densi ty lo2-lo3 1 .9 x 10 10 (molecules/cm3) ( a t 10-8 Torr) b) Temperature (OK) l o 3 3 Momenta of i n e r t i a -A We a r b i t r a r i l y choose a point 500 km above the ea r th ' s sur face . For purposes of gas drag i l l u s t r a t i o n t h i s rough choice w i l l be adequate and i n f a c t the not ion of ordinary gas drag i s q u i t e crude i n t h i s case. The behavior of these ob jec t s re levan t t o p rec i s ion r o t a t i o n s i s t h a t concerned with t h e i r secu la r spindown and t h e i r f luc tua t ions . The secu la r p a r t is assumed t o be exponential. That i s , the angular ve loc i ty i s where T* i s a time constant containing a l l forms of drags, Here I is the r o t o r moment of i n e r t i a and a is an e f f e c t i v e o v e r a l l drag coef f i c i e n t , a s i n the following d i f f e r e n t i a l equation of a "free" r o t o r , For present purposes we can take a t o be composed of two p a r t s , t h e gas drag ag and t h e bearing drag, ab. In the case of an astronomical body the "bearing drag" w i l l cons i s t of nonconservative e f f e c t s i n coupling t o other bodies. For the e a r t h t h i s i s primari ly t i d a l coupling t o t h e moon and sun. Other dis turbances lead t o both secu la r and f l u c t u a t i o n a l v a r i a t i o n s i n r o t o r motions. The "ponderomotive e f f e c t " discussed by ~ r a g i n s k y l s i s one such Figure 1. Cylindrical laboratory t e s t r o t o r i n suspension. Actual ro tors a r e of Zerodur glass-ceramic u l t r a high s t a b i l i t y mater ial . Typical r o t o r mass = 250 g, moment of i n e r t i a = 1100 g-cm2. mechanism. The d i f f e r e n t i a l heat ing of a r o t o r i n a uniform unid i rec t iona l f l u x of electromagnetic rad ia t ion ( t h e sun) l eads t o an increase i n angular ve loc i ty . (This i s l i s t e d a s a negat ive time constant i n Table 11, below.) Fluctuat ions i n r o t o r angular ve loc i ty ac tua l ly occur a s a spectrum. For purposes here, we l i s t only f luc tua t ions a t the fundamental r o t a t i o n a l frequency f o r t h e ea r th : t h e length of day (lod) variation.16 Table I1 lists t h e r o t a t i o n a l p roper t i es of the e a r t h and laboratory r o t o r s . In t h e l a t t e r case, small spheresl7.18, 1 t o 3 mm diameter, a t high speeds, l o 4 t o l o 5 Hz , a r e used f o r comparison although experiments t o be discussed i n following sec t ions use longer, slower ro tors . Earth ro ta f ions a c t u a l l y serve a s poor measurements f o r modern g r a v i t a t i o n a l questions. For G, the e a r t h r o t a t i o n s a r e used only i n d i r e c t l y , a s measurements of secu la r lunar o r b i t a l decay. The l a r g e observed f luctuat ions16 and varying secu la r decay17 of the e a r t h ' s r o t a t i o n i n t e r f e r e g rea t ly with the use of such data . As f o r d i r e c t measurement of 6, t h e ea r th ro ta t ions would be i n e f f i c i e n t . The e a r t h a c t s as 10 t o 17% of a r i g i d r 0 t o r ~ 0 . 2 ~ . That is, i t ' s moment of i n e r t i a would r e a c t t o G only 10 t o 17% a s much a s an aggregate of f r e e l y o r b i t i n g bodies, because although i t is g r a v i t a t i o n a l l y bound, i t s bulk compressibi l i ty is dominated by e l e c t r i c a l forces of repulsion. Calculations of t h e gas drag depend on the r e l a t i o n v e r i f i e d by ~eams",