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MACROSCOPIC ROTORS AND GRAVITATIONAL EFFECTS
R. Ritter
To cite this version:
R. Ritter. MACROSCOPIC ROTORS AND GRAVITATIONAL EFFECTS. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-429-C8-440. �10.1051/jphyscol:1981849�. �jpa-00221745�
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CoZZoque C8, suppZ6ment au n012, Tome 42, dgcembre 1981 page C8-429
MACROSCOPIC ROTORS AND GRAVITATIONAL EFFECTS
R.C. R i t t e r
Department o f Physics, U n i v e r s i t y of V i r g i n i a , charZottesvi ZZe, VA 22901, U. S. A.
Abstract.-Astronomical bodies have, i n t h e p a s 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 p r o v i d e s t h e p o s s i b i l i t y t h a t l a b o r a t o r y r o t o r s may b e made more p r e c i s e than a s t r o n o m i c a l ones. This a r t i c l e surveys t h e p r o p e r t i e s of some of b o t h t y p e s of r o t o r s and d e s c r i b e s s e v e r a l l a b o r a t o r y experiments f o r t e s t s of General R e l a t i v i t y .
Introduction.-Except f o r a s t r o n o m i c a l b o d i e s , we seldom t h i n k of p r e c i s i o n r o t o r s a s t o o l s f o r s t u d y i n g g r a v i t a t i o n . Three e x c e p t i o n s can be mentioned. 1 ) The Hughes-Drever e x p e r i m e n t s l r 2 with p a r t i c l e s a s p r e c i s i o n r o t o r s took advantage of
t h e p r i v i l e d g e d s t a t u s of t h e s e r o t o r s a s n o n i n e r t i a l frames i n o r d e r t o t e s t f o r t h e p o s s i b l e a n i s o t r o ~ y of s p a c e . 3 , 4 2) The S t a n f o r d R e l a t i v i t y Gyroscope w i l l provide a t e s t of General R e l a t i v i t y p r e d i c t i o n s of s p i n - o r b i t and s p i n - s p i n coupling of t h e gyro t o t h e 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 o r b i t . 5 Here t h e gyroscopic p r o p e r t i e s , n o t p u r e 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 t h e decay of a s p i n n i n g 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 a n i n v a l i d theory7 of g r a v i t a t i o n a l r a d i a t i o n .
This l a s t t e s t i s c l o s e s t i n experimental method t o t h o s e t o b e d i s c u s s e d h e r e , although t h e s e w i l l have r a d i c a l l y d i f f e r e n t o b j e c t i v e s from t h a t one.
The o b j e c t i v e s of concern h e r e a r e , i n s t e a d , mostly r e l a t e d t o a s e r i e s of Machian concepts which r e a c h beyond E i n s t e i n ' s General R e l a t i v i t y . This i n c l u d e s 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 t h e r e l a t e d q u e s t i o n of spontaneous, cosmological m a t t e r c r e a t i o n . We a l s o w i l l d i s c u s s 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 s c a l e s of t h e s e '%lachian" phenomena a r e huge, and Earthbound schemes must u s e u l t r a p r e c i s i o n t o cope w i t h t h e narrow spans a v a i l - a b l e 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 c o n s i d e r such a q u e s t i o n , and d i s c u s s i n what ways i t makes any s e n s e t o compete i n t h e ' l a b o r a t o r y a g a i n s t t h e reaches of astronomy.
I n succeeding s e c t i o n s we w i l l d e s c r i b e t h r e e experiments which u s e p r e c i s i o n l a b o r a t o r y 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 p r o g r e s s . Astronomical and Laboratory R o t o r s . - ~ i c k e ~ , and s u b s e q u e n t l y ~ u l l e r ~ , have used a n c i e n t o b s e r v a t i o n s of e c l i p s e s , e t c . to provide a long temporal b a s e l i n e f o r measuring t h e t i d a l d e f i c i t i n t h e s e c u l a r decay of t h e l u n a r o r b i t a l motion a s a p o s s i b l e means of e s t i m a t i n g 6. P r e c i s i o n 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 i s of much concern i n t h e time-keeping asDects of such c a l c u l a t i o n s .
Van ~ 1 a n d e r n l O h a s used l u n a r o c c u l t a t i o n s is combination w i t h atomic-clock timing of t h e s e c u l a r decay of t h e l u n a r o r b i t f o r t h e same reason. This does n o t i n v o l v e c o n s i d e r a t i o n s of p r e c i s i o n of r o t a t i o n a l m o t i o n , b u t i t does i n d i c a t e t h e d i r e c t i o n i n which modern s t u d i e s 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 i s t h e way t h e p r e c i s i o n of t h e atomic c l o c k makes up f o r t h e s h o r t temporal b a s e l i n e a v a i l a b l e i n t h e time span s i n c e i t s i n v e n t i o n and u s e . I n a d d i t i o n , t h e s e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981849
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experiments e x p l o i t t h e new way of c o n s i d e r i n g ~ i r a c ' s l ~ i d e a s about changing G . I n p a r t i c u l a r , h i s u s e of two m e t r i c s , atomic and cosmological, make comparison of t h e c l o c k time and l u n a r o r b i t time ( c o r r e c t e d 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 v e r s i o n of p r e d i c t i o n s f o r changing G.
Reference 1 3 l i s t s a number of o t h e r such t e s t s , t h e b a s i s of which w i l l be d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n .
Although even galaxy c l u s t e r s 1 4 have been involved i n c o n s i d e r a t i o n s of 6,
we w i l l u s e t h e e a r t h a s a more t a n g i b l e p r e c i s i o n s p h e r i c a l r o t o r f o r comparison with a l a b o r a t o r y r o t o r (of 5 cm r a d i u s ) . Table I l i s t s some of t h e p e r t i n e n t mechanical p r o p e r t i e s of t h e s e two r o t o r s .
Table I. Mechanical p r o p e r t i e s of a s t r o n o m i c a l and l a b o r a t o r y r o t o r s of i n t e r e s t .
Property E a r t h Laboratory Rotor
Radius (cm) 6.4 x lo8 5
Density (gmlcmL) 5.5 8
Surrounding atmosphere*
a ) Gas d e n s i t y lo2-lo3 1 . 9 x 1 0 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 p o i n t - 500 km above t h e e a r t h ' s s u r f a c e . For purposes of g a s drag i l l u s t r a t i o n t h i s rough c h o i c e w i l l b e adequate and i n f a c t t h e n o t i o n of o r d i n a r y gas drag i s q u i t e crude i n t h i s c a s e .
The behavior of t h e s e o b j e c t s r e l e v a n t t o p r e c i s i o n r o t a t i o n s i s t h a t con- cerned w i t h t h e i r s e c u l a r spindown and t h e i r f l u c t u a t i o n s . The s e c u l a r p a r t i s assumed t o be e x p o n e n t i a l . That i s , t h e a n g u l a r v e l o c i t y i s
where T* i s a time c o n s t a n t c o n t a i n i n g a l l forms of d r a g s ,
Here I i s t h e r o t o r moment of i n e r t i a and a i s an e f f e c t i v e o v e r a l l d r a g c o e f f i - c i e n t , a s i n t h e f o l l o w i n g d i f f e r e n t i a l e q u a t i o n of a " f r e e " r o t o r ,
For p r e s e n t purposes we can t a k e a t o b e composed of two p a r t s , t h e gas d r a g a g and t h e b e a r i n g d r a g , ab. I n t h e c a s e of a n a s t r o n o m i c a l body t h e "bearing drag" w i l l c o n s i s t of nonconservative e f f e c t s i n coupling t o o t h e r b o d i e s . For t h e e a r t h t h i s i s p r i m a r i l y t i d a l coupling t o t h e moon and sun.
Other d i s t u r b a n c e s l e a d t o both s e c u l a 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 " d i s c u s s e d by ~ r a g i n s k y l s i s one such
F i g u r e 1. C y l i n d r i c a l l a b o r a t o r y t e s t r o t o r i n suspension.
Actual r o t o r s a r e of Zerodur glass-ceramic u l t r a - h i g h s t a b i l i t y m a t e r i a l . 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 h e a t i n g of a r o t o r i n a uniform u n i d i r e c t i o n a l f l u x of e l e c t r o m a g n e t i c r a d i a t i o n ( t h e sun) l e a d s t o an i n c r e a s e i n a n g u l a r v e l o c i t y . (This i s l i s t e d a s a n e g a t i v e time c o n s t a n t i n Table 11, below.)
F l u c t u a t i o n s i n r o t o r a n g u l a r v e l o c i t y a c t u a l l y occur a s a spectrum. For purposes h e r e , we l i s t only f l u c t u a t i o n s a t t h e fundamental r o t a t i o n a l frequency f o r t h e e a r t h : t h e l e n g t h of day ( l o d ) v a r i a t i o n . 1 6
Table I1 l i s t s t h e r o t a t i o n a l p r o p e r t i e s of t h e e a r t h and l a b o r a t o r y r o t o r s . I n t h e l a t t e r c a s e , small s p h e r e s l 7 . 1 8 , 1 t o 3 mm diameter, a t h i g h s p e e d s ,
l o 4 t o l o 5 H z , a r e used f o r comparison although experiments t o b e d i s c u s s e d i n following s e c t i o n s use l o n g e r , slower r o t o r s .
E a r t h r o t a f i o n s a c t u a l l y s e r v e a s poor measurements f o r modern g r a v i t a t i o n a l q u e s t i o n s . For G, t h e 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 s e c u l a r l u n a r o r b i t a l decay. The l a r g e observed f l u c t u a t i o n s 1 6 and v a r y i n g s e c u l a r decay17 of t h e e a r t h ' s r o t a t i o n i n t e r f e r e g r e a t l y w i t h t h e u s e of such d a t a . A s f o r d i r e c t measurement of 6, t h e e a r t h r o t a t i o n s 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 a g g r e g a t e of f r e e l y o r b i t i n g b o d i e s , 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 c o m p r e s s i b i l i t y i s dominated by e l e c t r i c a l f o r c e s of r e p u l s i o n .
C a l c u l a t i o n s of t h e g a s drag depend on t h e r e l a t i o n v e r i f i e d by ~eams",
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Table 11. R o t a t i o n a l p r o p e r t i e s of a s t r o n o m i c a l and l a b o r a t o r y r o t o r s of i n t e r e s t .
P r o p e r t y E a r t h Laboratory r o t o r
T * - ~ e c a ~ c o n s t a n t from g a s drag ( s e c )
~ ~ * - ~ e c a ~ c o n s t a n t from %lo12
b e a r i n g d r a g ( s e c ) ( r e f . 16) ( r e f . 6) -T *-spin up time c o n s t a n t ,
pondromotive e f f e c t 1 5 ( s e c ) %6 x 1017
T*-observed ( s e c ) % 1 0 17
% 1 0 10
( r e f . 16) ( r e f . 17,18)
Observed r o t a t i o n a l
Q = w.r* %7 X 10 12 10 -10 14 15
Observed f r a c t i o n a l %3 x lo-8
f l u c t u a t i o n s ( r e f . 16) Not observed
This can b e put i n d i f f e r e n t u n i t s , 13,22
* = - = I
a g (413 a4; -)-'I, (5)
* 3
where k i s t h e g a s d e n s i t y , i n molecules/cm , p i s t h e mass of t h e molecule, i n gm, and T i s t h e g a s temperature, OK. Thus f o r s c a l i n g of T ~ * ,
T " ( e a r t h ) *
g RE PE kL TL %
T * ( l a b r o t o r ) = ( ) (T) (T/ '
g % " L E E
i s t h e r e l e v a n t r a t i o . For parameters i n t h e t a b l e s , t h i s t a k e s t h e v a l u e -10 15 .
I n summary, both b e a r i n g drag and g a s d r a g of t h e e a r t h a r e much l e s s t h a n f o r t h e l a b o r a t o r y r o t o r s of t h e p a s t , a l t h o u g h o t h e r v a r i a t i o n s a l s o render t h e e a r t h a r a t h e r i n e f f e c t i v e p r e c i s i o n r o t o r .
Improved Laboratory Rotors.-The r o t o r s of Beams and Fremerey had t h r e e major f a u l t s : t h e e x c e s s i v e gas f r i c t i o n , e x c e s s i v e b e a r i n g f r i c t i o n , and high-speed s t r e s s - r e l a t e d i n s t a b i l i t i e s .
From E q . (5) i t i s seen t h a t a vacuum of 10-18 t o r r would be needed t o achieve T*-1018 s e c f o r r o t o r s of a few cm s i z e . This i s e s s e n t i a l l y impossible, and a new scheme must b e found t o remove t h i s l i m i t a t i o n .
The method used i n our experiments was f i r s t conceived by ~ e a m s ~ ~ , although a t t h a t time h e lacked i n s t r u m e n t a t i o n t o develope and t e s t i t . I n t h i s method t h e gas i s f o r c e d t o r o t a t e along w i t h t h e r o t o r by means of an o u t e r , c o r o t a t i n g chamber. I f t h e p r e s s u r e i s i n t h e f r e e molecule regime one can expect t h e g a s drag on t h e i n n e r r o t o r t o approach z e r o a s t h e r o t o r s approach t h e same speed.
Two means have been used t o keep t h e i n n e r and o u t e r r o t o r s t o g e t h e r . 1 3 I n Method I t h e o u t e r c y l i n d e r r o t a t e s a t c o n s t a n t v e l o c i t y , locked t o a cesium beam c l o c k . The t i n y decay of t h e i n n e r r o t o r i s such t h a t an a p p r e c i a b l e d i f f e r e n c e i n a n g u l a r v e l o c i t y does n o t develope d u r i n g t h e l i f e t i m e of any doable experiment.
I n Method I1 a servomechanism s e n s e s slowdown of t h e o u t e r r o t o r and d r i v e s i t t o keep i t i n phase w i t h t h e i n n e r one.
These " c o r o t a t i o n p r o t e c t i o n " methods i n p r i n c i p l e and i n p r a c t i c e p r o v i d e a huge amount of g a s d r a g r e d u c t i o n . They do, however, p r e s e n t a new s e r i e s of problems r e l a t e d t o coupling i n t h e r o t a t i n g r e f e r e n c e frame, and t h e i r develop- ment has proving a c o n s i d e r a b l e t a s k .
The f e r r o m a g n e t i c suspensions which served a s b e a r i n g s f o r Beams and Fremerey e x h i b i t e d l i m i t i n g time c o n s t a n t s a t about T;* % 1012 s e c . This a r i s e s from t h e r o t o r s p i n coupling t o t h e e a r t h ' s s p i n , a " C o r i o l i s torquet118 which causes a r o t o r i n t h e n o r t h e r n hemisphere t o hang o f f m i c r o r a d i a n s toward t h e North. The n o n c o l i n e a r i t y of s p i n and suspension axes demands compensating eddy c u r r e n t s which have a t i n y component i n a d i r e c t i o n such a s t o c r e a t e drag.
S u r p r i s i n g l y t h i s e f f e c t i s v i r t u a l l y independent of a n g u l a r v e l o c i t y .
Even i f compensating schemes f o r t h e C o r i o l i s t o r q u e could b e d e v i s e d , i t i s n o t c l e a r t h a t t h e f e r r o m a g n e t i c suspension i s s u i t a b l e f o r g r a v i t a t i o n a l e x p e r i - ments. I t i s h a r d t o imagine how t h e a c t i v e s e r v o p r o c e s s of such suspensions c a n f a i l t o , through some form of mode coupling, remove o r add energy t o t h e r o t o r a t t h e minute l e v e l s of i n t e r e s t . I n one s e r i e s of experiments22 we have ob- s e r v e d some r o t o r s t o never l o s e speed, even i n a 10-6 t o r r non-corotating gas atmosphere. I n some c a s e s t h i s would correspond t o a d d i t i o n of %10-l5 w a t t s i n t h e r o t a t i o n a l mode, presumably pumped i n by a p a r a m e t r i c mode coupling from t h e suspension. 22
Diamagnetic s u s p e n s i o n s have been developed f o r superconducting ~ ~ h e r e s . 2 ~ The i n t e r e s t was f o r gyro work and t o our knowledge t h e " l o s s l e s s " r o t a t i o n a l
p o s s i b i l i t y of such r o t o r s was never pursued. It i s i n t h i s d i r e c t i o n t h a t t h e work o f o u r l a b o r a t o r y almost s u r e l y must u l t i m a t e l y go. A t t h e p r e s e n t , however, we a r e s t u d y i n g t h e problems of c o r o t a t i o n i n t h e more h o s p i t a b l e circumstances
of t h e ferromagnetic suspension.
F i n a l l y , t h e s t r e s s and thermal i n s t a b i l i t i e s of t h e r o t o r s of Beams were a d i r e c t r e s u l t of t h e h i g h speeds o f t h e r o t o r s . Lower speed r o t o r s , ~ $ 1 t o 10 r a d l s e c , of a few cm s i z e can avoid t h e s e problems. A t t h e same time, t h e moment of i n e r t i a goes up f a s t e r t h a n t h e drag, a n o t h e r improvement.
Laboratory Measurement of ;.-A r o t a t i n g Cavendish ~ a l a n c e ~ ~ can avoid t h e one major l i m i t a t i o n f o r G measurement, t h a t of a v a r i a k l e g r a v i t y g r a d i e n t a t t h e balance.
Since t h e d e s i r e d s e n s i t i v i t y is b e t t e r t h a n G / G = -1010 y r - l , g r a d i e n t s a t t h i s l e v e l would b e v i r t u a l l y impossible t o avoid otherwise. This has been d i s c u s s e d a t l e n g t h . 2 5 I n essence t h e r o t a t i o n s , d r i v e n by an u l t r a - p r e c i s e t u r n t a b l e , average o u t t h e t o r q u e s imposed on t h e b a l a n c e by non-rotating l o c a l g r a v i t y g r a d i e n t s .
To s e e t h e s e n s i t i v i t y needed and t h e c h a r a c t e r of t h e s e experiments t h e b a s i s f o r i n t e r e s t i n a p o s s i b l e v a r i a t i o n of G w i l l b e b r i e f l y d i s c u s s e d h e r e .
~ i r a c ' l developed h i s " l a r g e numbers hypothesis" along t h e l i n e s of a two- m e t r i c concept of g r a v i t a t i o n . 2 6 An "atomic" o r "quantum" m e t r i c a p p l i e s t o atomic e v e n t s such a s t h e t i c k i n g of a n atomic clock. An " E i n s t e i n " o r "cosmolo- g i c a l " m e t r i c a p p l i e s t o l a r g e s c a l e e v e n t s . I n t h i s way t h e General Theory of R e l a t i v i t y can s t i l l remain v a l i d , applying t o t h e l a r g e s c a l e e v e n t s , even though i t does n o t o t h e r w i s e p e r m i t v a r i a b l e G, which comes o u t of t h e development.
That is, v a r i a b l e G only a p p e a r s i n atomic-measured e v e n t s . This disengagement of t h e two m e t r i c s i s a s t r a n g e , b u t n o t new, concept.
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Viewed i n t h i s way, t h e l a r g e numbers appear a s dimensionless r a t i o s , f o r example, of t h e l a r g e s t (cosmological) p h y s i c a l l y d e f i n e d d i s t a n c e t o t h e s m a l l e s t (quantum) d i s t a n c e : t h e "radius" of t h e u n i v e r s e t o t h e r a d i u s of a n elementary p a r t i c l e . Since t h e r a d i u s i n c r e a s e s w i t h time f o r our expanding u n i v e r s e t h i s l a r g e number h a s a temporary P r e s e n t v a l u e , about A t one e a r l y time i t could have been u n i t y .
By i t s e l f t h e above number i s i n t e r e s t i n g only i n i t s l a r g e s i z e . Most dimensionless r a t i o s i n n a t u r e a r e only s e v e r a l o r d e r s of magnitude from u n i t y . But a n o t h e r dimensionless r a t i o , t h i s one of f o r c e s , has a n e a r l y e q u a l v a l u e of about 1040. This is t h e r a t i o of t h e e l e c t r i c a l (quantum?) t o g r a v i t a t i o n a l
(cosmological?) f o r c e s between a p a i r of e l e c t r o n s .
D i r a c assumed t h e s e numbers were e q u a l and were l a r g e n o t by a c c i d e n t but by growth. An a l t e r n a t e view could u s e t h e maximum s i z e of an o s c i l l a t i n g u n i v e r s e i n t h e f i r s t r a t i o and thereby c o n s i d e r i t a c o n s t a n t r a t h e r t h a n growing r a t i o .
Taking D i r a c ' s view, t h e n , t h e g r a v i t a t i o n a l f o r c e , lo4' times weaker, i s diminishing when measured by atomic e v e n t s . O r , t h e e l e c t r i c a l f o r c e i s i n c r e a s - i n g when measured by cosmological events. Such a n i d e a h a s been c a r r i e d f u r t h e r by ~ i r a c ~ ~ i n p o s t u l a t i n g t h a t t h e number of baryons i n t h e o b s e r v a b l e u n i v e r s e , about 1080, i s t h e n growing a s t 2 when measured by atomic events. He h a s since27 devised a n o t h e r v e r s i o n of t h e concept i n which, i n an a p p r o p r i a t e r e f e r e n c e frame, m a t t e r i s n o t b e i n g c r e a t e d . These i d e a s have been c a r r i e d f u r t h e r by ~ a n u t o l 2 i n h i s s c a l e - c o v a r i e n t theory.
The a t t r a c t i v e n e s s i n such i d e a s l i e s p a r t l y i n t h e i r Machian connection.13 They do l e a d t o Sciama's s t a t e m e n t of Mach's ~ r i n c i ~ l e . 2 8 A ~ o t h e r a t t r a c t i o n i s i n t h e h i n t of a connection t o grand u n i f i c a t i o n . I f a t v e r y e a r l y times when p r e s s u r e s and temperatures were v e r y g r e a t , and i n t h e u n i v e r s e a l l f o r c e s were of n e a r l y e q u a l s t r e n g t h , a n e v o l v i n g r a t i o of e l e c t r i c a l t o g r a v i t a t i o n a l would not b e a n u n t e n a b l e n o t i o n . Development of t h e electro-weak u n i f i c a t i o n , 29 grand u n i f i c a t i o n , and t h e r e l a t e d p r e d i c t i o n of a decaying proton30 have a growing e d i f i c e of t h e o r e t i c a l i n t e r e s t about them w i t h s i m i l a r i m p l i c a t i o n .
Thus t h e s c a l e of growth of t h e l a r g e number r a t i o s i s given d i r e c t l y by t h e Hubble expansion r a t e of t h e universe31, ~ ~ - 1 ?. 2 x 1010 y r . Consequently
k / ~ ?. Hg 2 5 x 10-l1 yr-l. This i s t h e " t a r g e t r a t e " f o r o b s e r v a t i o n of a non- zero change i n G. I t should be noted t h a t d i f f e r e n t v e r s i o n s of t h e concept l e a d t o d i f f e r e n t connections between b / ~ and t h e r e l a t e d changes i n p e r i o d s of o r b i t s , o r o t h e r p o t e n t i a l observables. T h i s i s d i s c u s s e d , e.g. i n Ref. 13.
The t o r q u e change i n one y e a r i n a modest-sized 6 experiment25 would be 3 x 10-l3 dyne-cm. T h i s i s 2000 times s m a l l e r t h a n a s i g n a l t o r q u e a t t h e l i m i t of Dicke's e q u i v a l e n c e p r i n c i p l e m e a ~ u r e m e n t . 3 ~ And, i t i s lo6-10 times s m a l l e r than t h e t o r q u e f o r t h e b e s t Cavendish balance measurements of G. The t r a d e - o f f of a b s o l u t e accuracy j n metrology of t h o s e experiments f o r t h e extreme s e n s i t i v i t y and s t a b i l i t y of t h e G experiment would o f f e r hope of r e a c h i n g t h e n e c e s s a r y l e v e l .
The experiment devised i s complex. It i s a r o t a t i n g , superconducting, symme- t r i z e d , fedback Cavendish balance. While l i m i t s of n a t u r e , i n p r i n c i p l e , do n o t appear t o b e s u r p a s s e d a t t h e r e q u i s i t e l e v e l of s e n s i t i v i t y and s t a b i l i t y , t h e p o s s i b i l i t y f o r d i f f i c u l t , p r a c t i c a l problems seems enormous.
Matter C r e a t i o n Experiment.-As broueht o u t stove, t h e l a r g e number h y p o t h e s i s a l s o p r e d i c t s m a t t e r c r e a t i o n a t a r a t e M/M = -2 G/G
.
10-lo p e r y e a r . I f M i s takent o b e t h e mass of a l l baryons i n t h e u n i v e r s e , and new ones a r e c r e a t e d uniformly throughout space, i t i s c a l l e d " a d d i t i v e c r e a t i o n " , and would be a r a t e s o low a s t o a f f e c t r o t a t i o n s i n an unobservable way. On t h e o t h e r hand, i f m a t t e r i s c r e a t e d where i t a l r e a d y e x i s t s , each macroscopic body would i n c r e a s e i n mass a t t h e above r a t e . This i s c a l l e d " m u l t i p l i c a t i v e c r e a t i o n " by ~ i r a c . 2 6
F i g u r e 2. Method I c o r o t a t i o n experiment f o r p r e l i m i n a r y measurement of m a t t e r c r e a t i o n . System r e s t s on
3600 kg s t o n e , below p i c t u r e . T o t a l h e i g h t
-
2.3 m.I f t h e m a t t e r i s c r e a t e d i n t h e s i m p l e s t conceivable Machian f a s h i o n , i . e . i n response t o a l l t h e o t h e r m a t t e r i n t h e u n i v e r s e , i t would be i n a s t a t e of r e s t f o r t h e frame of t h e average of a l l m a t t e r . I n t h i s c a s e a r o t o r i n a n earthbound l a b o r a t o r y would i n c r e a s e i n moment of i n e r t i a due t o t h e added m a t t e r , and i f s u f f i c i e n t l y p r o t e c t e d , would slow down a t a measurable r a t e . We c a l l t h i s a dynamic measurement of m a t t e r creation.33 The p a r t i c l e s c r e a t e d would, under t h e above assumption, a c t a s a "wind" a c r o s s t h e r o t o r o f no o b s e r v a b l e consequence. (On t h e o t h e r hand, i f m a t t e r was c r e a t e d i n t h e s t a t e of motion of t h e l o c a l m a t t e r r a t h e r t h a n t h e s i m p l e r Machian i d e a , i t would n o t slow down t h e r o t o r . ) An advantage of t h e dynamic method of measurement i s t h a t i t i s inde- pendent of t h e form of t h e c r e a t i o n (long a m a t t e r of d i s c u s s i o n ) a s l o n g a s i t s t a y s i n p l a c e once c r e a t e d i n t h e r o t o r .
A r o t o r s i m i l a r t o t h a t of F i g u r e 1, b u t of Zerodur, weighing 250 gm and having moment of i n e r t i a I = 1100 gm cm2, i s spun up t o 'bl r a d . / s e c i n a Method I c o r o t a t i o n system. The primary apparatus13334 f o r t h i s f i r s t , room temperature dynamic t e s t of m a t t e r c r e a t i o n i s ~ i c t u r e d i n F i g u r e 2.
A p r e c i s i o n t u r n t a b l e d r i v e s t h e o u t e r , q u a r t z c y l i n d e r a t c o n s t a n t speed.
A s p e c i a l magnetic-averaging motor34, phase-locked t o a cesium beam c l o c k , pro- v i d e s adequate speed constancy. A r o t a t i n g e l e c t r o n i c pump e v a c u a t e s t h e chamber t o 10-6 Torr. O p t i c a l systems observe mirrored s u r f a c e s on b o t h t h e i n n e r and o u t e r r o t o r s and p r o v i d e timing of each p e r i o d t o a b o u t 10-7 s e c . Averaging over 104 p e r i o d measurements i s done through a computer-operated timing system which r e s u l t s i n ~ 1 0 - l 1 sec. accuracy f o r t h e lo4 s e c (2.78 hour) b l o c k s . This i s s u f f i c i e n t f o r p r e s e n t system t e s t i n g .
C8-436 JOURNAL DE PHYSIQUE
F i n a l r u n s , a t t h e above " t a r g e t r a t e " f o r m a t t e r c r e a t i o n would have t o be months long i f t h e above p e r i o d averages were t h e only means of o b s e r v a t i o n . However, an i n t e g r a t e d phase l a g o f t h e i n n e r r o t o r 1 3 of 2 x r a d i a n s would occur every 106 s e c (%I2 days) and would be e a s i e r t o measure.
A t such high l e v e l s of s e n s i t i v i t y , of c o u r s e , a l a r g e number of o r d i n a r y d i s t u r b a n c e s must be e i t h e r removed o r known and accounted f o r (e.g. averaged).
For example, a 3600 kg g r a n i t e block on Weber i s o l a t o r s , followed by a 270 kg block on damped pneumatic s p r i n g s p r o v i d e s a two-stage mechanical i s o l a t i o n system.
A s p e c i a l s e t of problems a r i s e from c o r o t a t i o n . Coupling w i t h i n t h e r o t a t i n g r e f e r e n c e frame a p p l i e s s e c u l a r and o s c i l l a t i n g t o r q u e s t o t h e i n n e r r o t o r . 1 3 The " s i g n a l torque" which slows t h e r o t o r i s about 10-l3 dyne-cm a t M 1 0r . I m p e r f e c t i o n s i n symmetry, w i t h s t a n d a r d p r e c i s i o n machining, would l e a d t o g r a v i t a t i o n a l coupling on t h e r o t o r w i t h a t o r q u e of about 10-l7 t o 10-I* dyne-cm. For r e f e r e n c e , thermal n o i s e c o n t r i b u t e s a f l u c t u a t i n g t o r q u e of a b o u t 10-l6 dyne-cm on such a r o t o r a t room temperature f o r averaging times of 104 s e c .
Thus f a r our experiments have l a r g e l y been aimed a t a s s e s s i n g t h e e f f e c t s of unwanted coupling. S e r i o u s e f f o r t s have n o t y e t been made t o reduce f e r r o - magnetic s u p p o r t b e a r i n g f r i c t i o n . (The s u p p o r t p o l e p i e c e cannot r o t a t e a s i t developes a "cranking" mode on t h e r o t o r . 3 4 )
More o r d i n a r y coupling i n t h e r o t a t i n g frame c o n s i s t s of e l e c t r i c a l and mag- n e t i c e f f e c t s which a r e j u s t now b e i n g s t u d i e d . I n one i n t e r e s t i n g e x ~ e r i m e n t 3 5 , t h e r e s i d u a l magnetism i n a "nonmagnetic" clamp screw on t h e r o t o r coupled t o t h e assymmetry of t h e s m a l l s t r a y f i e l d (< $ g a u s s ) of t h e e l e c t r o n i c pump t o produce o s c i l l a t i o n s about t h e synchronous r o z a t i o n p o s i t i o n . These had p e r i o d s of 10 t o 30 min. and amplitudes of about 300. They decayed a t a r a t e of about 10-14 w a t t s .
I n o t h e r experiments we have p u t a p a i r of copper f o i l p l a t e s around t h e o u t e r c y l i n d e r and a p p l i e d a few kV p o t e n t i a l t o t e s t e l e c t r i c a l c o u p l i n g . Remarkably s t r o n g coupling o c c u r s , and confirms t h e need f o r conducting c o a t i n g s on a l l s u r f a c e s .
I n e r t i a l Clock Experiment.-A s u f f i c i e n t l y p r o t e c t e d and a p p r o p r i a t e l y i n t e r r o g a t e d r o t o r s h o u l d be a good clock. I f m a t t e r c r e a t i o n e x i s t s , such a c l o c k would
keep a p a r t i c u l a r kind of time, b u t t h i s would presumably b e smooth and p r e d i c t a b l e . There could b e many u s e s f o r such a clock, i f i t were made s u f f i c i e n t l y pre- c i s e and r e l i a b l e . One u s e would b e t o t a k e advantage of i t s p a r t i c u l a r n a t u r e from a fundamental p o i n t of view and a t t e m p t t o s e a r c h f o r nonmetric p r o p e r t i e s of R e l a t i v i t y .
W i l l and ~ o r d v e d t ~ ~ have suggested a measurement of d i f f e r e n t i a l time- keeping of two d i f f e r e n t types of c l o c k s , s e t s i d e by s i d e , a s they p r o g r e s s around t h e a x i s on t h e s u r f a c e of t h e e a r t h i n i t s r o t a t i o n . There i s a s i n u s o i d a l d a i l y v a r i a t i o n of t h e g r a v i t a t i o n a l p o t e n t i a l t h e y e x p e r i e n c e a s t h e y move c l o s e r , then f u r t h e r from t h e sun. I f non-metric e f f e c t s apply, t h e s e might c a u s e a d i f f e r e n t i a l red s h i f t between c l o c k s each of which obeys,
where g i s t h e mean g r a v i t a t i o n a l f i e l d of t h e sun a t t h e i r p o s i t i o n , h i s t h e i r h e i g h t v a r i a t i o n , and terms i n t h e b r a c k e t a r e t h e Lightman-Lee expansion i n t h e s o - c a l l e d TH&v formalism.37 I n e s s e n c e , t h e expansion h a s c o e f f i c i e n t s Oi of t h e o r d e r u n i t y which depend on t h e n a t u r e of t h e c l o c k s . A "magnetic clock",
t h e hydrogen maser, would have one s e t . The " e l e c t r o s t a t i c clock", e.g. our
Figure 3. Primary a p p a r a t u s f o r i n e r t i a l c l o c k . The main chamber, about 30 cm d i a m e t e r , houses t h e shroud and minor r o t o r s , s e e n through t h e h o l e i n f r o n t . Arms a t t o p house e l e c t r o n i c s f o r magnetic s u p p o r t and timing.
Tube a t lower l e f t connects t o vacuum pump.
i n e r t i a l clock, woyJd have another.38 The v a l u e of gh/c2 f o r d i u r n a l v a r i a t i o n would be a b o u t 10- .
Such a n experiment has a l r e a d y been performed by S t e i n and ~ u r n e a u r e ~ ' , comparing t h e hydrogen maser and t h e Superconducting Cavity S t a b i l i z e d O s c i l l a t o r (SCSO). A s y e t they have n o t had c o n c l u s i v e r e s u l t s .
F i g u r e 3 shows our i n e r t i a l c l o c k e x ~ e r i m e n t ~ ~ , and F i g u r e 4 show& one v e r s i o n of t h e i n n e r r o t o r f o r i t , i n suspension. The Method I1 c o r o t a t i o n p r o t e c t i o n i s used and t h e experiment i s a t room temperature. Double magnetic suspension23 i s used f o r t h e two b e a r i n g s . Gas b e a r i n g s have shown c o n s i d e r a b l e r 0 u ~ h n e s s 3 ~ , and i t i s e a s i e r t o o b t a i n smooth s e r v o p r o p e r t i e s w i t h t h e o u t e r
"shroud r o t o r " b e a r i n g being magnetic a l s o . The development of t h i s was a c o n s i d e r a b l e t a s k , b u t i t i s now f u n c t i o n a l .
Thus f a r only room temperature t e s t s have been c a r r i e d o u t , and n o t under vacuum. The exaggerated v i s c o u s c o u p l i n g s between r o t o r s , and between t h e shroud r o t o r and chamber have been u s e f u l i n t e s t i n g t h e behavior and corn a r i s o n w i t h t h e s e t s of coupled d i f f e r e n t i a l e q u a t i o n s which t h e system obeys. EO
The r o t a t i o n a l s e r v o i s an i n t e r e s t i n g example of c o n t r o l . A t p r e s e n t , t h e p e r i o d s of t h e two r o t o r s , shroud and i n n e r , a r e measured s e p a r a t e l y and compared i n a microcomputer.^^ The d i f f e r e n c e i s converted t o an analog s i g n a l which o p e r a t e s a n eddy-current d r i v e t o speed up o r slow down t h e shroud r o t o r , a s needed
C8-438 JOURNAL DE PHYSIQUE
F i g u r e 4. Lower r o t o r of i n e r t i a l c l o c k i n suspension w i t h shroud removed. P o s i t i o n - s e n s i n g c o i l i s immediately below r o t o r , and mounted on p o l e of p o s i t i o n - c o r r e c t i n g c o i l .
t o keep i t w i t h t h e i n n e r . This w i l l be recognized a s p u r e d e r i v a t i v e feedback, and i t p e r m i t s wandering of t h e b a s e l i n e . A new algorythm i s being prepared t o provide p r o p o r t i o n a l , and p o s s i b l y i n t e g r a l , feedback t o remove t h i s d i f f i c i e n c y .
I n t h e f i n a l c l o c k of t h i s t y p e ( a t low temperature) t h e u l t i m a t e s t a b i l i t y and p r e c i s i o n w i l l r e s t on t h e i s o l a t i o n from s t a n d a r d d i s t u r b a n c e s a s w e l l a s t h o s e which come from i n t e r r o g a t i o n of t h e i n n e r r o t o r . Disturbances and undesired i n t e r r o t o r c o u p l i n g s c o n s t i t u t e "leaks" a c r o s s t h e s e r v o c o n t r o l and a r e t h e m a t t e r of our most s e r i o u s study. A t r e s e n t t h e r e appear t o b e no l i m i t a t i o n s , & p r i n c i p l e , t o a c h i e v i n g Q % loP5 o r h i g h e r .
Conclusion.-Laboratory p r e c i s i o n r o t a t i o n s a r e a new f i e l d which p r e s e n t s i n t e r - e s t i n g new p o s s i b i l i t i e s f o r g r a v i t a t i o n a l experiments, s e v e r a l of which have been d e s c r i b e d . A t t h e same time, problems of new k i n d s appear, p a r t i c u l a r l y i n
i n t e r r o t o r c o u p l i n g s f o r t h e needed c o r o t a t i o n g a s drag e l i m i n a t i o n . Room tempera- t u r e experiments t o d a t e have shown some of t h e s e problems b u t have n o t e x h i b i t e d evidence f o r p r o h i b i t i v e l i m i t a t i o n s i n t h e main concepts. The v i r t u e s of high p r e c i s i o n timing c a p a b i l i t i e s f o r r o t a t i o n a l motion, p a r t i c u l a r l y w i t h averaging, have shown t h e p o t e n t i a l f o r a s t o n i s h i n g measurement s e n s i t i v i t y i n such r e s e a r c h .
We wish t o acknowledge s u p p o r t from t h e N a t i o n a l Science Foundation, g r a n t s PHY78-3208 and PHY80-07948 and t h e N a t i o n a l Bureau of S t a n d a r d s g r a n t G8-9025.
Also, t h e c o n t r i b u t i o n s of many people i n our l a b o r a t o r y , i n c l u d i n g George T.
G i l l i e s , Stephen T. Cheung, George R. Jones, C a r l Leyh and Bruce Bernard, have been c e n t r a l i n t h i s r e s e a r c h .
R e f e r ences. -
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