A P r o p o s a l f o r C o m b i n e d E f f o r t s R e g a r d i n g G e o p h y s i c a l R e s e a r c h a n d D e t e c t i o n o f G r a v i t a t i o n a l W a v e s V . D E S A B B A T A - P . F O R T I N I - C . G T T A L D I - S . P E T R A L I A ( * ) R i c e v u t o il 28 F e b b r a i o 1970 SUMMARY. — T h e possibility of s t u d y i n g t h e E a r t h f r e e oscillations w i t h a laser i n t e r f e r o m e t e r is considered. I n p a r t i c u l a r t h e p r o b l e m of d e t e c t i o n of g r a v i t a t i o n a l w a v e s is a n a l y s e d in detail. T h i s p r o b l e m seems t o be a v e r y p r o m i s i n g m a t t e r owing t o t h e f a c t t h a t w i t h a t w o - m o d e He-No laser one m a y resolve c h a n g e s in l e n g t h d o w n t o 10~u cm. O t h e r m e t h o d s t o r e v e a l g r a v i t a t i o n a l w a v e s are m e n t i o n e d . RIASSUNTO. — Vengono prese in e s a m e le p o s s i b i l i t à offerte d a un i n t e r f e r o m e t r o laser p e r lo s t u d i o delle oscillazioni libere della t e r r a . I n p a r t i c o l a r e viene considerato il p r o b l e m a della rivelazione delle onde gravi- t a z i o n a l i ; la cosa s e m b r a assai p r o m e t t e n t e s o p r a t u t t o se si tiene c o n t o che con u n laser H e - N é a d o p p i a f r e q u e n z a , si possono a p p r e z z a r e sposta- m e n t i dell'ordine di IO-11 c m . Vengono a c c e n n a t i a n c h e altri possibili m e t o d i di rivelazione delle o n d e g r a v i t a z i o n a l i . W e b e r f1) c l a i m s t o h a v e d e t e c t e d g r a v i t a t i o n a l r a d i a t i o n i n t h e 1 6 0 0 H z b a n d ; b e c a u s e of t h e e x t r e m e i m p o r t a n c e of t h i s e x p e r i m e n t a n d t h e s i g n i f i c a n t c o s m o l o g i c a l i m p l i c a t i o n s , i t is i n d i s p e n s a b l e t o c h e c k t h e e x i s t e n c e of g r a v i t a t i o n a l w a v e s i n d i f f e r e n t c o n d i t i o n s a n d w i t h d i f f e r e n t m e t h o d s a n d t e c h n i q u e s . H a v i n g t h i s i n m i n d w e p r o - p o s e d a t t h e b e g i n n i n g of 1 9 6 8 t o C . N . R . a n o u t l i n e of a n e x p e r i m e n t t h a t , b e s i d e s g i v i n g v a l u a b l e i n f o r m a t i o n s o n t h e soil p r e s e r v a t i o n , a l l o w s u s t o s t u d y t h e E a r t h f r e e o s c i l l a t i o n s a n d t h e p o s s i b i l i t y t h a t s o m e of t h e s e m a y b e d u e t o t h e i n t e r a c t i o n w i t h g r a v i t a t i o n a l r a d i a - (*) I s t i t u t o Nazionale di Fisica Nucleare I s t i t u t o di Fisica - U n i v e r s i t à di Bologna. - Sezione di Bologna V . D E S A B B A T A - P . F 0 R T I N I - C . G U A L D I - S . P F . T R A L I A tion. This project has been a t last approved and we hope to s t a r t doing practically as soon as possible. Our a p p a r a t u s consists of a laser interferometer which iillows to measure the soil deformations and which, in t h e ultimate model, should have an e x t e n t of the order of a kilometer. As previously said, this instrument, besides observing the microseismic activity, the deformation of the e a r t h crust, slower movements due to earthly tides a n d f a u l t y movements, would be also utilized to measure free quadru- pole oscillations of the E a r t h connected with t h e detection of gravi- tational waves. To discriminate f r o m seismic waves one needs to accumulate d a t a over a long interval of time and to look for Fourier components a t t h e presumed source frequencies. Also t h e s t u d y of the decay t i m e of the oscillations constitutes a tool to discriminate between waves of seismic and gravitational origin. The i n s t r u m e n t m a y be a Ile-Ne laser operating a t a wave length of 6328 A . W i t h this kind of an i n s t r u m e n t Yali a n d Bostrom ( 2 ^ 4 ) have been able to reach a sensitivity of Al/l~ 6-10 - 1 2 and to reveal microseismic activity of a period of 6 sec and amplitude from 500 to 1500 A. The instrument noise on this t y p e of measurements arises f r o m : a) optical p a t h length changes by variation of v a c u u m in pipe, length change of pipe due to atmospheric pressure changes or tem- p e r a t u r e changes. b) drift in the i n s t r u m e n t piers. c) laser frequency instability induced by changes of our F a b r y - P e r o t reference cavity, as usual disposed for frequency stabilization. d) fluctuations of the number of photons entering t h e detectors. With a laser interferometer we can hope to measure extremely small strains e (where e = Al/l) a n d we hope to increase the sensitivity of the i n s t r u m e n t with the use of a double frequency laser. Recently Eichler and Wiesemann (5) have prospected the possibility of apprais- ing a length shift of 10~3 A with a two-mode He—Ne laser in an optical resonator coupled to the laser, a n d Herzinger and Lindner (6) have pro- posed a laser device to resolve changes in length down to 10~n cm. Besides this we are planning to m a t c h the experiment with other experiments in coincidence, carried out with totally different methods. Dyson (') gives an estimate of the displacement Al which would be measured on the E a r t h crust if t h e flux of incomimr eravitational A P R O P O S A L F O R C O M B I N E D E F F O R T S R E G A R D I N G G E O P H Y S I C A L , E T C . 2 3 waves, iii t h e 1 - H z f r e q u e n c y b a n d , is of t h e order of C3 w2 H 2 F = — — — 7 = 2 • 10-5 erg c n r ! sec-1 . 64 7iG e H e gives f o r t h e d i s p l a c e m e n t Al: Al ~ 2 • 10~17 cm . This m e a n s t h a t a t t h e p e a k d i s p l a c e m e n t t h e strain is Al s ~ 2 — = 1 0 - ^ , A Q X = s being t h e w a v e l e n g h t c o n n e c t e d w i t h t h e s o u n d velocity i n v E a r t h i n t e r i o r t h a t is Cs = 4000 m / s e c . This figure m a y b e i m p r o v e d b y m a n y o r d e r s of m a g n i t u d e : as a m a t t e r of f a c t we m a y t a k e f o r t h e E a r t h a Q of ~ 400 as g i v e n b y geophysical e s t i m a t e s (see f o r i n s t a n c e C a p u t o (8)) i n s t e a d of Q = 1 implied b y D y s o n ' s e s t i m a t e , w h e r e Q = E/AE is t h e q u a l i t y f a c t o r . Moreover t h e flux of gravi- t a t i o n a l w a v e s on t h e 1 - H z b a n d m a y b e g r e a t e r t h a n t h a t a s s u m e d b y D y s o n . I n f a c t , f o r i n s t a n c e , t h e flux revealed b y W e b e r (!) in t h e 1 - K H z f r e q u e n c y b a n d , t h a t is F ~ 3 • 10 1 erg cm-= sec;-1 , is m a n y order of m a g n i t u d e g r e a t e r t h a n t h a t foreseeable on t h e g r o u n d b o t h of a n y k n o w n m o d e l of t h e U n i v e r s e a n d of e s t i m a t e s which t a k e i n t o a c c o u n t possible sources of g r a v i t a t i o n a l w a v e s . I f , f o r e x a m p l e , we a s s u m e a flux of 3 - 1 0 - 1 erg errr 2 sec 1 also in t h e 1 - H z b a n d , t h a t is f o u r o r d e r of m a g n i t u d e g r e a t e r t h a n t h a t a s s u m e d b y D y s o n , r e m e m b e r i n g t h a t e ~ G2 B'oto Qjm"- , where K'oio is t h e c u r v a t u r e t e n s o r c o m p o n e n t which drives a gravi- t a t i o n a l w a v e d e t e c t o r a n d is p r o p o r t i o n a l t o t h e s q u a r e r o o t of t h e flux B'oto oc \jF , t h e n t h e s t r a i n , w i t h t h e s e new e s t i m a t e s of Q a n d F, is e ~ 7-10- 1 8 , a n d f o r t h e p e a k d i s p l a c e m e n t we h a v e : Al ~ 1.4-10~12 cm . W e t h i n k of i m p r o v i n g f u r t h e r these figures using v e r y large masses, well isolated f r o m t h e E a r t h , a n d t h e laser as a t r a n s d u c e r t o 24 V . D E S A B B A T A - P . F O K T I N I - C. G U A L D I - S . P E T R A L I A detect their relative motion or, alternatively, t h e oscillations of a single large mass. I n this case we m a y h a v e a quality f a c t o r Q ~ 106 a n d t h e strain would be e ~ 2 - 1 0 - " , with Al ~ 4-10- 9 cm. B u t , as we h a v e said, t h e best would be to h a v e some other device which, exploiting t o t a l l y different principles, gives a measure of t h e g r a v i t a t i o n a l waves flux: in t h i s case we can look for coincidences between t h e two a p p a r a t u s . This new a r r a y will be f o u n d e d on t h e i n t e r a c t i o n between gravi- t a t i o n a l waves a n d a s t a t i c m a g n e t i c Held. L u p a n o v (9) has calculated t h e change of a s t a t i c electric field of a capacitor in t h e field of a gravi- t a t i o n a l wave. W e h a v e m a d e a calculation (10) along t h e same line, considering a m a g n e t o s t a t i c field parallel to t h e direction of propa- gation of t h e g r a v i t a t i o n a l wave direction). Between t h e surfaces of t h e polar expansions on t h e m a g n e t i we h a v e a s t e a d y electro- m a g n e t i c wave: Ey = — Ez = E^x A cos S sin <5 e<*°+~/2> sin h x where E^°>x is t h e static m a g n e t i c held, A is t h e a m p l i t u d e of t h e incident g r a v i t a t i o n a l wave, linked to the flux b y : C 3 w 2 U | 2 F — ---- 64 n G d is t h e angle between t h e « - a x i s a n d t h e direction of oscillation of t h e source of t h e g r a v i t a t i o n a l wave. The ratio between t h e change of t h e m a g n e t i c field and t h e static m a g n e t i c field, in t h e case of a flux F ~ 3 - 1 0 - 1 erg c m - 2 sec - 1 is: Ez Ey = = 10 10 . E^x E^x The case of a g r a v i t a t i o n a l wave i n t e r a c t i n g with a dipole m a g n e t i c field is being studied. This case seems to be promising to see if t h e r e is a n y relation between periodic micropulsations of t h e geomagnetic field and incident g r a v i t a t i o n a l waves. A P R O P O S A L FOLL C O M B I N E D E F F O R T S R E G A R D I N G G E O P H Y S I C A L , ETC. 2 5 R E F E R E N C E S ( ! ) W E B E R J . , " P h y s . R e v . L e t t e r s " 22, 1320 (1909). ( 2 ) V A L I V . - B O S T R O M R . C., " E a r t h a n d p l a n e t a r y science L e t t e r s 4 . 4 3 6 ( 1 9 6 8 ) . ( 3 ) V A L I V . - B O S T R O M R . C., " N a t u r e " , 2 2 0 . D e c e m b e r 1 9 6 8 . ( 4 ) V A L I V . - B O S T R O M R. C., " R e v . of Scient. I n s t r . " 3 9 , 1304 (1968). ( 5 ) E I C H L E R H . - W I E S E M A N N W . , " Z e i t s c h r i f t a n g e w . P h y s . " , 2 8 , 129 (1969). ( 6 ) I I E R Z I N G E R G r . - L I N D N E R I I . , " P h y s i c s L e t t e r s " , 2 4 A , 6 8 4 ( 1 9 6 7 ) . ( ' ) D Y S O N F . J . , " A s t r o p h . J o u r n . " , 1 5 6 , 5 2 9 ( 1 9 6 9 ) . ( 8 ) C A P U T O M., " E l a s t i c i t à e dissipazione " , Zanichelli (1969). (») L U P A N O V C. A., " Z u r n . E k s p . Teor. Fiz. " , 52, 118 (1967); " Sov. PJiys. J E T P " , 2 5 , 7 6 ( 1 9 6 7 ) . ( 1 0 ) B O C C A L E T T I D . - D E S A B B A T A V . - F O R T I N I P . - G U A L D I C., " N u o v o Ci- m e n t o " ( 1 9 7 0 ) in press.