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VOLUME 42, NUMBER 9

PHYSICAL REVIEW LETTERS

26 FEBRUARY 1979

Improved Laser Test of the Isotropy of Space

A. Brillet(a) and J. L. Hall Joint Institute for Laboratory Astrophysics, National Bureau of Standards and
University of Colorado, Boulder, Colorado 80309 (Received 20 November 1978)

Extremely sensitive readout of a stable "etalon of length" is achieved with laser fre-
quency-locking techniques. Rotation of the entire electro-optical system maps any cosmic
directional anisotropy of space into a corresponding frequency variation. We found a fractional length change AZ/Z = (1.5±2.5)xlO"15, with the expected P2(cos#) signature. This null result represents a 4000-fold improvement on the best previous measurement
of Jaseja et al.

Our conventional postulate that space is isot r o p i c r e p r e s e n t s a n idealization of the null e x p e r i m e n t s of Michelson and M o r l e y 1 and the l a t e r i m p r o v e d e x p e r i m e n t s of J o o s . 2 L o r e n t z 3 and FitzGerald3 showed that a specific longitudinal contraction could account for the null result. In his study of the a x i o m a t i c b a s i s of the s p e c i a l t h e o r y of r e l a t i v i t y , Robertson4 has shown how this result may be combined with similarly idealized experimental results from the KennedyThorndike5 and Ives-Stilwell6 experiments to lead unambiguously to the s p e c i a l theory of r e l a t i v i t y , a s s u m i n g the constancy of the s p e e d of light. He shows that—between two inertial frames moving along x—the m e t r i c t r a n s f o r m s a s
ds2 = dt2-c~2(dx2 + dy2 + dz2), (1)
dsf2 = {gQdt')2 - c ' 2 [ ( g l d x f ) 2 + g22{dy'2 + dz'2)]0
The s p e c i a l t h e o r y of r e l a t i v i t y c o r r e s p o n d s to g0 = g1=:g2= 1» A r e c e n t L e t t e r s u m m a r i z e s the excellent a g r e e m e n t obtained in a wide v a r i e t y of p r e c i s i o n e x p e r i m e n t s with the p r e d i c t i o n s of special relativity,7 Still, major advances in the t h r e e fundamental e x p e r i m e n t s a r e c l e a r l y of strong scientific interest, since in general we have only finite experimental limits for the velocity o r a b s o l u t e orientational dependences of the g{. F o r e x a m p l e , the J o o s v e r s i o n 2 of the M i c h e l s o n - M o r l e y e x p e r i m e n t shows that g2/gl - 1 = (0±3) xlO"11.
The s e n s i t i v i t y advantage of l a s e r frequency metrology for length measurements was first pointed out by Javan and Townes, and with coworkers they were the first to apply laser techniques to a Michelson-Morley-type measurement.8 Unfortunately their length etalons were in fact lasers, and a serious systematic frequency shift (275 kHz) was observed as the apparatus rotated. Thus, although their excellent intrinsic laser stability ( - 3 0 Hz) gave a g l i m p s e of future m e t r o -

logical possibilities, the large spurious systemat-

ic effect limited their test for cosmic anisotropy to gjgx ~ 1 =±2 x l O " 1 1 . T h i s value is about 10"3

of the " p r e d i c t e d e t h e r d r i f t , " b a s e d on E a r t h ' s o r b i t a l velocity [(v/c)2 -10""8] and r e p r e s e n t s only

a small improvement over the Joos result0 The

present paper extends the null result by a factor

4000 below the value of J a s e j a et al.* to a f r e -

quency shift l i m i t of ±205 xlO""15, c o r r e s p o n d i n g

to ±5 x l O - 1 5 in

g2/g1-l.

Our experiment has been designed to be clear

in its i n t e r p r e t a t i o n and free of s p u r i o u s effects.

Its principle may be understood by reference to

Fig. 1. A He-Ne l a s e r (A = 3.39 /im) wavelength

is servostabilized so that its radiation satisfies

optical standing-wave boundary conditions in a

highly stable, isolated Fabry-Perot interferom-

e t e r B e c a u s e of the s e r v o , length v a r i a t i o n s of

this cavity—whether accidental or cosmic—-ap-

p e a r a s v a r i a t i o n s of the l a s e r wavelength. They

can be read out with extreme sensitivity as a fre-

quency shift by optically heterodyning a portion

of the l a s e r power with a n o t h e r highly stable laser, provided in our case by a CH4-stabilized9

laser. To separate a potential cosmic cavity-

length variation from simple drift, we arranged

to r o t a t e the d i r e c t i o n of the cavity length by

mounting the length etalon, its laser and optical

accessories, onto a 9 5 - c m x 4 0 - c m x l 2 - c m gran-

ite slab which, along with servo and power-supply

electronics, may be continuously rotated. (The

frequency readout beam comes from a beam

splitter up along the rotation axis and is directed

over to the CH4-stabiIized laser. Electrical pow-

er comes to the rotating table through Hg-filled

channels and a contactor pin assembly below the

table.) The table rotation angle is sensed via 25

holes pierced in a metal band under the table. A

single, separate hole provides absolute resyn-

chronization each turn. The laser beat frequency

is counted for 0.2 sec under minicomputer con-

Work of the U. S. Government

Not subject to U. S. copyright

549

VOLUME 42, NUMBER 9

PHYSICAL REVIEW LETTERS

26 FEBRUARY 1979

FIG. 1. Schematic of isotropy-of-space experiment. A He-Ne laser (3.39 /im) is servostabilized to a t r a n s mission fringe of an isolated and highly stable FabryPerot resonator, with provision being made to rotate this whole system. A small portion of the laser beam is diverted up along the table rotation axis to read out the cavity length via optical heterodyne with an "isolation laser" which is stabilized relative to a CH4-stabilized reference laser. The beat frequency is shited and counted under minicomputer control, these frequency measurements being synchronized and stored relative to the table's angular position. After 30 minutes of signal averaging the data are Fourier transformed and printed out, and the experiment is reinitialized.
trol after each synchronizing pulse, scaled and transfered to storage and display. A genuine spatial anisotropy would be manifest as a beatfrequency variation ocp2(cos#). The associated laser-frequency shift may be conveniently expressed as a vector amplitude at twice the table rotation frequency, / , of 1 per -10 sec. Furthermore, its component in the plane perpendicular to Earth's spin axis should precess 360° in 12 h.
Our fundamental etalon of length is an interferometer which employs fused-silica mirrors "optically contacted" onto a low-expansion glass ceramic10 tube of 6-cm o.d. x l - c m wallx30.5-cm length. The choice of 50-cm mirror radii provides a well-isolated TEMM mode. Dielectric coatings at the mirrors' centers provide an inter ferometric efficiency of 25% and a fringe width —4.5 MHz. The interferometer mounts inside a massive, thermally isolated Al vacuum envelope. The environmental temperature is stable to 0.2 °C.
Fringe distortion due to optical feedback is p r e vented by a cascade of three yttrium-iron-garnet

Faraday isolators, each having a return loss ^26 dB. The laser is frequency modulated -2.5 MHz peak to peak at 45 kHz. Both first-harmonic and third-harmonic locking were tried, the unused one being a useful diagnostic for adjustment of the Faraday isolators. Based on the 200-/iW available fringe signal, the frequency noise of the cavity-stabilized laser is expected (and observed) to be about 20 Hz for a 1-sec measurement, using a first-harmonic lock.
Our CH4-stabilized "telescope-laser" frequency reference system achieves a comparable stability.9 The random noise of the beat signal in a typical 20-min data block is observed to be - 3 Hz, compared with the laser frequency of almost 1014 Hz. To ensure absolute isolation of the cavity-stabilized and CH4-stabilized lasers, the latter actually is used to phase lock a "local oscillator" laser offset by 120 MHz. The -35MHz beat of this isolation laser with the cavitystabilized laser is the measured quantity.
The useful sensitivity of our experiment is limited mainly by two factors: drift of the interferometer (--50 Hz/sec) and a spurious nearly sinusoidal frequency shift at the table rotation r a t e / . This latter "sine-wave" signal was typically about 200 Hz peak to peak, and arises from a varying gravitational stretching of the interferometer, if the rotation axis is not perfectly vertical. The centrifugal stretching due to rotation is -10 kHz a t / = ( l turn)/(13 sec) and implies a compliance -10 times that of the bulk spacer material.
We find that taking data in blocks of N table r o tations (N - 8 - 5 0 ) is helpful in minimizing the cross coupling of these noise sources into the interesting Fourier bin at 2 cycles per table revolution (actually at 2N cycles per N table revolutions). Typically 10-20 blocks of N revolutions were averaged together in the minicomputer before calculating the amplitude and phase of the signal at the second harmonic of the table rotation frequency. The average result is an amplitude of cos20 of —17 Hz (2xl0~13) with an approximately constant phase in the laboratory frame. A number of such f-h averages spanning a 24-h period are illustrated in Fig. 2 as radius vectors from the origin to the open circles. The noise level of each such average was estimated by computing the noise at the nearby Fourier bins of 2N ± 1 cycles per N table revolutions. For a ^-h average {N= 10, averaged 10 times) the typical noise amplitude was 2 Hz with a random phase.
To discriminate between this persistent spuri-

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VOLUME 42, NUMBER 9

PHYSICAL REVIEW LETTERS

26 FEBRUARY 1979

+ Sidereal Frame o Lab. Frame
24 Hours 4 4 Points + RESULT=(0.67±0.73) Hz

SPATIAL ANISOTROPY
Reference Axis Parallel to Earth's Cosmic Velocity
3r^

220

230

250

Day Numbers (1978)

FIG. 2. Second Fourier amplitude from one day's data. The vector Fourier component at twice the table rotation rate is plotted as the radius vector from the origin to the open circles. After precessing these vectors by their appropriate sidereal angles they are plotted as the (+). For the 24-h block of data the average "ether drift" term is 0.67± 0.73 Hz, corresponding to Av/v = (0.76 ± 0.83) x 10"14.
ous signal (17-Hz amplitude at 2/) and any genuine "ether" effect, we made measurements for 12 or 24 s i d e r e a l hours. We must rotate each vector to obtain its phase relative to a fixed sidereal axis prior to further averaging. Averaging after this rotation leads, as shown in Fig. 2, to a typical 1-day result below 1± 1 Hz. Averages for 24 h w e r e sometimes quieter than 12-h averages, an effect which may be related to the o b s e r v e d 24-h p e r i o d of t h e floor tilt (« /xrad). A n u m b e r of 12- a n d / o r 24-h a v e r a g e s a r e shown in Fig. 3. T h e s e data include m o s t of the points taken during various diagnostic experiments, The data taken after day 238 correspond to app r o x i m a t e l y " i d e a l " a u t o m a t e d operation of the p r e s e n t a p p a r a t u s . The lack of any significant signal or day dependence allows us to perform an o v e r a l l a v e r a g e . This final r e s u l t of our e x p e r i m e n t is a null " e t h e r d r i f t " of 0.13 ±0.22 Hz, which r e p r e s e n t s a fractional frequency shift of ( 1 . 5 ± 2 . 5 ) x l 0 - 1 5 . F r o m Eq. (1) we have Av(20)/v = %[(g2/gi) - 1]> s o t h ^ o u r e x p e r i m e n t a l r e s u l t 1 1 c a n be w r i t t e n in the f o r m gjgx - 1 = (3 ± 5) x 10"15. We may conservatively use Earth's velocity around the sun to calculate the "expected" shift j>(v2/c2) ^ ( 1 0 ~ 8 ) , which gives a null r e s u l t 1 1 some 5xl0T7 smaller than the classical prediction. This limit represents a 4000-fold improve-

FIG. 3. Averaged data of isotropy-of-space experiment. Data such as those in Fig. 2, were averaged in blocks of 12 h (thinner bars) or 24 h (thicker bars). For completeness this figure includes data from diagnostic experiments before day 225. The data after day 238 represent near-ideal automatic operation of the present apparatus. A 1-Hz amplitude represents ~ 1.1 xlO"14 fractional frequency shift. The reference axis for the projection is the direction identified by Smoot et al. [11.0-h R.A. (right ascension),6° dec. (declination)], Ref. 12.
ment over the most sensitive previous experiment., This advance is due to smaller spurious s i g n a l s in our e x p e r i m e n t ( 2 x l 0 ~ 1 3 i n s t e a d of 1(T9), to superior data-processing techniques, and to s u p e r i o r l o n g - t e r m stability of the length etalon and reference laser.
The present sensitivity limit arises from two sources: the finite averaging time and some mechanical problems. To improve our result another decade by simple averaging would require 15 y r . The same decade improvement should be possible in several months' averaging, with improved mechanical design (rotation speed stable to 10"4 and the rotation axis actively stabilized to ±1") and better vacuum stability inside the interferometer (to reduce the drift).
The r e c e n t d i s c o v e r y of a p u r e P^cosfl) a n i s o tropy in the cosmic blackbody radiation was interpreted as a Doppler shift produced by our motion (~400 km/sec) relative to a "privileged" inertial frame in which the blackbody radiation is isot r o p i c . 1 2 If t h i s velocity i s c o n s i d e r e d to be the relevant one, our sensitivity11 is ~3xl0~9 and c o n s t i t u t e s the m o s t p r e c i s e t e s t yet of the L o rentz transformation. It will be especially interesting in the near future to develop techniques to

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VOLUME 42, NUMBER 9

PHYSICAL REVIEW LETTERS

26 FEBRUARY 1979

look even more sensitively for some extremely small residual "preferred frame" or generalrelativistic effects.13
We a r e grateful to James E. Faller for stimulation and for help in identifying our one-cycleper-revolution spurious effect. One of us (J.L.H.) thanks J. Dreitlein, J. Castor, and R. Sinclair for useful discussions of general-relativistic effects; he is a staff member of the Quantum Physics Division of the U. S. National Bureau of Standard. The other (A.B.) acknowledges receipt of a NATO fellowship. We strongly thank P. L. Bender for his long-term interest in the experim e n t The clever mechanical design work of Co E. Pelander has been indispensable. This r e search has been supported by the National Bureau of Standards under its program of precision measurement for possible application to basic standards, by the National Science Foundation, and by the Office of Naval Research.
(^Permanent address: Laboratoire de l'Horloge Atomique, Or say, France.
*A. A. Michelson and E. W. Morley, Am. J . Sci. 34, 333(1887).
2G. Joos, Ann. Phys. T_, 385 (1930). 3For the works of H. A. Lorentz and G. F . FitzGerald, see, e.g., C. Miller, The Theory of Relativity (Clarendon P r e s s , Oxford, 1972), 2nd ed., p. 27, and references therein. 4H. P . Robertson, Rev. Mod. Phys. 21, 378 (1949);

H. P. Robertson and T. W. Noonan, Relativity and Cos-
mology (Saunders, Philadelphia, 1968). 5R. J. Kennedy and E. M. Thorndike, Phys. Rev. 42,
400(1932). 6H. E. Ives and G. R. Stilwell, J . Opt. Soe. Am. 28,
215 (1938), and 31, 369 (1941). 7D. Newman, G. W. Ford, A. Rich, and E. Sweetman,
Phys. Rev. Lett. 40, 1355 (1978). 8T. S. Jaseja, A. Javan, J. Murray, and C. H. Townes,
Phys. Rev. 133, A1221 (1964).
J. L. Hall, in Fundamental and Applied Laser Phys-
ics: Proceedings of the 1971 Esfahan Symposium, e d -
ited by M. S. Feld, A. Javan, and N. Kurnit (Wiley,
New York, 1973), p. 463. 10CER-VIT is a registered trademark of Owens Illinois
Inc., Toledo, Ohio. 11 For comparison with earlier work we also omit a
0.43x sensitivity reduction factor associated with our
40° latitude and the assumed.P2(cos(v\l )) dependence. 12G. F . Smoot, M. V. Gorenstein, and R. A. Muller,
Phys. Rev. Lett. 39, 898 (1977), and references there-
in. 13For example, Earth's gravitational field would pro-
vide a positive anisotropy signal due to the variation of
the metric with height if the apparatus were to be rota-
ted in a vertical plane, although it seems quite likely
that this small fractional frequency shift (GM/R)(1/ c2){L/R) ^ 3x 10"17 with a P2 (costf) signature would be toally obscured by the P^cosO) signal arising from
gravitational stretching of the interferometer. We note
that the present experiments concern the behavior of
"rigid measuring rods" as distinguished from "atomic
clocks" used, e.g., in R. F . C. Vessot and M. W. Le-
vine, Center for Astrophysics (Cambridge, Massachu-
setts) Report No. 993, 1978 (to be published), and
references therein, and in Experimental Gravitation
(Academia Nazionale dei Lincei, Rome, 1977), p. 372.

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