Both values, however, give a critical half thickness below 500 A. Thus, we see that a 61m somewhat thinner than 1000 A could break up into a mixed state. Whether it does, however, depends on whether it is energetically
favorable to do so. There is, though, one further piece of information. Even though s is greater than 0.'707 in a
thin film, the order will probably be constant across
I. the film thickness d, for we can show that &d for
, d&d„;s;. t. From (35)

&/I-=

A

-H, (&)

)~&(&)-
(a/4)"'.

0.91 Hs Xr, (0)

For diffuse scattering, which gives the slightly larger estimate, we obtain from (42) the result
. a/1. =0.45, at r=o'X. , a=a„;„... (43)
For thinner fibns, higher temperatures, or specular scattering, a/I. is even smaller. Thus we see that the

order probably does not vary across the 61m thickness in a thin film.
To summarize our results, we have shown that a
simple nonlocal model previously used with some success to calculate the critical Gelds of superconducting Alms can also be used to calculate the GinzburgLandau-Abrikosov-Gor'kov parameters such as the weak 6eld penetration depth 80, the dimensionless
parameter lr, and the range of order parameter J.=be/lr.
We have calculated these quantities in the local limit and have shown that the results are in good agreement with those obtained by other techniques. We have also obtained simple expressions for these parameters which are valid in the thin limit. From these limiting formulas, we show that ~ can get large in a thin 61m and estimate that ~ exceeds the critical value of 1/V2 in indium films somewhat thinner than 1000 A. We also conclude that
in the thin limit, one would expect the order parameter to be constant across the 61m thickness.

PHYSICAL REVIEW

VOLUME 1 38, NUMBER SA

2 MARCH I964

Test of Special Relativity or of the Isotropy of Space by Use of Infrared Masers*
t T. S. JasEJa, J. A. JAvaw, MrraRav, aNn C. H. TowNEs
hfassaehlsegs Issststlge of Teehssofogy, Casnhrsdge, MassachusNs (Received 26 July 1963; revised manuscript received 30 October 1963)
The highly monochromatic frequencies of optical or infrared masers allow very sensitive detection of any change in the round-trip optical distance between two reflecting surfaces. Hence, comparison of the frequencies of two masers with axes perpendicular to each other allows an improved experiment of the Michelson-Morley type, or a very precise examination of the isotropy of space with respect to light propagation. Two He-Ne masers were mounted with axes perpendicular on a rotating table carefully isolated from acoustical vibrations. Their frequency difference was found to be constant to within 30 cps over times
as short as about one second, or to one part in 10"of the maser frequency, which is near 3)&10'4 cps. Rotation of the table through 90' produced repeatable variations in the frequency difference of about 2f 3 kc/sec, presumably because of magnetostriction in the Invar spacers due to the earth's magnetic 6eld. Examin. a-
tion of this variation over six consecutive hours shows that there was no relative variation in the maser frequencies associated with orientation of the earth in space greater than about 3 kc/sec. Hence there is no anisotropy or effect of either drift larger than 1/1000 of the smaH fractional term (o/e)s associated with the earth's orbital velocity. This preliminary version of the experiment is more precise by a factor of about 3 than previous Michelson-Morley experiments. There is reason to hope that improved versions will allow as much as 2 more orders of magnitude in precision, and that similar techniques will also yield considerably improved precision in an experiment of the Kennedy-Thorndike type.

~M~PTICAL and infrared masers make possible and attractive a number of new experiments, and re-
6nements of old ones, where great precision in measurement of length is needed. On type is the examination of the lsotlopy of space fol light pIopagatlon, ol more speci6cally the examination of what eGects the earth"s
~ Work supported by the U. S. National Aeronautics and Space Administration and by a Tri-Service Contract in the Research
Laboratory of Electronics. )Present address: Indian Institute of Technology, Kanpur,
India.

velocity or various other 6elds may have on the velocity of light. We have completed the 6rst stages of an experiment with He-Ne masers which can be regarded as equivalent to a Michelson-Morley experiment of improved precision. These preliminary tests show that the effect of "ether drift" is less than 1/1000 of tliat which might be produced by the earth's orbital velocity.
I. INTRODUCTION
A synoptic treatment of the connections between measurements in coordinate systems in relative motion

JASEJA, JAVAN, MURRAY, AN D TOWNES

has been given by Robertson, ' whose discussion wi11 be experiment'4 using the very high short-term frequency

fo11owed herc.

stability of an ammonia beam maser has examined go

In a four-dimensional Euclidean space, one may de- to still greater precision. In this experiment, two

6ne the metric as

ammonia - Inascl s werc Inountcd with thclr beams

" in a particular coordinate frame called the "rest sys-
tem. Clocks and rods are used to measure time-like or space-like intervals, respectively. In a second coordinate system moving along the x axis at ve1ocity e with respect to the 6rst one, the metric becomes
do'= ge'd1" (1/c—')Lgr'Ch"+gs'(dy"+ds")), (2)

moving in opposite directions, and changes in frequency
upon rotation of the whole system through 180' were
examined. Observation of zero change in the relative
frequency of the two masers upon rotation can be shown' to verify the value of go predicted by special
— relativity. Each one-day experiment of this type veri-
6ed the expected value of 1 ao' to an accuracy of about
— one part in 1000, Repetition of the experiment during
four seasons throughout the year extablished 1 u00 to

where the intervals dt', dx', etc., are measured by clocks and rods in the moving system similar to those used in
the'rest system. Robertson' shows that

an accuracy of about one part in 2000. The same type of experiment was repeated' with the two maser beams perpendicular to each other in order to examine isotropies corresponding to a different type of directional

dependence, and again a null result was found to within

the precision of the experiment, the frequencies remain-

ing unchanged due to reorientation in space by any
amount greater than one part in 10".

where uoo represents the transformation codtlcient be-
tween dt and dt', ul' that between d'h and dx', and u2'
that between dy and dy'. Examination of the transformation between two such cordinate systems thus in-
volves determination of three independent quantities,
I. uo', uj.', and a2', or go, g~, and g2. Special relativity pre-
dicts of course that go= g&= gm= Usually the "rest system" is assumed to be one which
is stationary with respect to the 6xed stars and is taken,
as in (1), to be isotropic. Actually, in such a system there is no a priori reason why at the earth the metric
need be isotropic, since matter and 6C1ds are not iso-
tropic about the earth, at least on a local scale. Hence even in the "rest" system one must regard the assump-

The rotating Michelson interferometer used by

Miche1son and Morley~ should have produced, on the

2«, 2«, — — — basis of an ether theory, a shift in fringes due to a change

'/I 1 (s/c)sj

'/I 1 (s/c)sjris m the optical

I. path length. Here is the length of the interferometer

arm, and this path length change is the result of a 90'

rotation of the interferometer when one arm is oriented

— along the velocity v. Since no path length change was
observed, one can conclude that ass= ar'L1 (s/c)']'is.

' The most pcrcise measurement with this type of appara-

tus has conclude

been that

made (us'

—bayt'

Joos, from whose work one can
)/as'=-,'(s/c)' to an accuracy of

about one part in 375.

tion ges=grs=ger=1 in (1) as only emPirically estab-
lished, and probably not exact. Thus an examination with very high precision of the va]ues of these three
quantities serves not only as a test of special re1ativity,

An optica1 or infrared maser consisting of excited atoms between two parallel reQecting plates osci11atcs at a frequency given by'

but also of whatever other anisotropy there may be in

the propagation As Robertson

of light. explains,

'

the

Michelson-Mor1cy

experi-

ment, the Kennedy-Thorndike experiment, and the

where p is the atomic frequency and v, = nc/2t. , where
I. e is an integer and is the plate separation, or more

Ives-Stilwell experiment in concert determine experi-
mentally the three independent quantities go, gi, and gm
since they measure gt/gs, ge/gt, and ge, respectively. The time transformation, or go, was measured by
— Ives and StilwelP with great precision in 1938. This
experiment determined the quantity 1 ao', or s (s/c)', to an accuracy of about one part in 30. A more recent

' '

H. P. Eok

Robertson, Rev. Mod. Phys.
added ie proof. For tests of

21, 378 (1949). anisotropy of other

kinds,

sReeevV. .L%ett.eHrsug4h,es3,42H(.1G96. 0R)o;bRin.so%n,.

and V. Beltran-Lopez,
P. Drever, Phil. Mag.

Phys. 6, 683

(1961};K. C. Turner and H. A. Hill, Bull. Am. Phys. Soc. 8, 28

(1963); and Refs. 3, 4, and 6 below.
~ H. E. Ives and G. R. Stilwell, J. Opt. Soc. Am. 28, 215 (1938);

31) 369 (1941).

3 J. P. Cedarholm, G. F. Bland, %. %. Havens, Jr., and C. H.

Townes, Phys. Rev. Letters 1, 526 (1958).

4 J. P. Cedarholm and C. H. Townes, Nature 184, 1350 (1959).

5 It is shown in Ref. 4 that an assumption of time dilation is

needed to produce the observed null effect, and hence the comment

is made that the maser beam experiment is more closely related to

the Kennedy-Thorndike experiment than to that of Michelson and

Morley. However, since the frequency of oscillation is essentially

determined by interactions between the vibrating ammonia

molecules and. the electromagnetic Geld, length does not enter in

any critical way into the experiment. Thus the maser beam experi-

ment is not precisely parallel to that of Kennedy and Thorndike

either bu.t measures go and is equivalent in this sense to the Ives-

Stilwell experiment.

~
'

J.
A.

P.
A.

Cedarhohn Michelson

and C. H. Townes (private communication).
and E. %. Morley, Am. J. Sci. 34, 333 (1887).

s G. Joos, Ann. Phys. 7, 385 (1930).

9 C. H. Townes, in Advances jw QgaNS@tn E/eeIrowks, edited by
J. R. Singer (Columbia University Press, New York, 1961), p. 3.

I TEST OF S P E C I AL RE LAT V I T Y OR OF I SOT ROP Y OF SPACE A1223

precisely 2L/c is the time for a round trip of the light
between the two plates. Q = p /Ac, where Av is the
half-width at half-maximum of the atomic resonance
and Q, =c,/Ac. , where hc, is the half-width at half-

maximum of the optical resonance between
Ordinarily, Q&)Q so that p=c, = ec/2L.

the plates.

If the separation between the plates is taken as Lo

and the "ether" is assumed to be streaming parallel to

— tLh1e—ax(sis/co)'f7.thSe immialasrelry,

at velocity s,
if the ether

then drift

c,(1)= (ec/2LO)
is perpendicular

to the axis, v, (2)= (nc/2LO)t 1 (e/c)'7'I'. lf two such

masers are oriented at right angles, their relative fre-

quencies would hence change on rotation between the
two 90' positions by

2L~.(2) —"(1)7=(s/i)'

Since (n/c)' for a velocity e equal to the earth's orbital

10, velocity is about

this represents a frequency

change of 3&&10' cps for infrared light of wavelength
one micron, or of frequency w, =3X10'4 cps.

In principle, this change of frequency can be examined

' " with great precision because of the almost monochro-
matic nature of maser radiation. Spontaneous emis-

sion produces a frequency spread for each maser oscil-

lator of"

2b= Smhc/P(hc. )',

(6)

where P is the power in the oscillations and hv i the

e1n0er'gyWoafnodnehqpu, /acn,tu=m10o'f,

the radiation. For
which are 6gures

a power typical

of of

He-Ne masers 2b is from (7) somewhat less than 1/10

cps. Thus if a measurement of frequency is only as

precise as this theoretical width, the fractional accuracy

is about 3 parts in 10", since the frequency v, is near

3)& 10'4 cps.

There is an additional frequency spread due to ther-

mal vibrations of the spacers used to hold the two

reQecting plates at a Gxed separation. The primary con-

tribution to this frequency variation comes from the

lowest frequency stretching mode of the spacers, which

changes L and hence from expression (5), the frequency. If these spacers are cylindrical, then the frequency

spread due to this effect is given by

28'= 2v (2k T/Y V)'i'

(7)

where kT is the Boltzmann energy at the temperature T of the spacers, Y is Young's modulus, and V is the
total volume of the spacers. For a typical case 8' is about 3 cps, and hence some-
what larger than 8. This still allows a precision of one
part in 10" if the frequency is determined within this
limiting frequency variation. Of course, in principle measurements over times much longer than 1/8' can
give a still much improved precision by allowing a determination of the center of the frequency band.
For He-Ne masers which are carefully isolated from

"A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940
(1958).

I I
I

I I

I

I I

I I I

I&

g

MASER NQ. 2

I ~I

I

SHOCK- PROOF

X

ROTATING TABLE

cx

th

X

A U TO- COL L I MATQR 10

HALF SILVERED'

MIRROR

I

PHQTQMULT IPLIER

I cz-&pz~o

pc c
I gccc

I I

oc

~

~ ~~ cn cc:
I cn cc.
~zp&g I ~ o I ~IL'cc: c'

~K
cn cn ccc

I
o I ~~'c 02 I

& & ccc
p cn ccc cn

I

I

I

RECEIVER
ill TH 30mc IF OUTPUT

~ ~ RECORDER

DISCRIMINATOR

IF AMPLIFIER

DC OUTPUT

30mc

ii 30mc

J

SPECTRUM

ANALYSER

FIG 1 Schematic diagram for recording the variations in beat

frequency between two optical
through 90' in space. Apparatus

maser on the

oscillators shock-proof

when rotated rotating table

is acoustically isolated from the remaining electronic and recording

equipment.

acoustical noises and other disturbances, and which

are stationary, a precision of deinition of frequency

within one order of magnitude of the above limit has

" been achieved, since spectral widths as narrow as about
20 cps have been demonstrated. If this precision is achieved while two masers are rotated 90' for the experj. -

ment discussed here, any change in relative frequency
as large as one part in 10" could be detected. This

would allow a very much improved comparison of g&

and large

g2,
as

and 10

'

detection of of the (s/c)'

any change term which

with rotation as might be associ-

ated with the earth's orbital motion.

EXPERIMENTAL ARRANGEMENT
The experimental arrangement is shown schemati-
cally in Fig. 1. A photodetector, a discriminator, and a recorder produced a continuous record of the fre-
quency difference between the two oscillating masers. The two masers mere mounted on a rotating shock-proof
platform with their axes at right angles to e@ch other. The experiment consisted basically in rotating the plat-
form back and forth 90' and observing the change in
frequency difference between the two masers. In order to obtain the best short-term stability and
monochromaticity from the masers, it is important to minimize acoustic disturbances, mhich may change L, the separation of the mirrors. For this purpose the platform and equipment on it, weighing about 200 lb, were suspended from a metal plate on four rubber shock cords about 3 ft long. The metal plate was in turn suspended from a 2-ft length of i6-in. -diam rod of beryllium copper attached to a beam. Resonant periods of the various motions of the platform were of the order of a few seconds, so that direct acoustic coupling to the building was quite low. Acoustic disturbances transmitted through the air seemed usually to be the dominating
» T. S. Jaseja, A. Javen, and C. H. Townes, Phys. Rev. Letters
10, 165 (1963).

Pro. 2. A plot of frequency variation between lasers
about 2'IS kc/sec. Markers indicate rotational anguiar
overshot the zero and 90' positions on each swing.

due to 90' rotation of the table. Vertical scale positions zero and 90'. Double markers appear

is such that maznnuln variatjon is because the total rotation slightly

ones. The assembly was in a basement vault which had. previously been a wine cellar, on MIT's Round Hill Estate at New Bedford, Massachusetts. The experimenters and parts of the apparatus which produced acoustic noise were outside the vault, and the building was otherwise unused at the time. Vibrations due to strong minds outside the building or to waves on the shore produced appreciable frequency disturbances at
times, so that the experiments mere carried out in quiet
weather.
Relative stability of the masers indicated, as noted earlier" short-term Quctuations of about 20 cps in each maser and a frequency drift of the order of 10 cps/sec
under the best conditions. Torsion of the beryllium-coppcr rod gave a rotational
oscillation period for the platform of about 20 sec, with
a decay time for the osciUation of the order of IO min. Hence the platform and masers could be rotated back
and forth about 90' at a frequency near resonance with
the application of a very gentle torque. This torque mas supplied by a motor-driven oscillating rod beneath the platform and coupled to it by a thin rubber band
about onc foot, long, which RgRln gRvc very good 1solRtion from acoustic vibrations of the building.
The rotating platform had four legs mhich cleared
the Boor by a short distance. On rotation, these legs interrupted a light beam, producing a marker on the recorder which indicated rather accurately a rotation
of 90'.
Even if external space is completely isotropic, one must expect that rotation will produce some variation in the frequency difference between the two masers due to local CBects. For example, the earth's magnetic Geld produces magnetostriction in the spacers which separate the maser mirrors and Zceman effects on the atomic spectra, each of which can RGect the frequency of oscil-
lation. Rotation of the table by 90' will vary these
efkcts. Aceleration of the masers due to the oscillatory motion of the table may also produce a relative frequency change if the two masers are not identically constructed.
To discriminate between these local causes of frc-
"T.S. Jaseja, A. Javan, and C. H. Townes, Phys. Rev. Letters
IO, 165 (1963).

quency variation with rotation and an effect associated with a more basic aniaotropy in space, the observations need only to be repeated throughout some large part of a day, as was done in the beam-type maser experi-
ment. '4 Thus at noon and midnight the earth's orbital
velocity is in the plane of the rotating table and an ether drift CGect should be maximum, whereas at sunrise and sunset the orbital velocity is more nearly perpendicular to the table and any cGect due to it must be a minimum. Local laboratory effects such as the earth's magnetic Geld do not, of course, vary systematically with the earth's rotation as would an ether drift.
EXPERIMENTAL RESULTS
The measured variation in relative frequencies of the tmo masers with rotational oscillation of the platform shown in Fig. 2, which is a recording of the output of the discriminator over a number of periods of oscillation
of the table. The markers separated by 90', which may
be seen on this recording, allom determination of the relative frequency change with a rather precise and
reproducable 90' rotation. The magnitude of this fre-
quency change is about 250 kc/sec, or somewhat less than that attributable to the earth's orbital velocity on the simple ether theory. The change is mostly associated, as indicated above, with local CBects such as the earth's magnetic Geld, and must be measured throughout some appreciable part of the day to allow detection of any more fundamental spatial anisotropy.
A recording of frequency variations with rotation mas made over a period of some minutes at each half-hour interval during a little more than six hours. On each
recording, the frequency change between 90' markers
was measured for about 5 complete oscillations. From these the mean changes and a probable error mere com-
puted. The resulting data from 6:00 a.m. to 12:00 noon on 20 January 1963, are shown in Fig. 3. The lengths of
vertical lines indicate the probable errors of each point,
which are about +4 kc/sec.
As indicated above, any sinusoidal variation with a tmclvc"houl pcl lod ln thc frequency shlf ts showI1 1n Fig. 3 could indicate an cGcct of "ether drift" or anisotropy in light propagation. The six-hour period plotted

TEST OI SPECIAL RELATI VI TY oR. oF iso TRop Y oF SPAcE A1225

represents one-half cycle of such a vm.'iation. A ver'y detailed statistical analysis of the possible variation
revealed by these points is probably not warranted be= cause of the ever troublesome question of possible systematic errors, and because the present experiment is a preliminary one, even though it does represent an im-
provement over proviously available measurements. It
is easy to see quickly from this figure that the frequency shift does not appear to change in a systematic way more than a few kilocycles. A somewhat more definite numerical result may be obtained by averaging the six points from 6:00 a.m. to 8:30 a.m. and comparing this
with the average of the six points from 9:30 a.m. to 12:00noon. The difference is 1.6 kc/sec, with a probable error of 1.2 kc/sec calculated solely from the fluctua-
tions. Similarly, one may compare the average of the
seven points between 7:30 a.m. and 10:30a.m. with the
average of the remaining points. The difference between
these averages is again 1.6 kc/sec, with a probable error of 1.2 kc/sec based solely on the fluctuations.
From the above, one can conclude that the amplitude of the sinusoidal variation in the frequency shift due to an "ether drift" equal to the earth's orbital velocity—
— that is, f (v/c)', where w is the earth's orbital velocity
and v is the maser frequency is not greater than 3 kc/sec, or is hence less than 1/1000 of the effect of an "ether drift" as large as the earth's orbital velocity.
DISCUSSION AND FURTHER EXPERIMENTS
The present preliminary experiment with optical masers already gives a useful improvement over previous precision with which a Michelson-Morley type of experiment could practically be carried out. However, the experiment is still far short of any real limits set by the technique. %hen the rotating table was at rest under favorable conditions, the two masers changed frequency with respect to each other by no more than about 30 cps during a few seconds time. This is four orders of magnitude less than the background variation due to magnetostriction or other effects when the table was rotated, and about two orders of magnitude smaller than the limit of error set by the present experiment for any more interesting effects of anisotropy.
The next planned step in this experiment is the use of quartz spacers between the mirrors to eliminate magnetrostriction effects. Hopefully, this will allow another

280-
ox 276-
I-
—272--
N
g 268- g
LDIJ
c3 264

260 6 00 I '

I
7.00

f.

I

I

800

f

I

I

I

9.00

IO.OO

TIME (HOURS)

I

I

II.OO

I
I 2 QO

FzG. 3. Plot of 90' rotation as a

relative function

frequency variation of the time of day

of two masers with
between 6:00 a.m.

and 12:00 noon on 20 January, 1963.

order of magnitude in precision of the search for any
anisotropy. It appears likely that great care in this
experiment may eventually allow two orders of magni-
tude improvement, or detection of any eGects of anisotropy as large as 6ve orders of magnitude less than the (n/c)' term associated with an "ether drift" when w is the earth's velocity.
It is clear from the introduction that the Kennedy-
Thorndike experiment, or the comparison of time and
length, already represents the greatest uncertainty in
an experimental test of transformation of the line ele-
ment in a moving coordinate system. Fortunately this
too may be now redone with considerable accuracy by the use of infrared or optical masers.
Equation (4) shows that the frequency of oscillation of masers may be primarily determined by the separa-
tion between mirrors (when Q&)Q ), or primarily by
the frequency of the atoms involved (when Q~)Q, ).
In the first case, the frequency depends primarily on a length and in the second primarily on a time. Hence,
if one maser of each type is mounted on the rotating
— table and any change of their frequency difference with
rotation observed, one determines go/(g2 g~). Such an experiment is hence equivalent for our purpose to the Kennedy-Thorndike experiment. This method appears to give an opportunity of improving the precision of the Kennedy-Thorndike result from about ~& of the (v/c)' term to about 1/1000 of this term, or possibly better. To obtain some improvement, it is not essential to produce two masers with the extreme characteristics
Q, )Q and Q )Q„but only to have the two depend
on the atomic resonance and the mirror separation, according to expression (4), in some appreciably different quantitative way.