APPENDIX A Gravity-Gradient Couplings to Torsion Pendants A.I Theoretical Formalism In searching for a hypothetical fifth force using a torsion balance, care must be taken to distinguish between the genuine signals for such a force and those arising from conventional gravity gradients. Since gravity gradients can produce large signals with characteristics similar to those of a fifth force, almost all torsion balance experiments dating back to EPF have gone to some lengths to reduce or eliminate these spurious influences. In this appendix we describe in detail the coupling of gravity gradients to torsion balances and give numerical results for some of the actual experiments. As before we denote the external gravitational field by §(P), where r =- x x + y f} + z z is the distance from the center of mass of the torsion balance to an infinitesimal mass point in the source. If ro denotes the position of the center of mass of the torsion balance relative to the center of coordinates then the gravitational torque T will be given by T = J r x [§(P - ra)dm(p)]. (A.l.l) We can expand § in terms of lA/Ira I to give -§(P - ro) = [Vxx + Vyf} + Vzz] + [(xV xx + YV xy + zVxz)x + (xV xy + yVyy + zVyz)i) + (xV xz + yVyz + zVzz)z] 1 [( 2TT 2 2 ) A + 2" x vxxx + y Vxyy + z Vxzz + 2xyV xxy + 2xzV xxz + 2yzV xyz x + (x 2 Vxxy + y 2 Vyyy + z 2 Vyzz + 2xyV xyy + 2xzV xyz + 2yzV yyz )f) + (x 2 Vxxz + y 2 VyyZ + z 2 Vzzz + 2xyV xyz + 2xzV xzz + 2yZV yzz )z] +... (A.1.2)
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APPENDIX A Gravity-Gradient Couplings
to Torsion Pendants
A.I Theoretical Formalism
In searching for a hypothetical fifth force using a torsion balance, care must be taken to distinguish between the genuine signals for such a force and those arising from conventional gravity gradients. Since gravity gradients can produce large signals with characteristics similar to those of a fifth force, almost all torsion balance experiments dating back to EPF have gone to some lengths to reduce or eliminate these spurious influences. In this appendix we describe in detail the coupling of gravity gradients to torsion balances and give numerical results for some of the actual experiments.
As before we denote the external gravitational field by §(P), where r =x x + y f} + z z is the distance from the center of mass of the torsion balance to an infinitesimal mass point in the source. If ro denotes the position of the center of mass of the torsion balance relative to the center of coordinates then the gravitational torque T will be given by
It should be noted that if we demand that the first-order contributions to T vanish, i.e., TP) = T~l) = 0, then Til) = 0 as well. This can be seen as follows:
hence,
A.l THEORETICAL FORMALISM 221
(1) _ n V; _ n TT _ fzVxVy _ fzVxVy = 0 Tz - {.y X {.x Vy - Vz Vz -. (A.1.5)
When we include higher-order terms in this balance condition, the effect of any imbalance is of order Vx/Vz and Vy/Vz, which we take for these calculations to be negligible. Requiring that Tx = Ty = 0 then gives from Eq. (A.1.3)
Ixixj and QXiXjXk in Eq. (A.1.7) are, respectively, the components of the moment of inertia and quadrupole moment tensors relative to the external coordinate system (i.e., the coordinate system in which VX;Xj and VX;XjXk are measured). We can re-express these in terms of the body-fixed coordinate system of the pendant by rotating these quantities about the z-axis, using the definitions in Eqs. (A.1.4b,c), where
x ---+ xcosO - ysinO,
y ---+ x sin 0 + y cos O.
(A.1.8a)
(A.1.8b)
We will henceforth refer to the values for the 1's and Q's defined in the external coordinate system as Ix;xj (0) and QXiXjXk (0) to distinguish these from the quantities in the body-fixed coordinate system. We then have
Ixx(O) = Ixx cos2 0 + Iyy sin2 0 - Ixy sin 20,
Iyy (0) = Iyy cos2 0 + Ixx sin2 0 + Ixy sin 20, Ixy(O) = Ixy cos 20 + (Ixx - Iyy) sin 20, Ixz(O) = Ixz cos 0 - Iyz sin 0,
Iyz (0) = Ixz sin 0 + Iyz cos 0, Izz(O) = Izz ,
(A.1.9a)
(A.1.9b)
(A.1.9c)
(A.1.9d)
(A.1.ge)
(A.1.9f)
222 GRAVITy-GRADIENT COUPLINGS TO TORSION PENDANTS
+ [( Qxxz - Qyyz) sin 2B + 2Qxyz cos 2B)(Vxxz - Vyyz )
+ [(Qyyz - Qxxz)cos2B + 2Qxyz sin2B]Vxyz
+ ~ (QyzZ cos B + Qxzz sin B) Vxzz + ~ (Qxzz cos B - Qyzz sin B) Vyzz
+ . . . (A.1.11)
where C3 = cos 30 and 83 = sin 30. It is sometimes convenient to rewrite the previous expression as a Fourier series expansion by explicitly identifying the coefficients of sin nO and cos nO:
- (Qyyy - 3Qxxy)(Vxxx - 3Vxyy )] cos 3(}. (A.1.12)
A.2 Gravity Couplings to Various Experimental Systems
We consider in this section the coupling of the higher gravity multipoles to various experimental systems. To do so we introduce the generalized multipole tensor
(A.2.1)
In terms of this notation, for instance, MOO~ is simply the total mass of the pendant, M 200 is the quadrupole moment lxx, Mlll is the octapole moment Qxyz, etc. The utility of the definition of Mnpq is that it allows us to express all of the multipole moments in terms of a single analytic expression. Additionally, this form is especially suited for generating the desired terms algebraically via software such as MATHEMATICA, or numerically via any standard numerical integration package.
A.2.1 The Eotvos Experiment This experiment [EOTVOS, 1922, 1953] utilized a two-mass pendant,
as described previously. In this arrangement, both masses were always cylinders, with the lower hanging mass being attached in such a way that the axis
224 GRAVITy-GRADIENT COUPLINGS TO TORSION PENDANTS
of symmetry of the cylinder was (nearly) parallel to the axis of the torsion fiber. The standard mass, however, was attached to the brass torsion bar such that its axis of symmetry was parallel to the brass torsion bar, which was itself perpendicular to the fiber. Letting quantities with the subscript "I" refer to the lower hanging mass, and "2" refer to the horizontal standard mass, we obtain for this system
A.2 GRAVITY COUPLINGS TO VARIOUS EXPERIMENTAL SYSTEMS 225
We take as typical values from [EOTVOS, 1922], m1 ~ 25.4g, m2 ~ 30.0g, i1 = 20.0cm, h ~ 21.2cm, L2 = 11.1 cm, and R2 ~ 0.2cm. We also insert into Eq. (A.1.12) representative values for the various gravity gradients which are taken from our best model of the site of the Eotvos experiment [BOD, 1991]. We obtain for the net gravitational torque
T ~ -{ (0.378 + 0.478L~ - 1.43RD sinO
+ (1.33 + 1.42L~ - 4.27RD cosO - 5.56 sin 20 - 0.0944 cos 20
- 0.0290 sin 30 + 0.0780 cos 30} X 10-10 N m. (A.2.4)
Here L1 and R1 are expressed in units of meters, and we have used the convention of EPF that a positive torque is one which would tend to rotate the torsion bar clockwise as viewed from above. Eq. (A.2.4) gives values for the experimental quantities v and m defined by EPF (see Section 4.2) which are roughly in the correct proportion to the values they actually obtained, although these values are too large by a factor of '" 2.
The gravity-gradient contributions to T in Eq. (A.2.4) are large compared to the limits quoted by EPF for the validity of the equivalence principle, or to the size of the claimed signal for the fifth force, as inferred by [FISCHBACH, 1986A]. This is, of course, not surprising, since the EPF apparatus was originally designed to measure gravity gradients, which was the purpose of the set of experiments performed by Eotvos in the mountains of Hungary [EOTVOS, 1953]. To cancel out the effects of gravity gradients, EPF combined the results of measurements made with the torsion balance oriented in different directions, as explained in Section 4.2.
The fact that the EPF experiment was as sensitive as it was to gravity gradients leads to the suggestion that perhaps the correlation in the EPF data suggesting a fifth force is actually due to some uncanceled gradient coupling. A model of this sort suggested by Stubbs has been analyzed by Talmadge [1987 A], who shows (using the preceding analysis) that the gradient couplings are too small by roughly a factor of 10 to account for the EPF data.
A.2.2 The Eot-Wash Experiment In this section, we consider the coupling of gravity gradients to the
pendant in the experiment of Stubbs et al. [STUBBS, 1987]. The pendant for this experiment consisted of two hollow eu cylinders and two solid Be cylinders. All of the cylinders had a length L = 1.908 cm, radius R = 0.9525 cm, and mass M = 10.04 g. These were situated at the four corners of a square whose side was S = 3.9 cm, with the Cu masses being located at adjacent corners. In this discussion, we consider only the effects arising from
226 GRAVITy-GRADIENT COUPLINGS TO TORSION PENDANTS
the gravitational coupling of the compensating lead bricks to the difference in the density distribution between the two Cu masses and the two Be masses. We note that there will also be, for instance, effects due to the misalignment of the vertical positions of the centers of mass of the cylinders, which we are ignoring. For this mass configuration we then have
127r 1R-t 1L / 2 - t - PCu d¢ dr r dz (reos ¢ + S/2t(r sin ¢ + S/2)P(z - 8Z4)Q.
o 0 -L/2+t (A.2.5)
In this equation 8z1 , ... , 8z4 represent the errors in the vertical positioning of the centers of mass of the test bodies and, as mentioned above, will be taken to be zero for this analysis. Also, t ~ 0.71 mm represents the thickness of the Cu cylinders and their end caps (assumed for this analysis to be the same). The analytic forms of the various mass multipoles, which are somewhat involved, are not particularly useful in this case. For this reason, only the numerical results for the nonzero mass moments are quoted here:
Ixx = Iyy = 1.643 X 10-5 kgm2 ,
Izz = 1.553 X 10-6 kg m2 ,
Qxxx = 1.464 X 10-8 kg m3 ,
QXYy = 4.882 X 10-9 kg m3 ,
Qxzz = 6.519 X 10-9 kg m3 .
(A.2.6a)
(A.2.6b)
(A.2.6c)
(A.2.6d)
(A.2.6e)
The configuration we use for the compensating lead bricks is that described by Stubbs et al. [1988A]. In the present analysis, the configuration was built up of two parallelepipeds whose centers of geometry were along the +x-axis, with the origin of coordinates at the center of mass of the pendant, and the +z-direction pointing upwards along the torsion fiber. Both parallelepipeds
A.2 GRAVITY COUPLINGS TO VARIOUS EXPERIMENTAL SYSTEMS 227
Table A.1: Dimensions of the compensating masses in the experiment of Stubbs et al. [STUBBS, 1987, 1988A]' as used for the analysis this appendix. The coordinate positions given are for the faces of each parallelepiped along the coordinate axis to which it is perpendicular. All dimensions are given in inches, and the parallelepipeds were composed of lead, for which PPb 9:! 11.35gcm-3 .
were so aligned that their faces were parallel to the coordinate planes, with the coordinate positions along the axis perpendicular to each face given in Table A.1.
For this configuration we find for the nonvanishing components of the various (relevant) gravitational gradients
gx = +6.42 x 1O-8 ms-2,
gz = +2.31 x 1O-8 ms-2,
Vxx = -3.75 X 10-7 S-2,
Vyy = +2.02 X 10-7 S-2,
Vxz = -2.80 X 10-6 s-2,
Vxxx = -2.80 x 1O-6 m-I s-2, V xyy = +1.65 x 10-6 m- I S-2,
Vxxz = -2.91 x 1O-6 m-I s-2,
Vyyz = +0.63 X 10-6 m-I s-2,
Vxzz = +1.15 x 1O-6 m- I s-2, Vzzz = +2.29 X 10-6 m- I S-2.
(A.2.7a)
(A.2.7b)
(A.2.7c)
(A.2.7d)
(A.2.7e)
(A.2.7f)
(A.2.7g)
(A.2.7h)
(A.2.7i)
(A.2.7j)
(A.2.7k)
Substituting the results of Eqs. (A.2.6) and (A.2.7) into Eq. (A.1.12) gives
r(z) 9:! 9.4 x 1O-I6 sinBNm, (A.2.8)
with all other terms being negligible. To make a connection between this result and the experiment of Stubbs et al. [STUBBS, 1987], we write
(A.2.9)
228 GRAVITy-GRADIENT COUPLINGS TO TORSION PENDANTS
Since T ~ 420 s and I ~ 3.28 X 10-5 kg m2 , for this experiment, we then have K ~ 7.34 X 10-9 N m, and the implied net angular deflection is then 9.4 x 10-16 /7.34 X 10-9 ~ 0.13 fLrad. Comparing this value to the quoted result of Stubbs et al. which is 0.53 ± 0.59 wad, we see that this particular systematic was not a problem for the Stubbs experiment.
APPENDIX B
Luther-Towler Cavendish Experiment
B.l Theoretical Formalism The classic experiment of Luther and Towler [LUTHER, 1982; BAGLEY,
1997] is among the most accurate measurements of G in the laboratory. Since this result is used in many other experiments, it is important to understand the relationship between the measured value Ge = (6.6726 ± 0.0005) N m2 kg-2 and the Newtonian constant Goo. The following discussion illuminates how one analyzes the effects of non-Newtonian gravity on various laboratory measurements, such as the determinations of Ge, which were carried out for purposes other than studying non-Newtonian gravity .
- ::-L djsk
.... . ", .t:) .
t.::.. :
Figure B.t: Schematic diagram of apparatus used in the laboratory measurement of G by Luther and Towler [LUTHER, 1982).
The experimental arrangement for Luther and Towler is shown in Fig. B.l. The apparatus involved a small tungsten mass mounted in a dumbbell configuration suspended from a torsion fiber, and two large attracting masses also composed of tungsten. The experiment consisted of accurately constructing and measuring the mass configuration, and then comparing the predicted shift in frequency of the pendant for this configuration, with and
230 LUTHER-TOWLER CAVENDISH EXPERIMENT
without the attracting masses present, to the actual measured frequency shift of the system. The various dimensions and constants of the experiment are given in the Table B.l.
Table B.I: Physical constants for the experiment of Luther and Towler.
Constant Description Value
Ldisk length (thickness) of disk 0.0025472m
I!disk lever arm of disk 0.0155472m
Rdisk radius of disk 0.0035830m
Tdisk separation distance between disk & sphere 0.0547501 m
Lbar length of bar 0.0285472m
I!bar lever arm of bar 0.0071368m
Rbar radius of bar 0.0005174m
Tbar separation distance between bar & sphere 0.0631605m
Rsphere radius of sphere 0.05082545 m dB distance between sphere & center of pendant 0.07029727 m
mdisk mass of disk 0.001983 kg
mbar mass of bar 0.0004633 kg
msphere mass of sphere 10.490070 kg
Psphere inferred density of sphere 19074.2 kg/m3
As discussed above, Luther and Towler measure the frequency shift resulting from the introduction of the spherical attracting masses. If we let I be the moment of inertia, D the drag coefficient, K the torsion constant for the torsion balance, and e the angle between the torsion bar and the line connecting the centers of mass of the attracting spheres, then we can write from Eq. (4.2.50)
Ie + De + Ke = -Tme, where Tme is the torque produced for small deviations from e presence of T m leads to a shift in frequency given by
K D2 2_ Wo = I - 412.
2 2 Tm W =WO+y,
In this case, T m is given by
Tm = msphere Cdisk (gdisk - ~Fdisk '1>sphere)
+ msphere Cbar (gbar - ~Fbar '1>sphere ),
(B.l.I)
O. The
(B.l.2)
(B.l.3)
where the various acceleration terms gdisk, gbar, Fdisk, and Fbar are all calculated at e = 0, and
'1> sphere = '1> (Rsphere / A) , '1>(x) = 33 (xcoshx - sinh x). X
(B.I.4)
B.l THEORETICAL FORMALISM 231
The pendant configuration, which is composed of cylinders aligned along their axes relative to the center of mass of the sphere, is a particularly simple one in which to calculate both the gravitational and non-Newtonian torque contributions. The gravitational acceleration is given by
G - G fdisk (9disk - eFdisk <Psphere) + fbar (9bar - eFbar <Psphere) C - 00 (disk gdisk + (bar 9bar ' (B.1.12)
== Goo [1 - e<psphere <Ppendant] , (B. 1. 13)
if,. _ fdisk Fdisk + fbar Fbar (B 4) "'-pendant - f f ' .1.1
disk 9disk + bar 9bar
where
9bar = geyl (rbar; Rbar , Lbar /2),
Fbar = Feyl (rbar ; Rbar , Lbar /2),
9disk = geyl (r disk ; ~isk , Ldisk ),
Fdisk = Feyl (rdisk; Rdisk , Ldisk).
In terms of the quantities listed in Luther and Towler [1982],
Dbar -2-'
Ldisk Lbar =-2-+-2-'
(B.l.15)
(B.l.16)
(B.L17)
(B.L18)
(B.L19)
(B.L20)
(B.L21)
B.2 DISCUSSION OF RESULTS 233
Ddisk Rdisk = -2-' (B. 1.22)
l Ldisk disk = -4-' (B.1.23)
r disk = ds - ldisk , (B.1.24)
He Dsphere phere = 2
(B.1.25)
B.2 Discussion of Results
The operative equations in the previous section are Eqs. (B.1.13) and (B.1.14), which express the>. dependence of the laboratory measurement of G in terms of the Newtonian constant Goo:
It is useful to note that the "form factors" cPsphere (>.) and cPpendant (>.) factorize in this equation due to the presence of the spherical attracting mass. This result is easily shown to hold for the attraction of a spherical mass to any other mass of arbitrary shape.
To understand Eq. (B.2.1), we note that
(B.2.2)
The constant Go has the interpretation of the effective value of G for distance scales which are small compared to >.. Although it is often assumed that >. is large compared to the scale of laboratory measurements of G, one must also allow for the possibility that >. is comparable to this scale as well. We can combine Eqs. (B.2.1) and (B.2.2) to write
where ~Gc(>') = Gc(>') - Goo and ~Go = Go - Goo. The product cPsphere cPpendant can thus be interpreted as the fractional difference of the value of Gc between Goo and Go. The fraction ~Gc(>')/ ~Go is exhibited in Fig. B.2 as a function of >., in the model of Eq. (2.1.8).
234 LUTHER-TOWLER CAVENDISH EXPERIMENT
1.0
0.8
t.:J0 0.6 <I >-~ '(, 0.4 t.:J <I
0.2
0
101 10° 101 1et 103
A [em]
Figure B.2: The fractional difference b.Gc()")/ b.Go as a function of ).. plotted for the experiment of Luther and Towler. Note that for distances much less than a few centimeters, the expected value of Gc()") would be very nearly that of Goo, and it is only at distances larger than or comparable to one meter that Gc()") --> Go.
APPENDIX C
The Earth's Gravity Field
e.l Formulation of the Model
For a spherically symmetric nonrotating mass distribution, the local acceleration of gravity g(z) may be written as
GM(z) g(z) = (Rtf1 _ z)2' (C.l.l)
where G is the Newtonian constant of gravity, Rtf1 is the radius of the Earth, and M(z) is the total mass inside the sphere of radius (Rtf1 - z). Since in all of the geophysical experiments performed to date z « Rtf1 , we may expand Eq. (C.l.l) in small quantities to obtain [STACEY, 1977, 1983]
where p(z) is the local density as a function of depth. The above expression may be rewritten in the suggestive form
6.g(z) == g(z) - g(O) = U(z) - 47fGX(z),
U( ) = 2g(0) z Rtf1 z,
X(z) = 1z dz' p(z').
(C.l.3)
(C.l.4)
(C.l.5)
As discussed in Section 3.4, U(z) characterizes the increase in g(z) resulting from moving closer to the center of the Earth in the limit that p(z) ---+ 0 (Le., the "free-air gradient" term), and -47fGX(z) is the "double-Bouguer" term, which represents the decrease in g(z) resulting from removing the mass above the sphere of radius (Rtf1 - z).
Note: This appendix has been adapted from [TALMADGE, 1989B].
236 THE EARTH'S GRAVITY FIELD
Stacey et al. [STACEY, 1983] introduced a refinement of the above model by including effects due to ellipticity and rotation. They assumed that the Earth could be modeled as an elliptically layered structure, with each ellipsoidal surface of constant density having the same ellipticity.
Under this assumption, only the mass interior to the ellipsoidal shell passing through the point z will contribute to the gravitational acceleration g(z). The gravitational acceleration of the ellipsoidal body interior to z, including both Newtonian gravity and the centrifugal acceleration due to the rotation of the Earth, is then given to first order by the formula [STACEY, 1977]
(C.l.6)
where
(C.l.7)
is the distance from the center of the Earth to the surface of the Earth at the latitude ¢s at which the experiment is being performed. In Eq. (C.l.6) C(z) and A(z) are the axial and equatorial moments of inertia of the interior ellipsoid, P2(X) = ~(3x2 - 1) is the usual second Legendre polynomial, and w ~ 7.292115 X 10-5 rad s-1 is the angular rotation rate of the Earth. Keeping only terms of 0(1) in small quantities, Stacey et al. [STACEY, 1983] found
U z) ~ -z 1 + -- - 3J2 P2 sm ¢s) + 3w zcos ¢s, ( 2gs [ 3 z ( . 2] 3 2 rs 2 rs
(C.l.8)
c [ z 1 ( c2 )] l z 2 l z X(z) ~ - 1 + 2- + - 1- 2" dz' p(z') - - dz' z'p(z'), (C.l.9)
a rs 2 a 0 rs 0
where the subscript s denotes surface values, a and c are respectively the equatorial and polar radii of the Earth, and h is the height above sea level of the surface of the Earth at (rs, ¢s). Dahlen [1982] has noted that although Stacey et al. explicitly assumed a constant ellipticity with depth, which is clearly not the situation for the Earth, Eqs. (C.l.8) and (C.l.9) hold even when the effects from a variation of ellipticity with depth are included, provided one assumes that the Earth is in hydrostatic equilibrium.
Although the model of Stacey et al., when augmented by Dahlen's observation, appears to properly describe the effects of variable ellipticity, it would be useful to formulate an Earth model in which such effects were included from the outset. This would allow us to more easily examine certain questions such as i) the variation of g(z) with depth, ii)the magnitude and orientation of a possible fifth force field of the Earth for large ranges (,X r-..J Rtfj), and iii) the validity of various simplying assumptions that are usually made,
C.1 FORMULATION OF THE MODEL 237
such as the neglect of matter circulation, the neglect of distant topographic features , or the assumption of an oblate-spheroidally layered density distribution. This third point will be discussed in more detail below. We first enumerate the principal assumptions in this formulation:
1) The Earth can be represented by an oblate-spheroidally layered density distribution given by p(r, ¢).
2) Surfaces of constant pseudo-potential V align with surfaces of constant density p and constant pressure P to first order in the oblateness f. This is equivalent to the assumption that the Earth is in hydrostatic equilibrium.
3) The angular velocity w is constant throughout the Earth. 4) Nonradial accelerations are negligible (Le. , the effects of circulating mat
ter in the mantle are small).
North Pole
South Pole
Figure C.l: Pictorial representation of the relevant parameters of an Earth model with variable ellipticity. For a definition of these parameters see Table C.l.
We may now introduce a new nonorthogonal coordinate system (u, ¢, 'IjJ), where the "oblate spheroidal radius" u is related to the radius r via
r = u [1 - €(u)P2(sin¢)]. (C.l.IO)
238 THE EARTH'S GRAVITY FIELD
Table C.l: Table of notation used for calculating the Earth's gravity field. The equation numbers indicate where each quantity first appears in this appendix. The entries appear in alphabetical order.
Notation Description Equation
~M(z)
~g(z)
e TJ p(z)
</>
1/J w
A a C c
f. fo G
9 g(O),g. J2 P2(sin</» T
T., </>.
M(z) M. RfJ! U(z) u
X(z) z
mass difference = M. - M(z) . gravity difference = g(z) - g. eccentricity of Earth's figure . normalized derivative of ej TJ == ~ ~~ density as function of depth z geocentric latitude . longitude. angular rotation rate of the Earth
w ~ 7.292115 X 10-5 rad S-l
equatorial moment of inertia equatorial radius of the Earth ~ 6378 136 m axial moment of inertia polar radius of the Earth ~ 6356751 m . oblateness of the Earth's figure = 3e/2
(C.2.8) (C.1.3)
(C.l.!O) (C.l.!6) (C.1.2) (C.1.6)
(-)
(C.1.6) (C.1.6) (C.1.9) (C.1.6) (C.1.9)
centripetal acceleration scale parameter = w2u~/GM. Newtonian constant of gravity.
(C.2.4) (C.1.25) (C.l.!) (C.l.!) net gravitation acceleration
gravitational acceleration at surface . quadrupole moment of the Earth ~ 0.001082635 second Legendre polynomial = ~ sin2 </> - ~ •
distance to center of Earth radius, geocentric latitude of experiment on
the Earth's surface Earth's mass at depth z Earth's mass at the surface ." mean radius of Earth free-air gradient contribution to ~g(z) oblate spheroidal radius defined by
Here ¢ and 1/J measure the geocentric latitude and longitude respectively, and c(u) is defined so that p(r, ¢) = constant on surfaces of constant u. (See Fig. C.1 and Table C.1 for the definitions of various physical quantities.) Starting from Eq. (C.1.1O), the Newtonian gravitational potential can be explicitly written as [JEFFREYS, 1970]
VN(r,¢) = Vi(r,¢) + v;,(r,¢),
47TG r Vi(r, ¢) = -3r 10 du' p(u')
(C.1.11)
x ;" [U'3 - ~ ( :: ) c( U')P2 (8m ¢) l' (C.l.12)
47TG rs
Ve(r, ¢) = --3- lu du' p(u')
a [3,2 3 2 (') (. )] X au' 2"u - 5"r c u P2 sm ¢ . (C.1.13)
Here Vi denotes the potential arising from the mass interior to the oblate spheroid passing through (r, ¢), and v;, is the potential due to the mass exterior to (r, ¢). Expanding these equations gives
The content of assumption (2) above is that Veff must be a function of U
only, for U :S us. That is,
(C.1.19)
(We have used the fact that c(r) = c(u)+O(c2) to obtain the above relation.) This implies that the coefficient of P2(sinq'J) in Veff(u) must vanish for points interior to the surface of the Earth. This requirement leads to Clairaut's equation (see for instance [TASSOUL, 1978]), which we write in the form
where
d17 p( u) u-d + 6-(-) (17 + 1) + 17(17 - 1) = 6,
u Pm U
Pm(U) = 33 r p(U')U,2du', u io 17(U=O)=O.
From Eq. (C.1.16) we also have
c(u) = c(us) exp { _luS du' 17~')},
where
and W 2U3 w2a3
f, s '" 0= GMs = GMs'
(C.1.20)
(C.1.21)
(C.1.22)
(C.1.23)
(C.1.24)
(C.1.25)
and where Us is the value of u on the surface of the Earth. (An alternative notation used by some authors is m = w2a3/GMs. We introduce the symbol fo to avoid confusion of m with the mass.)
As discussed above, the coefficient of P2 (sin q'J) in Veff( u) is required by assumption 2) to vanish, and when this requirement is enforced, we are left with
The gravitational acceleration §( r, q'J) is thus given by
It is in principle possible to directly evaluate Eq. (C.1.37) to obtain an analytic result for J2 • In practice, however, it is much easier to obtain h by imposing the requirement that §(r, ¢) be continuous across the boundary rs(¢) = us[l - csP2(sin¢)]. For simplicity we look at only gq,(r, ¢), from which we find at the point (r=rs(¢), ¢):
(C.1.39)
Solving Eq. (C.1.39) for h and using Eq. (C.1.25) gives
(C.1.40)
The effective gravitational acceleration field in the frame of reference co-rotating with the Earth is given by Eq. (C.1.32) [u:=:; us] and Eq. (C.1.38) [u 2: us] for all values of rand ¢. Using Eq. (C.1.32) and the density distribution given by the Preliminary Reference Earth Model, [DZIEWONSKI, 1981]' we can evaluate g = I§I as a function of depth z, and the result is shown in Fig. C.2. We note that for z ;'S 2500 km, g is approximately constant as a function of depth. This well-known result [STACEY, 1983; FISCHBACH, 1987] can be understood as arising from the near cancellation of the free-air gradient and the double-Bouguer terms in the upper layers of the Earth.
12
cp= 45° 10
........ ~ 8
CIl
S '--' 6
~ ~ 4 c.o
2
0 0 0.2 0.4 0.6 0.8 1.0
x = rlrs (CP)
Figure C.2: Variation of the local acceleration g(x) as a function of x = r/rs(¢). As noted in the text, g(x) is approximately constant for x ;::: 0.6, corresponding to depths z ;S 2500 km.
C.2 ApPLICATIONS OF THE EARTH MODEL 243
We also obtain from this first-order theory a calculated surface oblateness is 9:! 1/299.9, which is in reasonable agreement with the results of earlier higher order analyses, such as that of Jeffreys [1963], who obtained is 9:! 1/299.67. However, the values for is obtained from hydrostatic theory are not in good agreement with the value inferred from satellite observations [RAPP, 1987], which give is = 1/298.257. The 0.5% discrepancy between the results obtained from these two methods is well known in the geophysics literature [STACEY, 1977], and is commonly interpreted as a breakdown of the assumption of hydrostatic equilibrium. As is noted by Stacey [1977], the nonequilibrium component of the Earth's mass distribution appears to be constrained to reside in the upper mantle, and is probably dynamically maintained. If the only effect of the nonequilibrium distribution were to change is or Es by 0.5%, it is clear that these effects would be negligible on the scale of a first-order theory. However, if the nonequilibrium mass resides in the upper mantle-perhaps within a few hundred kilometers of the surface-then it may be necessary to consider the direct effects of this mass on the free-air gradient. Such a treatment is, however, beyond the scope of the present discussion.
C.2 Applications of the Earth Model
We first wish to demonstrate that Eq. (C.1.32) above, which is the interior solution to the effective gravitational acceleration in the Clairaut formalism, gives the "standard gravity equation" for the magnitude of the net gravitational acceleration at the surface of the Earth. Taking the magnitude of Eq. (C.1.32) and evaluating at the surface gives
(C.2.1)
where as usual the subscript s denotes a quantity evaluated at a = as. We note that
and hence
(C.2.3)
and
(C.2.4)
244 THE EARTH'S GRAVITY FIELD
where a is the equatorial radius and Is is the oblateness. From Eq. (C.l.24), we also find
5 2 ss(1 +1]s) = 3/0 - 31s. (C.2.5)
Combining Eqs. (C.2.1)-(C.2.5) gives
(C.2.6)
(C.2.7)
This result is identical in first order to the standard surface gravity equation for the Earth [JEFFREYS, 1970; STACEY, 1977].
We next wish to rederive the results of Stacey et al. in Eqs. (C.l.8) and (C.l.9) starting from Eq. (C.l.32). Writing z = rs - r, we have
where !:l.M(z) == Ms - M(z). We wish to expand this equation about the point z = 0 in small quantities. For this purpose, we treat z2 / r;, S s, and w2rs/gs as 0(1) quantities. We write s(z) as
s(z) ~ Ss + z ddS I = Ss (1 -1]S~) . z z=o rs
(C.2.9)
Employing Eq. (C.l.20) and dropping higher order terms, we find for 1](z),
( ) (1 z ) 87rr;(1 + 1]s) l z d' ( ') 1] z = 'f}s - 'f}l - + M z P z , rs s 0
'f}l = l-1]s + 6/1]s.
(C.2.1O)
(C.2.11)
We next note that while in principle cp = cp(z), we have for the difference
sin2 CPs - sin2 cp(z) = ~ss sin2 2cps, 2rs
(C.2.12)
which is of 0(1). However since sin2 cp(z) always multiplies quantities of 0(1) or higher, then to first order we can write cp(z) ~ CPs. The mass difference !:l.M(z) may be obtained by first writing the mass as a function of u,
(C.2.13)
C.2 ApPLICATIONS OF THE EARTH MODEL 245
Upon substituting u = r[I + c(r)P2(sin¢s)], this becomes
(C.2.I4)
Finally making the substitution z = r s - r, we find for b.M (z) = Ms - M (z),
If we make the substitution cs = J2 + 10/3 in Eq. (C.2.I9), we recover Stacey's expression for U(z) given by Eq. (C.1.8). Similarly, we note that the only difference between Eq. (C.2.20) and Stacey's expression for X(z) given by Eq. (C.1.9) is the coefficient of the first integral. This coefficient from Eq. (C.1.9) is
c [1 2z 1 (a2 - c2 )] - +-+- -- . a rs 2 a2
(C.2.2I)
246 THE EARTH'S GRAVITY FIELD
Making the substitution cja = 1 - is, Eq. (C.2.21) becomes
Thus to 0(1) in is, Eq. (C.2.20) is identical to the result of Stacey et al. in Eq. (C.1.9).
C.3 Discussion
We have developed in Section C.1 a detailed model of the Earth's acceleration field g(r, cp), from which 9 can be calculated at any point inside or outside the Earth. Our starting point is somewhat different from that of Stacey et al., in that we allow at the outset for a variation of ellipticity with depth, and employ a formulation valid for all values of r and cp, not just for those values for which z2 jr~ «1. However, our results as given in Eqs. (C.1.32) and (C.1.38) were shown in Section C.2 to be identical to those of Stacey et al., to lowest order in various small quantities (such as the oblateness i, w2rjg(r,cp), and z2jr~).
Although we have demonstrated the equivalence of the two models in first order, it should be kept in mind that this "equivalence" was obtained by making a number of simplifying assumptions. While the standard arguments for the validity of these assumptions seem quite compelling, they must be carefully scrutinized, since they might eventually lead to the suggestion of non-Newtonian gravity.
Bibliography
[ACHILLI, 1997] V. Achilli, et al., "A geophysical experiment on Newton's
inverse-square law," Nuovo Cimento 112B, 775-804 (1997).
[ADELBERGER, 1987] E. G. Adelberger et al., "New constraints on composition
dependent interactions weaker than gravity," Phys. Rev. Lett. 59, 849-852
(1987).
[ADELBERGER, 1990] E. G. Adelberger et al., "Testing the equivalence principle
in the field ofthe Earth: Particle physics at masses below 1 p,eV?" Phys. Rev. D 42, 3267-3292 (1990).
[ADELBERGER, 1991A] E. G. Adelberger, B. R. Heckel, C. W. Stubbs, and Y. Su,
"Does antimatter fall with the same acceleration as ordinary matter?" Phys. Rev. Lett. 66, 850-853 (1991).
[ADELBERGER, 1991B] E. G. Adelberger and B. R. Heckel, "Adelberger and
Heckel Reply," Phys. Rev. Lett. 67, 1049 (1991).
[ADELBERGER, 1991c] E. G. Adelberger, B. R. Heckel, C. W. Stubbs, and W. F.
Rogers, "Searches for new macroscopic interactions," Ann. Rev. Nucl. Part. 41, 269-320 (1991).
[ADLER, 1996] S. Adler et al., "Search for the decay K+ ---- 7r+vil," Phys. Rev. Lett. 76, 1421-1424 (1996).
[AIRY, 1856] G. B. Airy, "Account of pendulum experiments undertaken in the
Harton Colliery, for the purpose of determining the mean density of the
Earth," Philos. Trans. R. Soc. London 146, 297-355 (1856).
[AKASAKA, 1989] N. Akasaka, H. Hirakawa, N. Mio, M. Ohashi, and K. Tsub
ono, "Dynamic null tests of the fifth force," In Proceedings of the Fifth Marcel Grossmann Meeting on General Relativity University of Western
Australia, Perth, Australia, 8-13 August, 1988, edited by D. G. Blair and M.
J. Buckingham (Singapore: World Scientific, 1989), pp. 1591-1594.
[ALIEV, 1989] T. M. Aliev, M. I. Dobroliubov, and A. Yu. Ignatiev, "Do kaon
decays constrain the fifth force?" Phys. Lett. B 221, 77-79 (1989).
248 BIBLIOGRAPHY
[ANDER, 1989A] M. E. Ander et al., "Test of Newton's inverse-square law in the
Greenland ice cap," Phys. Rev. Lett. 62, 985-988 (1989).
[ANDER, 1989B] M. E. Ander et al., "A new field experiment in the Greenland
ice cap to test Newton's inverse square law," In Ann. NY Acad. Sci. 571, Fourteenth Texas Symposium on Relativistic Astrophysics, 11-16 December,
1988, Dallas, Texas, 672--680 (1989).
[ANSEL'M, 1982] A. A. Ansel'm, "Possible new long-range interaction and meth
ods for detecting it," JETP Lett. 36, 55 (1982).
[ARONSON, 1982] S. H. Aronson, G. J. Bock, H.-Y. Cheng, and E. Fischbach,
"Determination of the fundamental parameters of the KO-1(o system in the
energy range 3D-110 GeV," Phys. Rev. Lett. 48, 1306-1309 (1982).
[ARONSON, 1983A] S. H. Aronson, G. J. Bock, H.-y' Cheng, and E. Fischbach,
"Energy dependence of the fundamental parameters of the KO _1(0 system. I.
Experimental analysis," Phys. Rev. D 28, 476-494 (1983).
[ARONSON, 1983B] S. H. Aronson, G. J. Bock, H.-y' Cheng, and E. Fischbach,
"Energy dependence of the fundamental parameters of the KO-1(o system.
II. Theoretical formalism," Phys. Rev. D 28, 495-523 (1983).
[ARONSON, 1986] S. H. Aronson, H.-Y. Cheng, E. Fischbach, and W. Haxton,
"Experimental signals for hyperphotons," Phys. Rev. Lett. 56, 1342-1345
(1986); 56, 2334(E} (1986).
[ARONSON, 1988] S. H. Aronson, E. Fischbach, D. Sudarsky, and C. Talmadge,
"The compatibility of gravity and kaon results in the search for new forces,"
In 5th Force-Neutrino Physics Proceedings of the XXlIIrd Rencontre de
Moriond (VIIIth Moriond Workshop), Les Arcs, France, 23-30 January, 1989,
edited by O. Fackler and J. Tran Thanh Van (Gif-sur-Yvette: Editions
Frontieres, 1988), pp. 593-602.
[ASTONE, 1991] P. Astone et al., "Evaluation and preliminary measurement of
the interaction of a dynamical gravitational near field with a cryogenic gravi
tational wave antenna," Z. Phys. C - Particles and Fields 50,21-29 (1991).
[BAGLEY, 1997] C. H. Bagley and G. G. Luther, "Preliminary results of a de
termination of the Newtonian constant of gravitation: A test of the Kuroda
hypothesis," Phys. Rev. Lett. 78, 3047-3050 (1997).
BIBLIOGRAPHY 249
[BARKER, 1966J B. M. Barker, S. N. Gupta, and R. D. Haracz, "One graviton
exchange interaction of elementary particles," Phys. Rev. 149, 1027-1032
(1966).
[BARTLETT, 1986J D. F. Bartlett and D. Van Buren, "Equivalence of active and
passive gravitational mass using the Moon," Phys. Rev. Lett. 57, 21-24
(1986).
[BARTLETT, 1988J D. F. Bartlett and S. Logl, "Limits on an electromagnetic fifth
force," Phys. Rev. Lett. 61, 2285-2287 (1988).
[BARTLETT, 1989AJ D. F. Bartlett and W. L. Tew, "The fifth force: Terrain
and pseudoterrain," In Tests of Fundamental Laws of Physics Proceedings
of the XXIVth Rencontre de Moriond (IXth Moriond Workshop), Les Arcs,
France, 21-28 January, 1989, edited by O. Fackler and J. Tran Thanh Van
(Gif-sur-Yvette: Editions Fronti(~res, 1989), pp. 543-548.
[BARTLETT, 1989BJ D. F. Bartlett and W. L. Tew, "Possible effect of the local
terrain on the Australian fifth-force measurement," Phys. Rev. D 40, 673-
675 (1989).
[BARTLETT, 1989cJ D. F. Bartlett and W. L. Tew, "Possible effect of the local
terrain on the North Carolina tower gravity experiment," Phys. Rev. Lett. 63, 1531 (1989).
[BARR, 1986J S. M. Barr and R. N. Mohapatra, "Range of feeble forces from
higher dimensions," Phys. Rev. Lett. 57, 3129-3132 (1986).
[BARR, 1993J G. D. Barr et al., "A new measurement of direct CP violation in
the neutral kaon system," Phys. Lett. B 317, 233-242 (1993).
[BARS, 1986J I. Bars and M. Visser, "Feeble intermediate-range forces from higher
dimensions," Phys. Rev. Lett. 57, 25-28 (1986).
[BEKENSTEIN, 1984J J. Bekenstein and M. Milgrom, "Does the missing mass
problem signal the breakdown of Newtonian gravity?" Astrophys. J. 286, 7-14 (1984).
[BELL, 1964J J. S. Bell and J. K. Perring, "271" decay of the Kg meson," Phys. Rev. Lett. 13, 348-349 (1964).
[BENNETT, 1989J W. R. Bennett, Jr., "Modulated-source EOtvos experiment at
250 BIBLIOGRAPHY
Little Goose Lock," Phys. Rev. Lett. 62, 365-368 (1989).
[BERNSTEIN, 1964] J. Bernstein, N. Cabibbo, and T. D. Lee, "CP invariance and
the 27r decay mode of the Kg," Phys. Lett. 12, 146-148 (1964).
[BERTOTTI, 1991] B. Bertotti and C. Sivaram, "Radiation of the 'fifth force'
field," Nuovo Cimento B 106, 1299-1304 (1991).
[BEVERINI, 1988] N. Beverini, V. Lagomarsino, G. Manuzio, F. Scuri, and G.
Torelli, "Possible measurements of the gravitational acceleration with neutral
[FEINBERG, 1989] G. Feinberg, J. Sucher, and C.-K. Au, "The dispersion theory
of dispersion forces," Phys. Reports 180, 83-157 (1989).
[FEYNMAN, 1995] R. P. Feynman, F. B. Morinigo, and W. G. Wagner, Feynman Lectures on Gravitation (Reading: Addison-Wesley, 1995).
[FIORENTINI, 1989] G. Fiorentini d!1d G. Mezzorani, "Neutrinos from SN1987 A
and long-range forces," Phys. Lett. B 221, 353-356 (1989).
[FINZI, 1963] A. Finzi, "On the validity of Newton's law at a long distance,"
Monthly Not. Royal Astron. Soc. 127, 21-30 (1963).
[FISCHBACH, 1981] E. Fischbach, B. S. Freeman, and W. K. Cheng, "General
Relativistic Effects in Hydrogenic Systems," Phys. Rev. D 23, 2157-2180
(1981).
[FISCHBACH, 1982] E. Fischbach, H.-y' Cheng, S. H. Aronson, and G. J. Bock,
"Interaction of the KO-j(o system with external fields," Phys. Lett. B 116,
BIBLIOGRAPHY 259
73-76 (1982).
[FISCHBACH, 1985] E. Fischbach, M. P. Haugan, D. Tadic, and H.-Y. Cheng,
"Lorentz noninvariance and the Eotvos experiments," Phys. Rev. D 32, 154-
162 (1985).
[FISCHBACH, 1986A] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "Reanalysis of the Eotvos experiment," Phys. Rev. Lett. 56, 3-6 (1986); 56, 1427 (E) (1986).
[FISCHBACH, 1986B] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "Fischbach et al. respond," Phys. Rev. Lett. 56, 2424 (1986).
[FISCHBACH, 1986c] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "A new force in nature?" In Proceedings, 2nd Conference on Intersections between Particle and Nuclear Physics, Lake Louise, Canada
May 26-31,1986, edited by D. Geesaman, AlP Conference Proceedings #150
(New York: American Institute of Physics, 1986), pp. 1102-1118.
[FISCHBACH, 1986D] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "Fischbach et al. reply," Phys. Rev. Lett. 56, 2424 (1986).
[FISCHBACH, 1986E] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "Alternative explanations of the Eotvos results," Phys. Rev. Lett. 57, 1959 (1986).
[FISCHBACH, 1987] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "The fifth force," In Proceedings of the XXIII International Conference on High Energy Physics, Berkeley, CA, 16-23 July, 1986, edited
by S. C. Loken (Singapore: World Scientific, 1987), pp. 1021-1301.
[FISCHBACH, 1988] E. Fischbach, H. T. Kloor, C. Talmadge, S. H. Aronson, and
G. T. Gillies, "Possibility of shielding the fifth force," Phys. Rev. Lett. 60, 74 (1988).
[FISCHBACH, 1988B] E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, and S.
H. Aronson, "Long-range forces and the Eotvos experiment," Ann. Phys. (NY) 182, 1-89 (1988).
[FISCHBACH, 1990] E. Fischbach and C. Talmadge, "Finite-size effects in Eotvos
type experiments," In New and Exotic Phenomena, Proceedings of the 1990
Moriond Workshop, Les Arcs, France, 20-27 January, 1990, edited by J. Tran
260 BIBLIOGRAPHY
Thanh Van (Gif-Sur-Yvette: Editions Frontieres, 1990), pp. 187-196.
[FISCHBACH, 1991] E. Fischbach, C. Talmadge, and D. Krause, "Exponential
models of non-Newtonian gravity," Phys. Rev. D 43,460-467 (1991).
[FISCHBACH, 1991B] E. Fischbach, B. S. Freeman, and W. K. Cheng, "General
relativistic effects in hydrogenic systems," Phys. Rev. D 23, 2157-2180
(1991).
[FISCHBACH, 1992A] E. Fischbach and C. Talmadge, "Six years of the fifth force,"
Nature 356, 207-215 (1992)
[FISCHBACH, 1992B] E. Fischbach, G. T. Gillies, D. E. Krause, J. G. Schwan,
and C. Talmadge, "Non-Newtonian gravity and new weak forces: An index of
measurements and theory," Metrologia 29, 213-260 (1992).
[FISCHBACH, 1994] E. Fischbach, H. Kloor, R. Langel, A. T. Y. Lui, and M.
Peredo, "New geomagnetic limits on the photon mass and on long-range fields
coexisting with electromagnetism," Phys. Rev. Lett. 73,514-517 (1994).
[FISCHBACH, 1995] E. Fischbach, D. E. Krause, C. Talmadge, and D. Tadic,
"Higher-order weak interactions and the equivalence principle," Phys. Rev. D 52, 5417-5427 (1995).
[FISCHBACH, 1996A] E. Fischbach, "Long-range forces and neutrino mass," Ann. of Phys. (NY) 247,213-291 (1996).
[FISCHBACH, 1996B] E. Fischbach, M. P. Haugan, and D. Tadic, "The equivalence
principle and weak interactions," In Proceedings of the STEP Symposium, Pisa, Italy, 6--8 April, 1993, edited by R. Reinhard (European Space Agency
publication ESA WPP-115, 1996), pp. 161-168.
[FITCH, 1988] V. L. Fitch, M. V. Isaila, and M. A. Palmer, "Limits on the ex
istence of a material-dependent intermediate-range force," Phys. Rev. Lett. 60, 1801-1804 (1988).
[FRANKLIN, 1993] A. Franklin, The Rise and Fall of the Fifth Force (New
York: American Institute of Physics, 1993).
[FRIEMAN, 1991] J. A. Frieman and B.-A. Gradwohl, "Dark matter and the
equivalence principle," Phys. Rev. Lett. 67, 2926-2929 (1991).
[FUJII, 1971] Y. Fujii, "Dilaton and possible non-Newtonian gravity," Nature
BIBLIOGRAPHY 261
(Phys. Sci.) 234, 5-7 (1971).
[FUJII, 1972] Y. Fujii, "Scale invariance and gravity of hadrons," Ann. Phys. (NY) 69, 494-521 (1972).
[FUJII, 1974] Y. Fujii, "Scalar-tensor theory of gravitation and spontaneous
breakdown of scale invariance," Phys. Rev. D 9, 874-876 (1974).
[FUJII, 1975] Y. Fujii, "Spontaneously broken scale invariance and gravitation,"
Gen. Rel. Grav. 6, 29-34 (1975).
[FUJII, 1986] Y. Fujii, "Theoretical models for possible nonzero effect in the
Eotvos experiment," Progress of Theoretical Physics 76, 325-328 (1986).
[FUJII, 1988] Y. Fujii, "On five-dimensional theories of the fifth force," Mod. Phys. Lett. A 3, 19-22 (1988).
[FUJII, 1991A] Y. Fujii, "Locally varying particle masses due to a scalar fifth-force
field," Phys. Lett. B 255, 439-444 (1991).
[FUJII, 1991B] Y. Fujii, "The theoretical background of the fifth force," Int. J. Mod. Phys. A 6, 3505-3557 (1991)
[FULIGNI, 1996] F. Fuligni and V. Iafolla, "Galileo and the principle of equiva
lence," In Proceedings of the STEP Symposium, Pisa, Italy, 6-8 April, 1993,
edited by R. Reinhard (European Space Agency publication ESA WPP-115,
1996), pp. 104-109.
[GABRIEL, 1990] M. D. Gabriel and M. P. Haugan, "Testing the Einstein equiv
alence principle: Atomic clocks and local Lorentz invariance," Phys. Rev. D 41, 2943-2955 (1990).
[GALlC, 1989] H. Galic, "Weak decays of K and 7r mesons," Phys. Rev. D 40, 2279-2289 (1989).
[GASPERINI, 1988] M. Gasperini, "Testing the principle of equivalence with neu
trino oscillations," Phys. Rev. D 38, 2635-2637 (1988).
[GASPERINI, 1989A] M. Gasperini, "Experimental constraints on a minimal and
nonminimal violation of the equivalence principle in the oscillations of massive
neutrinos," Phys. Rev. D 39, 3606-3611 (1989).
[GASPERINI, 1989B] M. Gasperini, "Phenomenological consequences of a direct
262 BIBLIOGRAPHY
fifth force coupling to photons," Phys. Rev. D 40, 3525-3528 (1989).
[GELL-MANN, 1954] M. Gell-Mann and F. E. Low, "Quantum electrodynamics
at small distances," Phys. Rev. 95, 1300-1312 (1954).
[GIBBONS, 1981] G. W. Gibbons and B. F. Whiting, "Newtonian gravity mea
surements impose constraints on unification theories," Nature 291, 636-638
(1981).
[GIBBONS, 1993A] L. K. Gibbons et al., "New measurement of the neutral kaon
parameters f}.m, Ts , ¢oo - ¢+_, and ¢+_," Phys. Rev. Lett. 70, 1199-1202
(1993).
[GIBBONS, 1993B] L. K. Gibbons et al., "New measurement of the CP-violation
parameter Re(fl If)," Phys. Rev. Lett. 70, 1203-1206 (1993).
[GILLILAND, 1987] R. L. Gilliland and W. Diippen, "Hypercharge, solar structure,
and stellar evolution," Astrophys. J. 313, 429-431 (1987).
[GILLIES, 1987] G. T. Gillies, "The Newtonian gravitational constant," Metrologia 24 (Suppl.), 1-56 (1987).
[GILLIES, 1990] G. T. Gillies, "Resource letter MNG-l: Measurements of Newto
nian gravitation," Am. J. Phys. 58, 525-534 (1990).
[GILLIES, 1992] G. T. Gillies, Measurements of Newtonian Gmvitation: Selected Reprints, College Park, MD, American Association of Physics Teachers
(1992).
[GLASS, 1987] E. N. Glass and G. Szamosi, "Intermediate-range forces and stellar
structure," Phys. Rev. D 35, 1205-1208 (1987).
[GLASS, 1989] E. N. Glass and G. Szamosi, "Astrophysical treatment of inter
mediate-range forces," Phys. Rev. D 39, 1054-1057 (1989).
[GOLDBERG, 1990] H. Goldberg, "Breakdown of perturbation theory at tree level
of theories with scalars," Phys. Lett. B 246, 445-450 (1990).
[GOLD HABER, 1974] A. S. Goldhaber and M. M. Nieto, "Mass of the graviton,"
Phys. Rev. D 9, 1119-1121 (1974).
[GOLDMAN, 1982] T. Goldman and M. M. Nieto, "Experiments to measure the
gravitational acceleration of antimatter," Phys. Lett. 112B, 437-440 (1982).
BIBLIOGRAPHY 263
[GOLDMAN, 1986] T. Goldman, R. J. Hughes, and M. M. Nieto, "Experimental
evidence for quantum gravity?" Phys. Lett. B 171, 217-222 (1986).
[GOLDMAN, 1987] T. Goldman, R. J. Hughes, and M. M. Nieto, "Gravitational
acceleration of antiprotons and of positrons," Phys. Rev. D 36, 1254-1256
(1987).
[GOLDMAN, 1988] T. Goldman, R. J. Hughes, and M. M. Nieto, "Gravity and
antimatter," Sci. Am. 258, 48-56 (1988).
[GOLDMAN, 1991] T. Goldman et al., "Comment on: 'Does anti-matter fall with
the same acceleration as ordinary matter?' " Phys. Rev. Lett. 67, 1048
(1991).
[GOLDSTEIN, 1980] H. Goldstein, Classical Mechanics (Reading: Addison
Wesley, 1980).
[GOOD, 1961] M. L. Good, "Kg and the equivalence principle," Phys. Rev. 121, 311-313 (1961).
[GRAHAM, 1987] D. M. Graham, Search for anomalous long-range spinspin interaction, Ph.D. Thesis, University of California, Irvine, unpublished
(1987).
[GRAHAM, 1989] D. M. Graham, P. G. Nelson, and R. D. Newman, "A search for
an anomalous intermediate range composition dependence in gravity," In Abstracts of Contributed Papers, 12th International Conference on General Relativity and Gravitation, Boulder, Colorado, 2-8 July, 1989, edited by N.
Ashby et al. (International Society on General Relativity and Gravitation,
1989), p. 513.
[GRIFOLS, 1986] J. A. Grifols and E. Masso, "Constraints on finite-range bary
onic and leptonic forces from stellar evolution," Phys. Lett. B 173, 237-240
(1986).
[GROSSMAN, 1987] N. Grossman et al., "Measurement of the lifetime of K~
mesons in the momentum range 100 to 350 GeV/c," Phys. Rev. Lett. 59, 18-21 (1987).
[GUNDLACH, 1997] J. H. Gundlach, G. L. Smith, E. G. Adelberger, B. R. Heckel,
and H. E. Swanson, "Short-range test of the equivalence principle," Phys. Rev. Lett. 78, 2523-2526 (1997).
264 BIBLIOGRAPHY
[HAGELIN, 1989] J. S. Hagelin and L. S. Littenberg, "Rare kaon decays," Prog. Part. Nucl. Phys. 23, 1-40 (1989).
[HALL, 1991] A. M. Hall, H. Armbruster, E. Fischbach, and C. Talmadge, "Is the
Eotvos experiment sensitive to spin?" In Progress in High Energy Physics, Proceedings of the Second International Conference and Spring School on Medium and High Energy Nuclear Physics, Taiwan, 8-18 May, 1990,
edited by W.-Y. P. Hwang, S.-C. Lee, C.-E. Lee, and D. J. Ernst (New York:
North-Holland, 1991), pp. 325-329.
[HALPRIN, 1991] A. Halprin and C. N. Leung, "Can the Sun shed light on neu
trino gravitational interactions?" Phys. Rev. Lett. 67, 1833-1835 (1991).
[HALPRIN, 1996] A. Halprin, C. N. Leung, and J. Pantaleone, "Possible viola
tion of the equivalence principle by neutrinos," Phys. Rev. D 53, 5365-5376
(1996).
[HARI DASS, 1976] N. D. Hari Dass, "Test for C, P, and T nonconservation in
gravitation," Phys. Rev. Lett. 36, 393-395 (1976).
[HARI DASS, 1977] N. D. Hari Dass, "A new spin test for the equivalence princi
ple," Gen. Rel. and Grav. 8, 89-93 (1977).
[HARTLE, 1970] J. B. Hartle, "Long-range weak forces and cosmology," Phys. Rev. D 1, 394-397 (1970).
[HARTLE, 1971] J. B. Hartle, "Long-range neutrino forces exerted by Kerr black
holes," Phys. Rev. D3, 2938-2940 (1971).
[HARTLE, 1972] J. B. Hartle. In Magic Without Magic: John Archibald Wheeler, edited by J. R. Klauder (San Francisco: W. H. Freeman, 1972),
pp. 259-275.
[HAUGAN, 1979] M. P. Haugan, "Energy conservation and the principle of equiv
alence," Ann. Phys. 118, 156-186 (1979).
[HAUGAN, 1976] M. P. Haugan and C. M. Will, "Weak interactions and the
Eotvos experiment," Phys. Rev. Lett. 37, 1-4 (1976)
[HAUGAN, 1987] M. P. Haugan and C. M. Will, "Modern tests of special relativ
ity," Phys. Today 40, 69-76 (May, 1987).
[HAYASHI, 1986] K. Hayashi and T. Shirafuji, "Interpretations of geophysical and
[LEITNER, 1964] J. Leitner and S. Okubo, "Parity, charge conjugation, and time
reversal in the gravitational interaction," Phys. Rev. 136, B1542-B1546
(1964).
[LI, 1986] M. Li and R. Ruffini, "Radiation of new particles of the fifth interac
tion," Phys. Lett. A 116, 20-24 (1986).
[Lm, 1983] H. Liu, P. Zhang, and R. Qin, "A null experiment of gravitational
inverse square law," In Proceedings of the Third Marcel Grossmann Meeting On General Relativity, Shanghai, China, 30 August - 3 September 1982,
edited by N. Hu (Amsterdam: Science Press and North-Holland Publishing
Company, 1983), 1501-1504.
[LOBOV, 1990] G. A. Lobov, "On the violation of the equivalence principle of
General Relativity by the electroweak interaction," Sov. J. Nucl. Phys. 52, 918-919 (1990).
[LONG, 1974] D. R. Long, "Why do we believe Newtonian gravitation at labora
tory dimensions?" Phys. Rev. D 9, 850-852 (1974).
[LONG, 1976] D. R. Long, "Experimental examination of the gravitational inverse
square law," Nature 260, 417-418 (1976).
[LONG, 1980] D. R. Long, "Vacuum polarization and non-Newtonian gravita
tion," Nuovo Cimento 55B, 252-256 (1980).
[LONG,1981] D. R. Long, "Current measurements of the gravitational 'constant'
as a function of the mass separation," Nuovo Cimento 62B, 130-138 (1981).
[LONG, 1988] D. R. Long, seminar given at conference on 5th Force-Neutrino Physics (VIIIth Moriond Workshop), Les Arcs, France, January 23-30, 1988.
[LONGO, 1988] M. J. Longo, "New precision tests of the Einstein equivalence
principle from SN1987 A," Phys. Rev. Lett. 60, 173-175 (1988).
270 BIBLIOGRAPHY
[LUSIGNOLI, 1986] M. Lusignoli and A. Pugliese, "Hyperphotons and K-meson
decays" Phys. Lett B 171, 468-470 (1986)
[LUTHER, 1982] G. G. Luther and W. R. Towler, "Redetermination of the New
tonian gravitational constant G," Phys. Rev. Lett. 48, 121-123 (1982).
[MACRAE, 1984] K.1. Macrae and R. J. Riegert, "Long-range antigravity," Nucl. Phys. B244, 513-522 (1984).
[MALONEY, 1989] F. P. Maloney, E. F. Guinan, and P. T. Boyd, "Eclipsing binary
stars as tests of gravity theories: The apsidal motion of AS Camelopardalis,"
Astron. J. 98, 1800-1813 (1989).
[MALANEY, 1995] R. A. Malaney, G. D. Starkman, and S. Tremaine, "Time de
lays of supernova neutrinos from new long-range interactions," Phys. Rev. D 51, 324-327 (1995).
[MANNHEIM, 1997] P. D. Mannheim, "Are galactic rotation curves really fiat?"
Ap. J. 479, 659-664 (1997).
[MARIS, 1988] H. J. Maris, "Comment on 'Search for a substance-dependent force
with a new differential accelerometer,' " Phys. Rev. Lett. 60, 964 (1988).
[MAZILU, 1996] P. Mazilu and H. Dittus, "The equivalence principle within the
Lorentz-invariant scalar field theory of gravity-report on theoretical studies
for experiments on drop tower 'Bremen' ," In Proceedings of the STEP Symposium, Pisa, Italy, 6-8 April, 1993, edited by R. Reinhard (European Space
Agency publication ESA WPP-115, 1996), pp. 85-95.
[MEMBRADO, 1988A] M. C. Membrado and A. F. Pacheco, "Implication of
Yukawa-like effects in a white dwarf structure," Astrophys. J. 327, 726-731
(1988).
[MEMBRADO, 1988B] M. C. Membrado and A. F. Pacheco, "Short-range effects
in large white dwarfs," Astrophys. J. 331, 394-396 (1988).
[MEMBRADO, 1990] M. C. Membrado, A. F. Pacheco, and H. Vucetich, "Introduc
tion of short-range effects in the Oppenheimer-Volkoff equation," Astrophys. J. 348, 212-220 (1990).
[MIKHEYEV, 1985] S. P. Mikheyev and A. Yu. Smirnov, "Resonance enhancement
of oscillations in matter and solar neutrino spectroscopy," Sov. J. Nucl. Phys.
BIBLIOGRAPHY 271
42, 913-917 (1985).
[MIKKELSEN, 1977] D. R. Mikkelsen and M. J. Newman, "Constraints on the
gravitational constant at large distances," Phys. Rev. D 16,919-926 (1977).
[MILGROM, 1983A] M. Milgrom, "A modification of the Newtonian dynamics as
a possible alternative to the hidden mass hypothesis," Astrophys. J. 270, 365-370 (1983).
[MILGROM, 19838] M. Milgrom, "A modification of the Newtonian dynamics:
Implications for galaxies," Astrophys. J. 270, 371-383 (1983).
[MILGROM, 1983c] M. Milgrom, "A modification of the Newtonian dynamics:
Implications for galaxy systems," Astrophys. J. 270, 384-389 (1983).
[MILGROM, 1986] M. Milgrom, "On the use of Eotvos-type experiments to detect
medium-range forces," Nucl. Phys. B 277, 509-512 (1986).
[MINAKATA, 1995] H. Minakata and H. Nunokawa, "Testing the principle of
equivalence by solar neutrinos," Phys. Rev. D 51, 6625-6634 (1995).
[MILYUKOV, 1985] V. K. Milyukov, "Experimental verification of the law of grav
ity for laboratory distances," Soviet Physics JETP61, 187-191. [Translation
of Zh. Eksp. Teor. Fiz. 88, 321-328 (1985).]
[MIO, 1986] N. Mio and H. Hirakawa, "Dynamic null experiment to test the law
of gravitation," J. Phys. Soc. Japan 55, 4143-4146 (1986).
[Mro, 1987] N. Mio, K. Tsubono, and H. Hirakawa, "Experimental test of the
law of gravitation at small distances," Phys. Rev. D 36, 2321-2326 (1987).
[MISNER, 1973] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: W. H. Freeman, 1973).
[MITROFANOV,1988] V. P. Mitrofanov and 0.1. Ponomareva, "Experimental test
of gravitation at small distances," Sov. Phys. JETP 67, 1963-1966 (1988).
[Translation of Zh. Eksp. Teor. Fiz. 94, 16-22 (1988).]
[MOFFAT, 1987] J. W. Moffat, "Nonsymmetric gravitation theory: A possible
new force in nature," In New and Exotic Phenomena, Proceedings of the
VIIth Moriond Workshop, Les Arcs, France, 24-31 January, 1987, edited by O.
Fackler and J. Tran Thanh Van (Gif-sur-Yvette: Editions Frontieres, 1987),
pp. 623-635.
272 BIBLIOGRAPHY
[MOFFAT, 1988] J. W. Moffat and E. Woolgar, "Motion of massive bodies: Testing
the nonsymmetric gravitation theory," Phys. Rev. D 37, 918-930 (1988).
[MOFFAT, 1989] J. W. Moffat, "Detection of dark matter and tests of the weak
equivalence principle," Phys. Rev. D 40, 2499-2501 (1989).
[MOODY, 1984] J. E. Moody and F. Wilczek, "New macroscopic forces?" Phys. Rev. D 30, 130-138 (1984).
[MOODY, 1993] M. V. Moody and H. J. Paik, "Gauss's law test of gravity at
short range" Phys. Rev. Lett. 70, 1195-1198 (1993).
[MOORE, 1988A] G. I. Moore et al., "Determination of the gravitational constant
at an effective mass separation of 22 m," Phys. Rev. D 38, 1023-1029 (1988).
[MOORE, 1988B] G.!. Moore et al., "A balance for precise weighing in a disturbed
environment," J. Phys. E: Sci. Inst. 21, 534-539 (1988).
[MORPURGO, 1991] G. Morpurgo, "Comment on 'Does antimatter fall with the
same acceleration as ordinary matter?' " Phys. Rev. Lett. 67, 1047 (1991).
[MORRISON, 1957] P. Morrison and T. Gold, In Essays on Gravity (New Boston:
Gravity Research Foundation, 1957), pp. 45-50.
[MORRISON, 1958] P. Morrison, "Approximate nature of physical symmetries,"
Am. J. Phys. 26, 358-368 (1958).
[MOSTEPANENKO, 1987 A] V. M. Mostepanenko and I. Yu. Sokolov, "Restrictions
on long-range forces following from the Casimir effect," Sov. J. of Nucl. Phys. 46, 685-688 (1987). [Translation of Yad. Fiz 46, 1174-1180 (1987).]
[MOSTEPANENKO, 1987B] V. M. Mostepanenko and I. Yu. Sokolov, "The Casimir
effect leads to new restrictions on long-range force constants," Phys. Lett. A 125, 405-408 (1987).
[MOSTEPANENKO, 1988] V. M. Mostepanenko and I. Yu. Sokolov, "New restric
tions on the parameters of the spin-1 antigraviton following from the Casimir
effect, Ei:itvi:is and Cavendish experiments," Phys. Lett. A 132, 313-315
(1988).
[MOSTEPANENKO, 1989] V. M. Mostepanenko and I. Yu. Sokolov, "Restrictions
on the parameters of the spin-1 antigraviton and the dilaton resulting from
the Casimir effect and from the Ei:itvi:is and Cavendish experiments," Sov. J.
BIBLIOGRAPHY 273
of Nucl. Phys. 49, 1118-1120 (1989). [Translation of Yad. Fiz. 49, No.6,
1807-1811 (1989).J
[MOSTEPANENKO, 1993J V. M. Mostepanenko and I. Yu. Sokolov, "Hypothet
ical long-range interactions and restrictions on their parameters from force
measurements," Phys. Rev. D 47, 2882-2891 (1993).
[MULLER, 1989J G. Miiller, W. Ziirn, K. Lindner, and N. ROsch," "Determination
of the gravitational constant by an experiment at a pumped-storage reservoir,"
Phys. Rev. Lett. 63, 2621-2624 (1989).
[MULLER,1990J G. Miiller, W. Ziirn, K. Lindner, and N. ROsch," "Search for non
Newtonian gravitation-a gravimetric experiment in a hydroelectric lake,"
Geophys. J. International 101, 329-344 (1990).
[NACHTMANN, 1969J O. Nachtmann, "ep violation and cosmological fields," In
Particle Physics, edited by P. Urban (Berlin: Springer, 1969), pp. 485-500.
[NELSON, 1988J P. Nelson, D. Graham, and R. Newman, "A 'fifth force' search
using a controlled local mass," In 5th Force-Neutrino Physics, Proceedings
of the XXIIIrd Rencontre de Moriond (VIIIth Moriond Workshop), Les Arcs,
France, 23-30 January, 1988 edited by O. Fackler and J. Tran Thanh Van
(Gif-sur-Yvette: Editions Frontieres, 1988), pp. 427-430.
[NELSON,1990J P. G. Nelson, D. M. Graham, and R. D. Newman, "Search for an
intermediate-range composition-dependent force coupling to N - Z," Phys. Rev. D 42, 963-976 (1990).
[NEUFELD, 1986J D. A. Neufeld, "Upper limit on any intermediate-range force
associated with baryon number," Phys. Rev. Lett. 56, 2344-2346 (1986).
[NEWMAN, 1955J J. R. Newman, The World of Mathematics, Volume Two (New York: Simon and Schuster, 1956), pp. 828-839.
[NEWMAN, 1987J R. D. Newman, D. M. Graham, and P. G. Nelson, "Searches for
anomalous long-range forces." In New and Exotic Phenomena, Proceedings
of the VIIth Moriond Workshop, Les Arcs, France, 24-31 January, 1987, edited
by O. Fackler and J. Tran Thanh Van (Gif-sur-Yvette: Editions Frontieres,
1987), pp. 599-606.
[NEWTON, 1960) I. Newton, Principia, Book 3, Proposition 6, Theorem 6, (Uni
versity of California Press, Cajori Edition, 1960), p. 411.
274 BIBLIOGRAPHY
[NI, 1977] W.-T. Ni, "Equivalence principles and gauge fields," Phys. Rev. Lett. 38, 301-304 (1977).
[NI, 1987] W.-T. Ni, "Equivalence principles and gauge fields," Phys. Lett. A 120,174-178 (1987).
[NI, 1990] W.-T. Ni, "Test of the equivalence principle for nuclear-polarized bod
ies at low temperature," Physica B 165, 166, Part I, 157-158 (1990).
[NIEBAUER, 1987] T. M. Niebauer, M. P. McHugh, and J. E. Faller, "Galilean
test for the fifth force," Phys. Rev. Lett. 59, 609-612 (1987).
[NIETO, 1988] M. M. Nieto, T. Goldman, and R. J. Hughes, "The Principle
of equivalence, quantum gravity, and new gravitational forces," Austmlian Physicist 25, 259-262 (1988).
[NIETO, 1991] M. M. Nieto and T. Goldman, "The arguments against 'antigrav
ity' and the gravitational acceleration of antimatter," Phys. Rep. 205, 221-
281 (1991).
[NOBILl, 1987] A. M. Nobili, A. Milani, and P. Farinella, "Testing Newtonian
gravity in space," Phys. Lett. A 120, 437-441 (1987).
[NOBILl, 1988] A. M. Nobili, A. Milani, and P. Farinella, "The orbit of a space
laboratory for the measurement of G," Astron. J. 95, 576-578 (1988).
[NOBILl, 1990] A. M. Nobili et al., "The Newton mission-A proposed man
made planetary system in space to measure the gravitational constant," ESA Joumall4, 389-408 (1990).
[NOBILl, 1996] A. M. Nobili, D. Bramanti, E. Polacco, and G. Catastini, "Galileo
Galilei (GG): Test of the equivalence principle at room temperature," In Proceedings of the STEP Symposium, Pisa, Italy, 6-8 April, 1993, edited by R.
Reinhard (European Space Agency publication ESA WPP-115, 1996), p. 374.
[NORDTVEDT, 1968A] K. Nordtvedt, "Equivalence principle for massive bodies,
[NORDTVEDT, 1968B] K. Nordtvedt, "Equivalence principle for massive bodies,
II: Theory," Phys. Rev. 169, 1017-1025 (1968).
[NORDTVEDT, 1972] K. Nordtvedt, Jr., "Gravitation theory: Empirical status
from solar system experiments," Science 178, 1157-1164 (1972).
BIBLIOGRAPHY 275
[NORDTVEDT, 1988] K. Nordtvedt, "Lunar laser ranging and laboratory Eotvos
type experiments," Phys. Rev. D 37, 1070-1071 (1988).
[NUSSINOV, 1986] S. Nussinov, "Further tests and possible interpretations of a
suggested new vectorial interaction," Phys. Rev. Lett. 56, 2350-2351 (1986).
[O'CONNELL, 1974] R. F. O'Connell, "Spin, rotation, and C, P and T effects
in the gravitational interaction and related experiments," In Experimental Gravitation, Proceedings of the International School of Physics, Enrico Fermi,
Course LVI, edited by B. Bertotti (New York: Academic Press, 1974), pp. 496-
514.
[OGAWA, 1982] Y. Ogawa, K. Tsubono, and H. Hirakawa, "Experimental test of
the law of gravitation," Phys. Rev. D 26, 729-733 (1982).
[O'HANLON, 1972] J. O'Hanlon, "Intermediate-range gravity: A generally covari
ant model," Phys. Rev. Lett. 29, 137-138 (1972).
[OLDHAM, 1991] M. Oldham, Testing for non-Newtonian gravity using pumped storage reservoirs, Ph.D. Thesis, University of Newcastle-Upon
Tyne, unpublished (1991).
[OLDHAM, 1993] M. Oldham, F. J. Lowes, and R. J. Edge, "A decametric scale
investigation of the gravitational constant," Geophys. J. Int. 113, 83-94
(1993).
[OLIVE, 1996] K. Olive, "Why do we need non-baryonic dark matter?" In Dark Matter in Cosmology, Quantum Measurements, Experimental Gravitation, Proceedings of the XXXIst Rencontre de Moriond, Les Arcs, France,
20-27 January, 1996 edited by R. Ansari, Y. Giraud-Heraud, and J. Thin
Thanh Van (Gif-sur-Yvette: Editions Frontieres, 1996), pp. 3-24.
[OVERHAUSER, 1952] A. W. Overhauser, unpublished (1952).
[PAIK, 1979] H. J. Paik, "New null experiment to test the inverse square law of
gravitation," Phys. Rev. 19, 2320-2324 (1979).
[PAKVASA, 1989] S. Pakvasa, W. A. Simmons, and T. J. Weiler, "Test of equiva
lence principle for neutrinos and antineutrinos," Phys. Rev. D 39, 1761-1763
(1989).
[PAN, 1992A] S.-S. Pan, W.-T. Ni, and S.-C. Chen, "Polarized-body vs. polarized-
276 BIBLIOGRAPHY
body torsion balance experiment for measuring possible anomalous spin-spin
interactions," In Proceedings of the Sixth Marcel Grossmann Meeting on General Relativity, Kyoto, Japan, 23-29 June, 1991, edited by H. Sato and
T. Nakamura (Singapore: World Scientific, 1992), 364-370.
[PAN, 1992B] S.-S. Pan, W.-T. Ni, and S.-C. Chen, "Experimental search for
anomalous spin-spin interactions," Mod. Phys. Lett. A 7, 1287-1299 (1992).
[PANOY, 1979] V. I. Panov and V. N. Frontov, "The Cavendish experiment at
large distances," Sov. Phys. JETP 50, 852-856 (1979). [Translation of Zh. Eksp. Teor. Fiz. 77, 1701-1707 (1979).]
[PANTALEONE, 1993] J. Pantaleone, A. Halprin, and C. Leung, "Neutrino mixing
due to a violation of the equivalence principle," Phys. Rev. D 47, R4199--4202
(1993).
[PARKER, 1989] R. L. Parker and M. A. Zumberge, "An analysis of geophysical
experiments to test Newton's law of gravity," Nature 342, 29-32 (1989).
[PDG, 1982] Particle Data Group, "Review of particle properties," Phys. Lett. 1UB, 1-294 (1982).
[PDG, 1996] Particle Data Group, "Review of Particle Properties," Phys. Rev. D 54, 1-720 (1996).
[PAYER, 1989] N. Paver, "Rare kaon decays: Theoretical overview," Il Nuovo Cimento 102A, 97-111 (1989).
[PECCEI, 1987] R. D. Peccei, J. Sola, and C. Wetterich, "Adjusting the cosmo
logical constant dynamically: Cosmons and a new force weaker than gravity,"
Phys. Lett. B 195, 183-190 (1987).
[PECHLANER, 1966] E. Pechlaner and R. Sexl, "On quadratic lagrangians in
General Relativity," Communications in Mathematical Physics 2,165-175
(1966).
[PHILLIPS, 1987] P. R. Phillips, "Test of spatial isotropy using a cryogenic torsion
pendulum," Phys. Rev. Lett. 59, 1784-1787 (1987).
[PRESTAGE, 1985] J. D. Prestage, J. J. Bollinger, W. M. Itano, and D. J.
Wineland, "Limits for spatial anisotropy by use of nuclear-spin-polarized 9Be
ions," Phys. Rev. Lett. 54, 2387-2390 (1985).
BIBLIOGRAPHY 277
[PRICE, 1972A] R. H. Price, "Nonspherical perturbations of relativistic gravita
tional collapse. I. Scalar and gravitational perturbations," Phys. Rev. D 5, 2419-2438 (1972).
[PRICE, 1972B] R. H. Price, "Nonspherical perturbations of relativistic gravi
tational collapse. II. Integer spin, zero-rest-mass fields," Phys. Rev. D 5, 2439-2454 (1972).
[PRICE, 1988] J. C. Price, "Gravitational strength forces below 1 em," In International Symposium on Experimental Gravitational Physics, edited by
P. F. Michelson, H. En-ke and G. Pizzella (Singapore: World Press, 1988),
436-439 (1988).
[PRIMAKOFF, 1939] H. Primakoff and T. Holstein, "Many-body interactions in
atomic and nuclear systems," Phys. Rev. 55, 1218-1234 (1939).
[RAPP, 1974] R. H. Rapp, "Current estimates of mean earth ellipsoid parame
ters," Geophys. Res. Lett. 1, 35-38 (1974).
[RAPP, 1977] R. H. Rapp, "Determination of potential coefficients to degree 52
from 5° mean gravity anomalies," Bull. Geod. 51, 301-323 (1977).
[RAPP, 1987] R. H. Rapp, "An estimate of equatorial gravity from terrestrial and
satellite data," Geophys. Res. Lett. 14, 730-732 (1987).
[REINHARD, 1996] Proceedings of the STEP Symposium, Pisa, Italy, 6-8 April,
1993, edited by R. Reinhard (European Space Agency publication ESA WPP-
115, 1996).
[RENNER, 1935] J. Renner, "Kiserleti vizsgaIatok a tomegvonzas es a
tehetetlenseg aranyossagarol," Matematikai es Termeszettudomanyi Ertesito 53, 542-568 (1935)
[ROMAIDES, 1994] A. J. Romaides et al., "Second tower experiment: Further
evidence for Newtonian gravity," Phys. Rev. D 50, 3613-3617 (1994).
[ROMAIDES, 1997] A. J. Romaides, R. W. Sands, E. Fischbach, and C. Talmadge,
"Final results from the WABG tower gravity experiment," Phys. Rev. D 55, 4532-4536 (1997).
[ROZSA, 1931] M. Rozsa and P. Selenyi, "Uber eine experimentalle methode zur
priifung der proportionalitiit der triigen und gravitierenden masse," Z. fUr
278 BIBLIOGRAPHY
Physik 71, 814-816 (1931).
[RITTER, 1990] R. C. Ritter, C. E. Goldblum, W.-T. Ni, G. T. Gillies, and C. C. Speake, "Experimental test of equivalence principle with polarized masses,"
Phys. Rev. D 42, 977-991 (1990).
[RIVEROS, 1986] C. Riveros and H. Vucetich, "Bounds on the validity of Newton's
gravitational law from electromagnetic solar deflection," Phys. Rev. D 34,
321-326 (1986).
[RIZZO, 1986] T. G. Rizzo, "Hyperphoton production in W-boson decay," Phys. Rev. D 34, 3519-3520 (1986).
[ROLL, 1964] P. G. Roll, R. Krotkov, and R. H. Dicke, "The equivalence of inertia
and passive gravitational mass," Ann. Phys. (NY) 26, 442-517 (1964).
[SAKURAI, 1967] J. J. Sakurai, Advanced Quantum Mechanics (Reading:
Addison-Wesley, 1967).
[SANDERS, 1984] R. H. Sanders, "Anti-gravity and galaxy rotation curves," Astron. Astrophys. 136, L21-L23 (1984).
[SANDERS, 1986A] R. H. Sanders, "Alternatives to dark matter," Monthly Not. Royal Astron. Soc. 223, 539-555 (1986).
[SANDERS, 1986B] R. H. Sanders, "Finite length-scale anti-gravity and observa
tions of mass discrepancies in galaxies," Astron. Astrophys. 154, 135-144
(1986).
[SANDERS, 1992] A. J. Sanders and W. E. Deeds, "Proposed new determination
of the gravitational constant G and tests of Newtonian gravitation," Phys. Rev. D 46, 489-504 (1992).
[SANTALO, 1976] L. A. Santal6, Integral Geometry and Geometric Probability (Reading: Addison-Wesley, 1976), p. 212.
[SCHECTER, 1987] B. Schecter, "May the force be with you," Omni 9,36-43 and
68-71 (1987).
[SCHERK, 1979A] J. Scherk, "Antigravity: A crazy idea?" Phys. Lett. B 88, 265-267 (1979)
[SCHERK, 1979B] J. Scherk, "From supergravity to antigravity," In Supergravity,
BIBLIOGRAPHY 279
Stony Brook, NY, September 27-29,1979, edited by D. Freedman and P. van
Nieuwenhuizen (Amsterdam: North Holland, 1979), pp. 43-51.
[SCHMIEDMAYER, 1989] J. Schmiedmayer, "The equivalence of the gravitational
and inertial mass of the neutron," Nucl. Instr. Meth. Phys. Res. A 284, 59-62 (1989).
[SCHIFF, 1958] L. I. Schiff, "Sign of the gravitational mass of a positron," Phys. Rev. Lett. 1, 254-255 (1958).
[SCHIFF, 1959] L. I. Schiff, "Gravitational properties of antimatter," Proceedings of the National Academy of Sciences (USA) 45, 69-80 (1959).
[SCHIFF, 1960] L. I. Schiff, "On experimental tests of the general theory of rela
tivity," Am. J. Phys. 28, 340-343 (1960).
[SCHIFF, 1966] L. I. Schiff and M. V. Barnhill, "Gravitation-induced electric field
near a metal," Phys. Rev. 151, 1067-1071 (1966).
[SCHINDEL, 1986] Ulrich Schindel (private communication) has brought the fol
lowing reference to our attention: "Geschaftliche Mitteilungen der Koniglichen
Gessellschaft der Wissenschaft zu Gottingen," pp. 37-41 (1909).
[SCHWARZSCHILD, 1986] B. Schwarzschild, "Reanalysis of old Eotvos data sug
gests fifth force ... to some," Physics Today 39, p. 17-20 (1986).
[SCHWARZSCHILD, 1988] B. Schwarzschild, "From mine shafts to cliffs-the 'fifth
force' remains elusive," Physics Today 41, p. 21-24 (1988).
[SCHURR, 1991] J. Schurr, H. Meyer, H. Piel, and H. Walesch, "A new laboratory
experiment for testing Newton's gravitational law," In Relativistic Gravity Research, edited by J. Elhers and G. Schafer (Berlin: Springer Verlag, 1991),
pp. 341-347.
[SCHWINGER, 1954] J. Schwinger, "Theory of quantized fields. VI," Phys. Rev. 94,1362-1384 (1954).
[SILVERMAN, 1987] M. P. Silverman, "Satellite test of intermediate-range devia
tion from Newton's law of gravity," Gen. Rel. Grav. 19, 511-514 (1987).
[SMITH, 1985] D. E. Smith et al., "A global geodetic reference frame from LA
GEOS ranging in (SL5.1AP)," J. Geophys. Res. 90, 9221-9235 (1985).
280 BIBLIOGRAPHY
[SPALLICCI, 1990] A. D. A. M. Spallicci, "Orbiting test masses for an equivalence
principle space experiment," Gen. Rel. Gmv. 22, 863-871 (1990).
[SPEAKE, 1986] C. C. Speake and T. J. Quinn, "Beam balance test of weak
[SPEAKE, 1988] C. C. Speake and T. J. Quinn, "Search for a short-range, isospin
coupling component of the fifth force with use of a beam balance," Phys. Rev. Lett. 61, 1340-1343 (1988).
[SPEAKE, 1990] C. C. Speake et al., "Test of the inverse-square law of gravitation
using the 300 m tower at Erie, Colorado," Phys. Rev. Lett. 65, 1967-1971
(1990).
[SPERO, 1980J R. Spero, J. K. Hoskins, R. Newman, J. Pellam, and J. Schultz,
"Test of the gravitation inverse-square law of laboratory distances," Phys. Rev. Lett. 44, 1645-1648 (1980).
[SPRUCH, 1986J L. Spruch, "Retarded, or Casimir, long-range potentials," Phys. Today 39, 37-49 (1986).
[STACEY, 1977] F. D. Stacey, Physics of the Earth, 2nd edition (New York: J.
Wiley & Sons, 1977).
[STACEY, 1981] F. D. Stacey and G. J. Tuck, "Geophysical evidence for non
Newtonian gravity," Nature 292, 230-232 (1981).
[STACEY, 1983] F. D. Stacey, "Subterranean gravity and other deep hole geo
physics," In Science Underground, Los Alamos, 1982, edited by M. M. Nieto
et al., AlP Conference Proceedings #96 (New York: American Institute of
Physics, 1983), pp. 285-297.
[STACEY, 1984] F. D. Stacey, "Gravity," Sci. Prog. Oxf. 69, 1-17 (1984).
[STACEY, 1987A] F. D. Staceyet al., "Geophysics and the law of gravity," Rev. Mod. Phys. 59, 157-174 (1987).
[STACEY, 19878J F. D. Stacey, G. J. Tuck, and G.!. Moore, "Geophysical tests of
the inverse square law of gravity," In New and Exotic Phenomena, Proceed
ings of the XXIIrd Rencontre de Moriond (VIIth Moriond Workshop), Les
Arcs, France, 24-31 January, 1987 edited by O. Fackler and J. Tran Thanh
Van, (Gif-sur-Yvette: Editions Frontieres, 1987), pp. 557-565.
BIBLIOGRAPHY 281
[STUBBS, 1987] C. W. Stubbs et al., "Search for an intermediate-range interac
tion," Phys. Rev. Lett. 58, 107(}-1073 (1987).
[STUBBS, 1988A] C. W. Stubbs, A search for a new composition-dependent interaction: An experimental test of the ''fifth force" hypothesis, Ph.D.
Thesis, University of Washington, unpublished (1988).
[STUBBS, 1988B] C. W. Stubbs, E. G. Adelberger, and E. C. Gregory, "Con
straints of proposed spin-O and spin-1 partners of the graviton," Phys. Rev. Lett. 61, 2409-2411 (1988).
[STUBBS, 1989A] C. W. Stubbs et al., "Limits on composition-dependent inter
actions using a laboratory source: Is there a 'fifth force' coupled to isospin?"
Phys. Rev. Lett. 62, 609-612 (1989).
[STUBBS, 1989B] C. W. Stubbs, "Eot-Wash constraints on multiple Yukawa in
teractions and on a coupling to 'isospin' ," In Tests of Fundamental Laws of Physics, Proceedings of the IXth Moriond Workshop, Les Arcs, France, 21-28
January, 1989, edited by O. Fackler and J. Tran Thanh Van (Gif-sur-Yvette:
Editions Frontieres, 1989), pp. 473-484.
[SU, 1994] Y. Su et al., "New tests of the universality of free fall," Phys. Rev. D 50, 3614-3636 (1994); D 51, 3135(E) (1995).
[SUDARSKY, 1991] D. Sudarsky, E. Fischbach, and C. Talmadge, "Effects of ex
ternal fields on the neutral kaon system," Ann. Phys. (NY) 207, 103-139
(1991).
[SUGIMOTO, 1972] D. Sugimoto, "Astrophysical test for dilaton theory in non
[TAYLOR, 1993] J. H. Taylor, "Pulsar timing and relativistic gravity," Class. Quantum Gravity 10, S167-S174 (1993).
BIBLIOGRAPHY 283
[TEW, 1989] W. L. Tew, Development of a He II supported torsion balance Ph.D. Thesis, University of Colorado at Boulder, 1989, unpublished (1989).
[THODBERG, 1986] H. H. Thodberg, "Comment on the sign in the reanalysis of
the Eotvos experiment," Phys. Rev. Lett. 56, 2423 (1986); 57, 1192 (1986).
[THOMAS, 1989] J. Thomas et al., "Testing the inverse-square law of gravity on
a 465-m tower," Phys. Rev. Lett. 63, 1902-1905 (1989).
[THOMAS, 1990] J. Thomas and P. Vogel, "Testing the inverse-square law of
gravity in boreholes at the Nevada test site," Phys. Rev. Lett. 65, 1173-
1176 (1990); 65, 2478 (E) (1990).
[THIEBERGER, 1986] P. Thieberger, "Hypercharge fields and Eotvos-type exper
iments," Phys. Rev. Lett. 56, 2347-2349 (1986).
[THIEBERGER, 1987 A] P. Thieberger, "Search for a substance-dependent force
with a new differential accelerometer," Phys. Rev. Lett. 58, 1066-1069
(1987).
[THIEBERGER, 1987B] P. Thieberger, "Search for a new force," In New and Exotic Phenomena, Proceedings of the VIIth Moriond Workshop, Les Arcs,
France, 24-31 January, 1987, edited by O. Fackler and J. Tran Thanh Van
(Gif-sur-Yvette: Editions FronW~res, 1987), pp. 579-589.
[THIEBERGER, 1988] P. Thieberger, "Thieberger replies," Phys. Rev. Lett. 60, 965 (1988).
[THIEBERGER, 1989] P. Thieberger, "Thieberger replies," Phys. Rev. Lett. 62, 2333 (1989).
[THIRRING, 1972] W. Thirring, "Gravitation," In Essays in Physics, Vol. 4,
edited by G. K. T. Conn and G. N. Fowler (New York: Academic, 1972), pp.
125-163.
[TOHLINE, 1983] J. E. Tohline, "Stabilizing a cold disk with a l/r force law,"
In Internal Kinematics and Dynamics of Galaxies, IAU Symposium 100,
edited by E. Athanassoula (Dordrecht: Reidel, 1983), pp. 205-206.
[TRAMPETIC, 1989] J. Trampetic, S. H. Aronson, H.-Y. Cheng, E. Fischbach,
and C. Talmadge, "Detecting hyperphotons in kaon decays," Phys. Rev. D 40,1716-1719 (1989).
284 BIBLIOGRAPHY
[TUCK, 1988] G. J. Tuck, M. A. Barton, G. D. Agnew, G. I. Moore, and F. D.
Stacey, "A lake experiment for measurement of the gravitational constant on
a scale of tens of metres," In Proceedings of the Fifth Marcel Grossmann Meeting on General Relativity, edited by D. G. Blair and M. J. Bucking
ham, University of Western Australia, Perth, Australia, 8-13 August, 1988,
(Singapore: World Scientific, 1989), pp. 1605-1612.
[UEHLING, 1935] A. E. Uehling, "Polarization effects in the positron theory,"
Phys. Rev. 48, 55-62 (1935).
[VAN DAM, 1970] H. van Dam and M. Veltman, "Massive and massless Yang-Mills
and gravitational fields," Nucl. Phys. B22, 397-411 (1970).
[VANICEK, 1986) P. Vanicek and E. Krakiwsky, Geodosy, 2nd edition (Amster
dam: North-Holland, 1986).
[VENEMA, 1992) B. J. Venema et al., "Search for a coupling ofthe Earth's gravita
tional field to nuclear spins in atomic mercury," Phys. Rev. Lett. 68, 135-138
(1992).
[VECSERNYES, 1987) P. Vecsernyes, "Constraints on a vector coupling to baryon
number from the Eotvos experiment," Phys. Rev. D 35, 4018-4019 (1987).
[VOROBYOV, 1988) P. V. Vorobyov and Ya. I. Gitarts, "A new limit on the arion
interaction constant," Phys. Lett. 208B, 146-148 (1988).
[WAGONER, 1970] R. V. Wagoner, "Scalar-tensor theory and gravitational
waves," Phys. Rev. D 1, 3209-3216 (1970).
[WAPSTRA, 1955] A. H. Wapstra and G. J. Nijgh, "The ratio of gravitational to
kinetic mass for the constituents of matter," Physica 21, 796-798 (1955).
[WATANABE, 1988] R. Watanabe, C. W. Stubbs, and E. G. Adelberger, "Shielding
the 'fifth force'?" Phys. Rev. Lett. 61, 2152 (1988).
[WEINBERG, 1964] S. Weinberg, "Do hyperphotons exist?" Phys. Rev. Lett. 13, 495-497 (1964).
[WEINBERG, 1972] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (New York: J. Wiley & Sons, 1972).
[WILL, 1987) C. M. Will, "Experimental gravitation from Newton's Principia
BIBLIOGRAPHY 285
to Einstein's General Relativity," In Three Hundred Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge: Cambridge University
Press, 1987), pp. 80-127
[WILL, 1989] C. M. Will, "Experimental gravitation in space: is there a future?"
Advances in Space Research 9, 147-155 (1989).
[WILL, 1990] C. M. Will, "Twilight time for the fifth force?" Sky f3 Telescope 80, 472-479 (1990).
[WILL, 1993] C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge: Cambridge University Press, 1993).
[WINELAND, 1991] D. J. Wineland, J. J. Bollinger, D. J. Heinzen, W. M. Itano,
and M. G. Raizen, "Search for anomalous spin-dependent forces using stored
ion spectroscopy," Phys. Rev. Lett. 67, 1735-1738 (1991).
[WITTEBORN, 1967] F. C. Witteborn and W. M. Fairbank, "Experimental com
parison of the gravitational force on freely falling electrons and metallic elec
trons," Phys. Rev. Lett. 19, 1049-1052 (1967).
[WITTEBORN, 1968] F. C. Witteborn and W. M. Fairbank, "Experiments to de
termine the force of gravity on single electrons and positrons," Nature 220,
436-440 (1968).
[WOLFENSTEIN, 1978] L. Wolfenstein, "Neutrino oscillations in matter," Phys. Rev. D 17, 2369-2374 (1978).
[WORDEN, 1996] P. W. Worden, Jr. and M. Bye, "The Stanford equivalence
principle experiment," In Proceedings of the STEP Symposium, Pisa, Italy,
6-8 April, 1993, edited by R. Reinhard (European Space Agency publication
ESA WPP-115, 1996).
[Yu, 1979] H.-T. Yu et al., "Experimental determination of the gravitational
forces at separations around 10 meters," Phys. Rev. D 20, 1813-1815 (1979).
[ZACHOS, 1978] K. Zachos, "N = 2 supergravity theory with a gauged central
charge," Phys. Lett. B 76, 329-332 (1978).
[ZAKHAROV, 1970] V. I. Zakharov, "Linearized gravitation theory and the gravi
ton mass," JETP Lett 12, 312-314 (1970).
[ZAKHAROV, 1991] V. I. Zakharov, "Unitarity constraints on multiparticle weak
286 BIBLIOGRAPHY
production," Nucl. Phys. B 353, 683-688 (1991).
[ZUMBERGE, 1991] M. A. Zumberge et al., "Submarine measurement of the New
tonian gravitational constant," Phys. Rev. Lett. 67, 3051-3054 (1991).
A
Achilli, v., 103 Adelberger, E. G., viii, 12, 14, 26,
Bagley, C. H., 229 Barker, B. M., 13, 207 Barnothy, J., 131 Barr, G. D., 202 Barr, S. M., 9 Bars, 1., 9 Bartlett, D. F., 93, 108, 140, 151,
214,216
Author Index
Barton, M. A., 102 Bekenstein, J., 48 Bell, J. S., 6, 17, 198, 200 Beltran-Lopez, V., 50, 212 Bennett, Jr., W. R., 29, 163 Bernstein, J., 6, 17, 198, 200 Berthias, J.-B., 61, 62, 112, 114,
115 Bertotti, B., 180 Beverini, N., 195 Bizzeti, P. G., 8, 48, 169, 175, 176 Bizzeti-Sona, A. M., 48, 169, 175,
176 Blinnikov, S. 1., 4 Bobrakov, V. F., 12, 210 Bock, G. J., 7, 17, 197, 200, 215 Bod, L., 8, 225 Bohr, A., 54, 55, 208 Bollinger, J. J., 50, 212 Bondi, H., 139, 140 Boothroyd, A. J., 61 Bordag, M., 74 Boslough, J., viii Bouchiat, C., 203, 205 Boulware, D. G., 2 Bowler, M. G., 189, 190 Boyd, P. T., 218 Boynton, P. E., 29, 48, 145, 154,
155, 158, 161, 162, 216 Braginskil, V. B., 137, 146, 153 Bramanti, D., 218 Buchman, S., 207 Burgess, C. P., 218 Butler, M. N., 61 Bye, M., 184
288 AUTHOR INDEX
c Cabibbo, N., 6, 17, 198, 200 Camp, J., 14 Carlson, E. D., 9 Carosi, R., 201 Carusotto, S., 164, 166 Casimir, H. B. G., 74 Catastini, G., 218 Cavasinni, V., 164, 166 Chan, H. A., 4, 73, 89, 90 Chandrasekhar, S., 217 Chang, D., 9 Chanmugam, G., 57 Chardin, G., 195, 215 Chen, S.-C., 211 Chen, S.-G., 75 Chen, Y. T., viii, 73 Cheng, H.-Y., 7, 17, 26, 50, 51,197,
200, 203, 204, 205, 208, 215 Cheng, W. K., 9, 207 Cho, Y. M., 9 Chou, Y., 12,211 Christenson, J. H., 6, 198 Chu, S. Y., 23, 149, 213 Chui, T. C. P., 210 Chupp, T. E., 50, 212 Ciufolini, I., viii, 1 Cloutier, J., 218 Cohen, J. M., 9 Colella, R., 192 Condon, E. U., 24 Cook, A. H., viii, 73 Cornaz, A., 99, 103, 104 Cornwall, J. M., 59 Coupal, D. P., 201 Cowsik, R., 29, 161, 163 Cranshaw, T. E., 60 Cronin, J. W., 6, 198 Crosby, D., 29, 48, 145, 154, 155,
161, 162, 216 Cvetic, M., 9
D
Dahlen, F. A., 97, 236 Damour, T., 18 Dappen, W., 217 Darling, T. W., 92, 93, 192, 216 Davidson, C., 131 Davisson, R., 169 de Rlijula, A., 62 de Sabbata, V., 9 Deeds, W. E., 185, 218 Deser, S., 2 Dessler, A. J., 192 Dicke, R. H., 23, 55, 137, 138, 146,
149, 153, 184, 213 Dickey, J. 0., 115, 116, 118 Dittus, H., 167 Dobroliubov, M. I., 205 Donoghue, J. F., 9 Drake, S., 163 Drever, R. W. P., 50, 212 Dyer, P., 14 Dyson, F. W., 131 Dziewonski, A. M., 242
E
Eckhardt, D. H., 49, 107, 108, 216 Eddington, A. S., 131 Edge, R. J., 102 Ekstrom, P., 29, 48, 145, 154, 155,
161, 162, 216 Elizalde, E., 74 Ellis, J., 9 Eotvos, R. v., 5,124-127,130,131,
134, 135, 213, 223, 225 Ericson, T. E. 0., 192 Everitt, C. W. F., 185, 207
AUTHOR INDEX 289
F
Fackler, 0., 108, 216 Fairbank, W. M., 189, 192 Faller, J. E., 108, 137, 139, 146,
Fitch, V. L., 6, 29, 162, 198 Fortson, E. N., 50, 212 Franklin, A., viii, 6 Freeman, B. S., 9, 207 Frieman, J. A., 49 Frontov, V. N., 4, 72, 73, 82, 85,
Gilliland, R. L., 217 Gitarts, Ya. L, 12, 210 Glass, E. N., 217 Gold, T., 189 Goldberg, H., 59 Goldblum, C. E., 12, 209, 210 Goldhaber, A. S., 2 Goldman, T., 11, 14, 45, 193, 194,
205 Goldstein, H., viii Good, M. L., 6, 17, 189 Goodwin, B. D., 4, 91, 102 Gradwohl, B.-A., 49 Graessle, G., 14 Graham, D. M., 12, 29, 158, 161,
163, 187, 210 Greene, G. L., 216 Gregory, E. C., 45, 194 Grifols, J. A., 218 Grossman, N., 201 Guinan, E. F., 218 Gundlach, J. H., 29, 154, 155, 161,
163, 167, 186, 187 Gupta, S. N., 13, 207
H
Hagelin, J. S., 205 Hagiwara, pc, L M., 104 Hall, A. M., 213, 214 Halprin, A., 61 Haracz, R. D., 13, 207 Hari Dass, N. D., 211 Hartle, J. B., 52, 57 Haugan, M. P., 26, 50, 51, 53, 212 Haxton, W., 203, 204, 205 Hayashi, K., 8, 136, 218 Heckel, B. R., viii, 12, 26, 27, 29,
184 Kruglyak, L., 49 Kuhn, J. R, 49 Kiindig, W., 99, 103, 104 Kuroda, K., 4, 29, 48, 119, 120,
164, 165, 166
L
Lagomarsino, V., 195 Lamoreaux, S. K., 50, 74, 212 Langel, R, 216 Langlois, W. E., 171 Lazarewicz, A. R, 107, 216 Lee, T. D., 6, 17, 124, 130, 198, 200 Leitner, J., 211 Leung, C. N., 61 Li, M., 180
AUTHOR INDEX 291
Lindner, K, 102 Littenberg, L. S., 205 Liu, H., 81 Lobov, G. A., 53 Lockhart, J. M., 189 Logl, S., 216 Long, D. R, 4, 65, 66, 72, 74-77,
81, 82, 84, 214 Longo, M. J., 60, 61 Low, F. E., 75 Lowes, F. J., 102 Lui, A. T. Y., 216 Lusignoli, M., 203, 205 Luther, G. G., 68, 229, 232
M
Macrae, K 1., 189 Madey, J. M. J., 189 Malaney, R A., 60, 61 Maloney, F. P., 218 Mannheim, P. D., 49 Manuzio, G., 195 Maris, H. J., 175 Marx, G., 8,134,225 Masso, E., 218 Mazilu, P., 167 McHugh, M. P., 108, 150, 164, 165,
166,216 Membrado, M. C., 217 Metherell, A. J., 73 Meyer, H., 84 Mezzorani, G., 60, 61 Michel, F. C., 192 Mikheyev, S. P., 61 Mikkelsen, D. R, 4, 66 Milani, A., 218 Milgrom, M., 8, 48 Milyukov, V. K, 84 Minakata, H., 61 Mio, N., 29, 48, 73, 164, 165, 166,
179
Misner, C. W., 1 Mitrofanov, V. P., 74 Moffat, J. W., 9, 44 Mohapatra, R N., 9 Moody, J. E., 211 Moody, M. V., 4,73,90 Moore, G. 1., 4, 91, 102 Moorhead, G. F., 192 Morinigo, F. B., 13, 52, 57, 189 Morpurgo, G., 194 Morrison, P., 189 Mostepanenko, V. M., 74 Mottelson, B. R, 54, 55, 208 Miiller, G., 102
N
Nachtmann, 0., 7, 17, 197 Naray-Ziegler, M., 8, 225 Nelson, P. G., 12,29, 158, 161, 163,
187,210 Neufeld, D. A., 139 Newman, J. R, 111, 112 Newman, M. J., 4, 66 Newman, RD., 4, 12, 29, 72, 73,
74, 78, 79, 81-84, 158, 161, 163, 187, 210, 214
Newton, 1., 125 Ni, W.-T., 4, 5, 12, 73, 209-212 Niebauer, T. M., 108, 150, 164,
165, 166, 216 Nieto, M. M., 2, 11, 14, 45, 92, 93,
193, 194, 205, 216 Nijgh, G. J., 189 Nobili, A. M., 218 Nordtvedt, K, 53, 140, 141 Nozawa, S., 61 Nunokawa, H., 61 Nussinov, S., 9, 136
292 AUTHOR INDEX
o O'Connell, R. F., 211 Odishaw, H., 24 Ogawa, Y., 4, 73, 120 o 'Hanlon, J., 4, 91 Ohashi, M., 29, 179 Oide, K, 4, 119 Okubo, S., 211 Oldham, M., 102 Olive, K A., 9, 48 Opat, G. 1., 192 Overhauser, A. W., 54, 192
p
Pacheco, A. F., 217 Paik, H. J., 4, 73,88, 89, 90 Pakvasa, S., 61 Pal, P. B., 9 Palmer, M. A., 29, 162 Pan, S.-S., 211 Panov, V. 1., 4, 72, 73, 82, 85, 86,
90, 137, 146, 153 Pantaleone, J., 60, 61 Park, D. H., 9 Parker, R. L., 67, 92, 93, 97, 99,
101,216 Paver, N., 205 Peccei, R. D., 9, 12 Pechlaner, E., 9 Pekar, D., 5, 124, 127, 130, 131,
172-177,215 Thirring, VV., 17 Thodberg, H. H., 8 Thomas, J., 93, 108, 216 Thorne, K. S., 1 Tohline, J. E., 49 Torelli, G., 195 Towler, VV. R, 68, 229, 232 Trammell, G. T., 192 Trampetic, J., 203 Tremaine, S., 60 Tsamis, N. C., 9 Tsubono, K., 4, 29, 73, 119, 120,
179 Tuck, G. J., 4, 91, 92, 93, 95, 102,
175, 214, 215 Turlay, R, 6, 198
u
Uehling, A. E., 75 Unnikrishnan, C. S., 29, 161, 163
v Van Baak, D. A., 150 Van Buren, D., 140 van Dam, H., 2 Vanicek, P., 98 Vecsernyes, P., 136 Veltman, M., 2 Venema, B. J., 212 Visser, M., 9 Vogel, P., 93, 216 Voloshin, M., 9 Vorobyov, P. V., 12, 210 Vucetich, H., 60, 217
w VVagner, VV. G., 13, 52, 57, 189 VVagoner, R V., 4 VValesch, H., 84 VVang, S.-L., 12, 211 VVapstra, A. H., 189 VVatanabe, R, 14, 26, 27, 29, 30,
152, 154, 159, 161, 163, 175, 225, 227
VVeiler, T. J., 61 VVeinberg, S., 1, 7, 18, 203 VVeisberg, J. M., 18, 59, 180, 203 VVerner, S. A., 192 VVetterich, C., 9, 12 VVheeler, J. A., viii, 1 VVhiting, B. F., 5, 66, 91 VVilczek, F., 211 VVill, C. M., viii, 1, 8, 50, 53, 60,
189, 190, 212, 218 VVineland, D. J., 50, 212 VVitteborn, F. C., 189, 192 VVolfenstein, 1., 61 VVolszcan, A., 18 VVoolgar, E., 9 VVorden, Jr., P. VV., 184
local, 8, 146, 162, 163, 167, 250 Spin-dependence, tests for
Bobrakovet al., 210, 250 Chou et al., 211, 253 Chui et al., 210-211, 253 Gravity probe B, 257 Graham et al., 210, 263 Hsieh et al., 211-212, 266 Ni et al., 212, 274 review, 12 Ritter et al., 210, 278 Su et al., 281 Vorobyov et al., 210, 284 theor~ 12, 207, 210, 211
Spin-dependent interaction (see Non-Newtonian interactions)