Tests of the Newton gravity law at various distances

 V.N.Rudenko.

SAI.MSU, INR RAS

Precision Physics & Fundamental Physical Constants, (Dubna, December 5-9, 2011)

G= 6.6742.. → G(r) ?

Contents

1. History of “fifth force” hypothesis

2. Theoretical motivations for the ISL probing.

3. Tests at long and intermediate distances.

4. Motivation of ISL probing at short distances.

5. Recent short range ISL tests.

6. Casimir force measurements.

7.Current limitations at non-Newton gravity.

Start of the “fifth force” hypothesis at early 70th 

Some experiments had found a difference between space measured constant GN and lab measured constant G0 

• Geophysical measurements results in GN > G0 

Stacey F.D., Tuck G.J. Nature 292, 230 (1981);Holding S.C., Tuck G.J. Nature 307,714 (1984);Stacey F.D., Tuck G.J.et .al. Rev. Mod. Phys. 59, 157 (1987)…. 

• Lab. measurements: Long D.R. Phys.Rev.D9, 850, (1974) ; Nature 260, 417, 1976 

• Re-examination of Eotvos experiment data 

Fischbach E. et.al. Phys.Rev.Lett. 56,(n1), 3-6, 1986 

.we find that the Eotvos-Pekar-Fekete data are sensitive to the compositionof the materials used, and that their results support the existence of an intermediate-range coupling to baryon number or hypercharge…”

V(r) = VN(r) + V(r)

Gravity law phenomenology

T.D.Lee, C.N. Yang, Phys.Rev. 98,1501, (1955). Lee, Yang –were the first speculating that the conservation of baryon number B was associated with a vector field coupled to B and had given limits derived fromknown EP experimental tests: the matter is –(additional to gravity) scalar or vector interactions violate EP, so as they couple toa specific “hypercharge” (q) not masses of test bodies  equivalent potential and acceleration of body (1) toward an attractor (A) 

r

eqqV

r

AA

)/(

11 4

1

rerr

q

m

q

m

Va rAA

/

21

1

1

11

11

4

ratio “hypercharge” to mass is not universal (!) EP violation

G metrology is very bad !

|G/G| has accuracy ~ 10 -4

at contrast : |c/c| ~ 10 -9

fine str. | = e2/c| ~ 10 -10

geocentric |GM| ~ 10 -8 etc.

G = (6.6742 0.0042 ) 10 -11 m 3 kg –1s -

2

Absolute G measurements : r ~ 5 – 50 cm

SAI MSU : Sagitov M.U., Milyukov V.K., Monakhov E.A. et. al.

Sov.Phys. Doklady (1979), v.245, (3), pp.

Metrological uncertainty of G measurements

Cavendish type measurement at range 1m < r < 1000 m using GW detectors as very sensitive gradiometers:

One - as a dynamically driven source of alternative g-field; Second - as a sensitive receiver

with sensitivity x ~ 10-17 cm, τ ~ 3 10-4 sec

it would be able to achieve G/G ~ 0.1% at the distances up to r ~100 m.

Planetary dynamics restrictions

The Cavendish experiment at large distancesV. I. Panov and V. N. FrontovMoscow State UniversityZh. Eksp. Teor. Fiz. 77, 1701-1707 (November 1979)

m = 10g, M = (60 – 600) kg, τ ~103 s, τr ~ 106 s.

min Torq ≈ ∙10-6 dyn∙cm , 2l = 40 cm

0.3 m < r < 10 m

1. G(r1)/ G(r0) = 1.003 ± 0.006 r1= 0.3 m

2. G(r2)/ G(r0) = 0.998 ± 0.013 r2 = 10 m

Experimental test of gravitation at small distancesV. P. Mitrofanov and 0. I. PonomarevaM. V. Lomonosov State University, MoscowZh. Eksp. Teor. Fiz. 94,16-22 (October 1988)

3.8 mm < r < 6.5 mm

for small test mass FN → 0 as R-4

requairement to sensitivity (!),

min Torq ≈ 5∙10-10 dyn∙cm

r1 = 3.7 mm , r2 = 6.4 mm.

(F1/F2)exp - (F1/F2)cal= (1.0 ± 5.4)10-2

1.E.Fischbach, C.L.Talmadze. The search for Non-Newtonian Gravity, Spriger- gerlach……

 2. M.Bordag, G.L.Klimchitchaya, U.Mohideen, V.M.Mostepanenko, Advance in the Casimir Effect. Oxford Science Publishing

 3..E.G. Adelberger !, J.H. Gundlach, B.R. Heckel, S. Hoedl, S. Schlamminger, Torsion balance experiments: A low-energy frontier of particle physics Progress in Particle and Nuclear Physics 62 (2009) 102–134

References : a “new motivation” for short distance ISL tests

Dimopoulos’s picture Sci.Am. 2000

E.G.Adelberger, et.al. , PPNP 62 (2009) 102 – 134, C.D.Hoyle, et.al., Phys.Rev.D 70 (2004) 042004 Phys.Dept., University of Washington, Seattle, WA

groupWASHTOE .""

Sub-millimeter tests of ISL (1mm – 50 m)

It is a new experimental idea was proposed:

to adapt the “Cavendish type” experiment for “short interaction distances” it is profitable to deal with “lost test masses” (!), i.e. to use torsion balances with “holes instead of balls”. A simplest construction is two plane gravitating discs with bored holes.

Several versions of the setup were developed by Eot-Wash group for to probe ISL at 1mm –10 mkm

one rotation cycle at produces the torque harmonic at N, N – number of holes along disc circle (folds), 2N , etc.

first version (2004) with n = 10

second version (2009) with n=21

Adelberger et.al. experiments

attractor consists two discs;

more thick lower one has a phase shift in the hole structure;

this allows to compensate the classical Newtonian force for a definite gap between discs (~ 2 mm at the picture) in the first harmonic ….

just in this region a sensitivity to Yukawa forces has a maximum

Adelberger et.al experiments

Output record for one rotation circle

a) raw data

b) fitted data

c) residuals

Adelberger et.al.experiments

Plot of measured (calculated) torque

black – N10, blue – N20 , red – N30

(orange – no compensation Nn)

N10- residuals for | | = 1, = 250 m (Yukawa);

and k=0.005 for the “power law” model

Best final result:

| | 1, = 56 m

| | 1 , = 44 m R n=2 , M 3.2 Tev/c2

“Eot-Wash” results in general world labs experiments

A.A.Geraci et.al. PR D78, 022002, 2008 Stanford University range 5 – 15 m

test osc.– silicon micro cantilever 250•50•0.3 m test mass – 1.5 g (gold foil 27 m ; Pt/Co film )

measured force F = kz / Q;

k~0.006 N/m ; Q ~ (8 – 1)104

Fmin ~ 200 aN / Hz ½ ; T ~ 10 K

drive mass – 100 m deep gold-silicon strips 100 m • 1mm

magnetic calibration – current in the drive strips

read out –FP cavity “test mass – fiber”; P~1 W

Results:- the new limit Yukawa forces below 20 m

the best bound: || > 14 000 at = 10 m

At the range 1 m – 10 m electromagnetic field vacuum fluctuation screens the Newton gravitational attraction: one has to measure the Casimir force.

Lamoreaux exp.: first reliable measure of Casimir force; PRL 78,№1,5-8,1997

test of QED,… not Newtonian gravity !

torsion pendulum; feedback, null method

plate: D=2.5 cm , h=0.5 cm (optical quartz, film Cu, Au) spherical lens: Rcurv = 11.3 cm

0.5 a 12 m

demonstration of the Casimir force 5%

Washington University, WA

Sub micrometer range 0.48-6 µm

M.Masuda et.al. PRL 102, 171101, 2009 ICRR, Tokyo University

P1→r=20mm, Rcurv=207mm

P2→r=15mm, h=2mm, roughness ~ 22 nm

3

3

360 z

RcFcas

tungsten wire 60µm, 400mm

Δφmin~ 10-6 rad/Hz½

feedback, null method

Conclusions:

up to the distance on the order of few micrometers experiment confirms Newtonian ISL for gravitational interaction with high confidential limit

Thus a range of extra dimensions (if they exist) has to be less then 1 km

Further search for extra dimensions (if continues) will not be associated with a measurement of gravitational forces

Thanks for attention.

Authors, year of publication

Value of G10-11

м3kg-1s-2

STD 10-11 m3kg-1s-

ppm

[1] Facy and Ponticis 1972 6.6714 0.0006 90 [2] Sagitov, Milyukov, et al. 1979 6.6745 0.0008 120 [3] Luther and Towler, 1982 6.6726 0.0005 75 CODATA 1986 6.67259 0.00085 128 [5] Michaelis, et al. 1995 6.7154 0.0006 90 [6] Karagioz, Izmailov, 1996 6.6729 0.0005 75 [7] Bagley and Luther, 1997 6.6740 0.0007 105 CODATA 1998 6.673 0.010 1500 [9] Jun Luo, et al., 1999 6.6699 0.0007 105 [10] Fitzgerald and Armstrong 1999 6.6742 0.0007 105 [11] Gundlach and Merkowich, 2000 6.674215 0.000092 14 [12] Quinn, Speake et all. 2001 6.67559 0.00027 41 [13] Schlamminger et all. 2002 6.67407 0.00022 33 [14] CODATA 2002 6.6742 0.0010 150 [15] Armstrong and Fitzgerald 2003 6.67387 0.00027 40 [16] Schlamminger et all. 2006 6.674252 0.000109 16 CODATA 2006 6.67428 0.00067 100 [17] Jun Luo, et al. 2009 6.67349 0.00018 26 [18] Parks and Faller 2010 6.67234 0.00014 21

The best The best world world experiments experiments on the on the measurement measurement of G andof G andCODATA CODATA valuesvalues

1975 1980 1985 1990 1995 2000 2005 2010

6.668

6.67

6.672

6.674

6.676

6.678

6.68

Year

G

10-1

1 [m

3 k

g-1 s

-2]

[1]

[2]

[3] CODATA-86 [6]

[7]

CODATA-98

[9]

[10]

[11]

[12]

[13]CODATA-02

[15]

[16]

CODATA-06

[17]

[18]

CODATA-11

?