importance of g in physics? motivation bipm/b™ham

Moriond27th March 2003

Progress in determining GClive Speake

University of Birmingham

• Importance of G in physics?

• Motivation

• BIPM/B�ham determination

• Recent developments

Moriond27th March 2003 Importance of G in physics?

• Why are we interested in the value of G?

Newton 1687 Einstein 1915

G is the UNIVERSAL constant of Gravitation

• Defines the dynamics of the Universe?Perhaps holds the key to Unification of forces. No Quantum theory of gravitation

122

12

2112 r̂

rMMGF −=

vµνµνµν

πTc

GgG4

8=Λ−

Moriond27th March 2003 Importance of G in physics?

• Original motivation was to determine the densities of planets (those with satellites).

Kepler

The Geocentric Gravitational constant is very accurately knownGME=398600.4415+/-0.0008 km3 s-2 (2ppb)

{ } 32 1)(

RmMG +=ω

• In dynamics we only find G in the product GM eg in binary pulsars; precession rate { } 3/2GM∝

• However masses of ZAMS 5/1

7

∝

GLM

• Chandrasekhar limit for White Dwarfs2/3

2

2

≈

pp Gm

cAZmM h

• G is calculable from other coupling constants and Unification scale; with gu

2=1/25 at 2.1016GeV, gives G=2.108!

Moriond27th March 2003 Motivation

•Our knowledge of gravity is weak!

dG/G = 0.15% , cf dα/α = 3.7 ppb (CODATA 1998)

•Inverse square law cf for electromagnetism 1/r2+ε, ε<3.10−16

Gravity


Values for Newton's G 1998

6.66 6.67 6.68 6.69 6.7 6.71 6.72

PTB

Wuppertal ZurichJILABIPM98

MSL new

CODATA 86

Luther Towler

MSL old

Moskow

Bagley Luther

G 1011 m3 kg-1s-2

• Least well-determined fundamental constant.

• Were torsion balance results biased by frequency dependent losses?

Torsion balance

• Was PTB value correct?

Mercury suspendedtorsion balance

Motivation

)128(10)0009.06726.6( 23111 ppmsmkgG −−−×±=• 1986 CODATA value:


Frequency dependent fibre losses

Fractional change in spring constant

02468

101214

-6 -5 -4 -3 -2 -1 0 1 2

Log(frequency)

xQ

Maxwell unit:

+

∆+=ωτ

ωτj

jk

kK1

1

F

k

∆

∆.τ

• Extend to a distribution with

density of states ~1/τ

Real part of spring constant:

ττω

τωττ

τ

τdKreal ∫

∞

∞ +∆=

022

2

0 1)/ln(

Quinn et al 1992Kuroda 1995

• Leads to an overestimate of G

Moriond27th March 2003 Determination of G

T.J.Quinn, CCS, S.J.Richman, R.S.Davis and A. Picardco-workers and experiment at BIPM, France.

•Four-fold symmetry: low sensitivity to gravity gradients

•Torsion-Strip: 96% of restoring torque is gravitational. Relaxationtime 4 months. Torque is104 bigger than Luther 1981.

•Two quasi-independent methods:Electrostatic servo and Cavendishmethods.

•Experiment mounted on CMM.

T.J.Quinn, C.C.Speake, S.J.RichmanR.S.Davis and A.Picard. Phys Rev Lett 87, 111101, 2001


12kg source massesCu -Te. Density gradient 200ppm across diameter

1.2kg test masses

AutocollimatorVacuum-canTorsion strip

Torsional stiffness:

Round section;

Rectangular section;2

.4R

LFk π=

21 4

2

RR

MgL

ππ

+

+

=12

112

433 tb

abMg

Lbt

LFk


•Electrostatic torques applied tobalance G.

•Capacitance gradient hasmaximum versus angle (θ).

•Use capacitance bridge/autocollimatorto measure components of C(θ).

• Frequency dependent losses incapacitances could explain PTBresult. Use ac servo at frequency of Capacitance bridge.


Plot of variation with angle of capacitance between one set of electrodes and torsion balance.

Moriond27th March 2003 Loss induced errors in

Capacitance calibration

( ) 121 )( −+>> CCRω ( )

+

+≡21

21CC

CCdd

ddC

ddC

θθθ

• Stray capacitance to lossyshields gives extra capacitance

C1

C2

RV C

• Determine C(θ) usingac bridge at 1kHz

• Use { }∑ −==Γ 2)(21

jiij VVCdd

ddU

θθ

Moriond27th March 2003 Loss induced errors in

Capacitance calibration

( )( )

++

+=Γ 221

22

21

222

2

12 CCRCR

ddC

ddCV

ωω

θθ

•Stray capacitance to shieldsgives extra frequency dependenttorque

C1

C2

R

( ) 121 )( −+<< CCRω θd

dCV2

2

→Γ

• Calibration includes variation of C2: Overestimate of G• Possible explanation of PTB result?• Calibrate and apply torques at same frequency.

• Apply torques with lowfrequency voltage

V C


Uncertainty Source pts in 105

(a) Servo-method:

test mass value 0.25

source mass value 0.25

test and source mass coordinates 3.2

angle calibration 2

calibration of electrical instruments 4

mean of torque measurements (n=25) 2.3

Sub-total 6.0

(b) Cavendish method

test mass value 0

source mass value 0.25


timing 3.5

angle calibration 4

anelasticity 0.4

source-mass density inhomogeneity 0.6

mean of deflection measurements (n=38) 3.2

Sub-total 6.7

A ve rage o f (a) and (b),

tak ing account o f corre lations

mass values 0.3


source-mass density inhomogene ity 0.3

anelastic ity 0.2

capacitance calibration 2

angle calibrat ion 1

tim ing 1.75

means of torque and deflection 2.0

C ombine d unce rtainty 4 .1


Final value:G = 6.67559(27) × 10-11 m3 kg-1 s-2 (41ppm)

• Cavendish Method: G = 6.67565 × 10-11 m3 kg-1 s-2 (67ppm)

• Servo method: G = 6.67553 × 10-11 m3 kg-1 s-2 (61ppm)

• Cross-correlation in uncertainty budgets -18%

CODATA 1999: )1500(10)010.0673.6( 23111 ppmsmkgG −−−×±=


Mk3 Torsion strip balance at BIPM 26 March 2003


Torsion-strip gimbal and simple pendulum damper.


Richard Davis, Terry Quinn (his optics), Harold Parkes


Recent Developments

Values of Newton's Constant of Gravitation 2003.

CODATA 1986Bagley Luther

MoskowHUST

CODATA 99

WuppertalMSL

BIPMSeattle

Zurich

6.66 6.67 6.68 6.69

G. 1011 m3 kg-1 s-2

Measurements in progress: BIPM, HUST, Irvine, JILA, MSL.

importance of g in physics? motivation bipm/b™ham

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