Search for Lorentz invariance using a torsion-strip balance

Clive Speake,Hasnain Panjwani

and Ludovico Carbone.

Rencontres de Moriond, La Thuile, 23rd March 2011.

Outline

• The torsion-strip balance at BIPM and Birmingham.• Design of a search for Lorentz violation signal: Polarised,

non-magnetic masses.• Test of Lorentz invariance in gravitational sector.• Future improvements.

Torsion-strip balances

• At BIPM in 1990’s, whilst investigating internal damping mechanisms in flexures, we examined ribbon suspensions.

• All torsion fibres have two contributions to their stiffness. In the case of rectangular fibres:

• b is width, t is thickness, L is length, M is supported mass, F is shear modulus.

• Ratio of thermal s/n for torsion-strip balance to that in round fibre balance

~ ~ 20 for BeCu with r = 10 m and max = 800 MPa.

• ~ 3 x 105 , period 123 s, drift 1 rad/week.

L

bt

bt

MgFc

12

4 3

bt

4/1

max

Ftr

b

e

g

c

c

F

FQ

Apparatus used to determine G at BIPM

1.2kg test massesAutocollimator

Carousel for 12kg source masses

Three determinations with partially correlated uncertainties:

• Free deflection

• Electrostatic servo

• Time-of-swing

T.J.Quinn et al PRL 2001 realised by Harold Parks whilst at BIPM

Current Status of G

Recent values of G

CODATA-86

Uni-Zurich

Uni-Washington

JILA

Huazhong

CODATA 06

BIPM

0

6.67 6.672 6.674 6.676 6.678 6.68

Assembling the torsion balanceAssembling the torsion balance

The torsion-strip balance at Birmingham

• Initial goal was to search for Lorentz invariance violating forces coupling to intrinsic spin. We aimed at exploiting the superior thermal signal-to-noise of the torsion strip with ~4 kg of test mass.

• We looked for a scalable way of making spin-polarised non-magnetic test masses. We decided to use a combination of Sm Co and Nd B Fe magnets rather than Dy Fe (Ritter et 1990) and SmCo/Alnico (Heckel et al 2006) because of convenience and potentially higher spin density.

Nested SpheresNested Spheres Nested CylindersNested Cylinders

-Matlab images from 2d analysis using FEM software – FEMM 4.2-Also used 3d analysis with ANSYS.

Hasnain Panjwani

logB (T) logB (T)

Search for preferred frame effects

• Variation in G reported by Gershteyn of 5x10-4 over 12 sidereal hours.

• Kosteleckỳ proposed Lorentz and CPT violation as a by-product of quantum gravity Jan 2009.

a

Sun

Earth

Primordial vector field

• Lorentz transform into Earth frame wrt to Solar system

zzyyxxtt aaaaa

Kosteleckỳ and Tasson PRL 2009

taN

Na

N

Na

taN

Na

N

Na

M

N

G

G

Eey

n

epy

n

pny

Eex

n

epx

n

pnx

atom

nE

cos

sin4

Measurement technique

• move source masses from one position to the other every 800s• any movement is a measurement of G: 108 “G measurements” per day

alternatively move position of the source masses around the pendulum

look at the coherent modulation of the pendulum equilibrium angle

• “Cleaning” the data from imperfection in sampling rate or incorrect readings of the autocollimator• Convert data to torque using quadratic fitting

20 2

tX

tXXtX

• Filter out possible residuals of pendulum resonance (~120 s)

• Low pass filtering the data (to eliminate high frequency noise >0.1Hz)

tXtXtXItN

Data analysis procedure.

Ludovico Carbone

m

SINCOS

mm

mm T

tG

T

tGGtN

2sin

2cos100

Multi-linear fitting

Investigate coupling to environmentals

Example: measurement of coupling to temperature variationHigh coupling!!! High coupling!!!

on purpose!on purpose!

• “memory kernel” effect from temperature• Sensitive also to Tilt X, Tilt Y, Pend eq. angle, Source Mass position

• mutual relations between environmentals

A.R.M.A. fitting

S.V.D.

Estimation and subtraction of environmental effects

(…things are much better….)

Subtraction of environmental signals Subtraction of environmental signals from “science” datafrom “science” data

rel 210 4

rel 810 5

Effect on first ~ 80 days data

Fitting to search for sidereal related signalsFitting to search for sidereal related signals

Preliminary results on first ~ 80 days data

Statistical errors at ppm level, null result for ~24h signal, ~3 null result for ~12h

6

24

624

1050.145.0 :sinG

1053.179.0 :cosG

G12 cos : 4.431.52 10 6

G12 sin : 3.961.51 10 6

Preliminary results on first, 80 days data ~ Autumn 2008.

(3 months) Total 8500 datapoints

Fitting to search for sidereal related signals

24 sidereal hours

12 sidereal hours

Carbone et al Marcel Grossmann 2009

Preliminary results:Preliminary results:• No preferred frame effect (12 hour) is observed at level of few 10-6

(Gershteyn et al detected G/G ~ 5 10-4)

• Preliminary upper limit on one of Kostelecky’s parameters ( 24hr 1st time)

Further development required:Further development required:• extend/improve data analysis • better temperature control in quieter room.• new interferometric readout (<10-10 rad Hz-1/2) overcome the C.V. Boys’ fallacy.

GeVaaa ex

px

nx 2.083.0

GeVaaa ey

py

ny 4.083.0

Panjwani et al CPT10 2010

Design and construction of angle interferometer (insensitive to tilt of rotating mirror over 1o or so).

Reinstall experiment in quieter basement room with better possible temperature control.

Peña-Arellano CS App Opt 2011 Lost ~ 5 months due to vacuum problems

10-4

10-3

10-2

10-1

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

Sensitivity to Kost Field 100 days observation 4.8e24 spins

Frequency (Hz)

b e (

eV)

Current

best bx

Thermal Noise

Heckel et al

PRD 2008

• We need the spin-compensated test masses (prototype in process).

• We need a rotating platform to maximise the s/n.

• Limited by autocollimator above few 10-3 Hz. Using the interferometer the thermal noise is within our reach.

Current status of spin-coupling experiment

Summary

• We are developing a torsion-strip balance to search for spin-related forces.

• We have placed upper limits on possible sidereal variations of G by direct measurement. Further improvement is possible in s/n and data analysis.

• With more work and investment the experiment has the potential to make a contribution to our knowledge of long range spin-coupling forces.

• Thank you for your attention

and STFC for funding the experiment.

.

Current sensitivity with autocollimator

10-4

10-3

10-2

10-1

10-15

10-14

10-13

10-12

10-11

10-10

10-9

Frequency (Hz)

S1/

2N

(N

m H

z-1/2

)

Current

Autocollimator Ultimate (5nrad.Hz-1/2)

Readout (10-10.Hz-1/2)

Pendulum Thermal

Nested SpheresNested Spheres

• “Cleanest” solution (dipole field!)• Easy to match magnetic moments

• Alignment issues• Manufacturing issues

VinM in VoutMout

Two possible solutionsTwo possible solutions

Nested CylindersNested Cylinders

• Simpler to manufacture• Mechanically stable & self aligning

• Mag. multipole moment expansion to null low order moments

• Non negligible leakage field

q1IN q1

OUT r 3

q3IN q3

OUT r 5

Class. Quantum Grav. 26 (2009) 145009

Hasnain Panjwani

Torsion Balance and Vac data – Night of 13-09-2010

8 10 12 14 16 18 20 22 24 26 28

-11

-10

-9

-8

-7

-6

-5

-4

x 10-6

16.43 mins after start

17.45 mins after start

18.52 mins after start