Search for Lorentz invariance using a torsion-strip balance

1. Search for Lorentz invariance using a torsion-strip balance Clive Speake, Hasnain Panjwani and Ludovico Carbone. Rencontres de Moriond, La Thuile, 23rd March 2011.

2. 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.

3. t b 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 mm and smax = 800 MPa. • ~ 3 x 105 , period 123 s, drift 1 mrad/week.

4. Apparatus used to determine G at BIPM Autocollimator 1.2kg test masses • Three determinations with partially correlated uncertainties: • Free deflection • Electrostatic servo • Time-of-swing Carousel for 12kg source masses T.J.Quinn et al PRL 2001 realised by Harold Parks whilst at BIPM

5. Current Status of G

6. Assembling the torsion balance

7. 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.

8. Nested Spheres Nested Cylinders logB (T) logB (T) • Matlab images from 2d analysis using FEM software – FEMM 4.2 • Also used 3d analysis with ANSYS. Hasnain Panjwani

9. Earth Sun 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. • Lorentz transform into Earth frame wrt to Solar system Primordial vector field Kosteleckỳ and Tasson PRL 2009

10. Measurement technique alternatively move position of the source masses around the pendulum look at the coherent modulation of the pendulum equilibrium angle • move source masses from one position to the other every 800s • any movement is a measurement of G: 108 “G measurements” per day

11. Data analysis procedure. Ludovico Carbone • “Cleaning” the data from imperfection in sampling rate or incorrect readings • of the autocollimator • Convert data to torque using quadratic fitting • Filter out possible • residuals of pendulum • resonance (~120 s) • Low pass filtering the data • (to eliminate high • frequency noise >0.1Hz)

12. Multi-linear fitting

13. Investigate coupling to environmentals on purpose! Example: measurement of coupling to temperature variation High coupling!!!

14. Estimation and subtraction of environmental effects • “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.

15. (…things are much better….)

16. Subtraction of environmental signals from “science” data Effect on first ~ 80 days data

17. Fitting to search for sidereal related signals Preliminary results on first ~ 80 days data

18. Fitting to search for sidereal related signals Preliminary results on first, 80 days data ~ Autumn 2008. (3 months) Total 8500 datapoints 24 sidereal hours 12 sidereal hours Statistical errors at ppm level, null result for ~24h signal, ~3s null result for ~12h Carbone et al Marcel Grossmann 2009

19. Preliminary results: • No preferred frame effect (12 hour) is observed at level of few 10-6 • (Gershteyn et al detected dG/G ~ 5 10-4) • Preliminary upper limit on one of Kostelecky’s parameters ( 24hr 1st time) • 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. Panjwani et al CPT10 2010

20. Reinstall experiment in quieter basement room with better possible temperature control. Design and construction of angle interferometer (insensitive to tilt of rotating mirror over 1o or so). Peña-Arellano CS App Opt 2011 Lost ~ 5 months due to vacuum problems

21. Current status of spin-coupling experiment 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.

22. 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 directmeasurement. 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. .

23. Current sensitivity with autocollimator

25. Two possible solutions Nested Spheres Nested Cylinders • “Cleanest” solution (dipole field!) • Easy to match magnetic moments • Alignment issues • Manufacturing issues • Simpler to manufacture • Mechanically stable & self aligning • Mag. multipole moment expansion • to null low order moments • Non negligible • leakage field Class. Quantum Grav. 26 (2009) 145009 Hasnain Panjwani