Ring Laser Gyroscope Measurement of Absolute Earth Rotation

Ring Laser Gyroscope Measurement of Absolute Earth Rotation Rate Bob Hurst Currently involved: Associated: Jon-Paul Wells Geoff Steadman Rob Thirkettle Clive Rowe Ulli Schreiber Richard Graham Nish Rabeendran John Holdaway Marsden Fund support: M 1142: A Terrestrial Measurement of the Frame Dragging of the Rotating Earth 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Michelson-Gale experiment (1925) (38 years after the famous Michelson-Morley experiment. ) “Well, gentlemen, we will undertake this, although my conviction is strong that we shall prove only that the earth rotates on its axis, a conclusion which I think we may be said to be sure of already. ” • Motivated by speculations on ether-motionrelated effects • Rectangular Sagnac interferometer, 612 m x 339 m • Built from 12 -inch evacuated sewer pipe • Observed just the fringe shift expected from earth rotation • Astrophysical Journal, 61, pp 137 -145 (1925) 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Detection of Chandler wobble (A ‘Eulerian’ wobble, amplitude several metres, period ~435 days K. U. Schreiber, T. Klugel, J. -P. R. Wells, R. B. Hurst, A. Gebauer: “How to Detect the Chandler and the Annual Wobble of the Earth with a Large Ring Laser Gyroscope. ” Physical Review Letters, 107 173904, November 2011. 40 G raw data 20 (prad/s) 0 Subtract polar motion, local tilt -20 -40 Rotation rate change predicted from IERS data -60 55320 55340 55360 55380 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013 m. JD

Why measure absolute rotation rate? 1 Length of day (LOD) There are many geophysical mechanisms that redistribute angular momentum between mantle, core, oceans, atmosphere. Results in LOD variation at a level of a few millisec (Acknowledgment: http: //xkcd. com/162/ ) (Acknowledgment: GFZ, Potsdam http: //www. ceos. org ) 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Length of day (LOD) (ctd) At present, derived from Radio-astronomical observations of quasars (VLBI, international network of telescopes) Accuracy: < 100 µs (1 in 109) But: latency and incompleteness 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

2 Relativistic precessions of the rotating Earth: (Not observable by astronomical measurements ) Thomas precession A purely Special Relativistic effect ΩT = -(v dv/dt)/2 c 2 ΩT/Ω = 6. 3 x 10 -13 at Cashmere Geodetic precession Gyro moving through curved space-time ΩG = -2 GM/(c 2 R) Ω cos 2(lat) ΩG/Ω = 7. 28 x 10 -10 at Cashmere Lense-Thirring effect “Frame-dragging”, gravitomagnetism ΩB = GI/(c 2 R 3) (3 sin 2 (lat) -1) Ω ΩB/Ω = 0. 98 x 10 -10 at Cashmere de Sitter precession (Earth orbital motion around Sun) ΩG/Ω = 1. 4 x 10 -11 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Can absolute rotation rate be measured (to 1 ppb) with a ring laser? (Earth) rotation rate Area enclosed Sagnac frequency Angle between rotation and gyro axes Perimeter At face value, can’t be done! - Cannot measure A, P , cos to ~1 part in 109 However…. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Strategy: 1 Control of geometry: cos : -Make nominally equal to zero; (i. e. align laser with Earth rotation axis) Then cos = 1+O(Δ )2 - For acceptable accuracy, requires to be < 10 μrad Ratio A: P - Make the cavity a nominal equilateral triangle (side L) (Then A = P 2/(12√ 3) + O(ΔL)2 ) - or a square ( A = P 2/16 + O(ΔL)2 ) -Requires sides to be equal to few tenths of 1 mm -not easy, but possible 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Strategy: 2 Scale factor determination: -Estimate perimeter by measuring mode spacing f. L (‘split mode’ technique: P=c/ f. L with error < 0. 05μm ) (Requires split-mode beat frequency to ~50 m. Hz – (easy) -Estimate absolute optical frequency (compare against iodine-stabilized laser) to accuracy ~ a few MHz -(easy) -Calculate (vacuum) wavelength to better than 1 part in 109 -Note that P = (N + ½) (triangle) : calculate N (exactly!) Then or Ω = f 3 3 /(N + ½) (triangle) Ω = f 4 / N (square) with N a large whole number (~108). 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Backscatter effects: Backscatter coupling between the clockwise and counterclockwise beams is usually the largest source of systematic error. Δf. S ½ f. S m 1 m 2 cos φ where m 1 and m 2 are the fractional beam modulations, and φ is the phase angle between them. For given mirror quality, m 1 and size L. m 2 scale approximately as L-2. 5 for cavity of linear Δf. S / f. S scales approximately as L-5 !!! It is extremely important to maximize the size of the laser. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Strategy: 3 Correction of backscatter effects: -Currently under investigation. -(Obvious first step) Select best available mirrors -Most promising approach then appears to be a calculated correction based on modulation of the clockwise and counterclockwise beams. Result for G-0 laser 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

New laser in Cashmere Cavern – ‘Artist’s impression’ Innovative features: -triangular -tilted to south celestial pole -structural use of carbon-fibre reinforced tube -redesign of mirror boxes -use of ‘getter’ to control outgassing 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Is that all there is to it? Well, several more things… Details of mirror reflections: - ~ 1 part in 106 of the Sagnac effect happens inside the mirrors and this must be treated correctly; - The reflected beam at a mirror is shifted transversely outward, enlarging the area (by ~ parts in 107 ) and therefore increasing the Sagnac effect; - Non-ideal dielectric layer thickness may cause reflection phase shift different from 180 deg - There is some dispersion associated with the mirror reflections 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Dispersion in gain medium: Change of refractive index with frequency systematically decreases the Sagnac frequency by typically 1 part in 107 (requires cavity loss to be known to better than 1%) Fresnel drag due to He. Ne gas: This is not negligible. RI of He and Ne are well enough known, but we will require knowledge of gas pressure to ~1% accuracy. (We have not usually achieved this in the past. ) 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Problem!! Since the Feb 2011 earthquake, the Cashmere Cavern has not been available as a laboratory. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Alternative proposal: Relocate to Italy! Gran Sasso National Laboratory A large team based at Uni of Pisa has plans for a project with aims that overlap ours. Already set up at Gran Sasso in preliminary configuration. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Conclusion: The Canterbury earthquakes have jolted the project and it is well behind schedule The goals of the project may possibly be achieved, but not at Cashmere. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Thank you for your attention. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Sagnac Effect The fundamental effect: For an optical system with a bi-directional path that encloses an area A, and rotating rigidly in inertial space at rate Ω , there is a time difference between two light signals travelling in opposite directions: Δt = 4 A·Ω/c 2 (True in both an ether-theoretic picture and according to Special Relativity. ) In a passive interferometer, the time difference appears as a phase difference: Δφ = 8 A·Ω/( c) Demonstrated in 1913 by Georges Sagnac, trying to show existence of ether. 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013

Ring Laser Gyros: ‘Intuitive’ description: • Imagine light following circular path in both directions; Detector • Creates a standing wave. • In absence of rotation, standing wave is fixed in laboratory frame. • When laboratory is rotated, standing wave remains fixed in inertial space. • Sagnac signal detected as movement of detector relative to standing wave. Correct description: Area enclosed (Earth) rotation rate Angle between rotation axis and gyro axis Sagnac frequency Perimeter 3 rd International Workshop on Rotational Seismology 22 -25 Sept 2013