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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Ring Laser Gyroscope Measurement of Absolute Earth Rotation Rate Currently involved: Jon-Paul Wells Rob Thirkettle Ulli Schreiber Nish Rabeendran John Holdaway Associated: Geoff Steadman Clive Rowe Richard Graham Bob Hurst Marsden Fund support: M1142: A Terrestrial Measurement of the Frame Dragging of the Rotating Earth

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Michelson-Gale experiment (1925) “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-motion-related 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, pp137-145 (1925) (38 years after the famous Michelson-Morley experiment.)

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Detection of Chandler wobble (A ‘Eulerian’ wobble, amplitude several metres, period ~435 days 55320553805536055340 mJD (prad/s) 0 40 20 -20 -40 -60 G raw data Subtract polar motion, local tilt Rotation rate change predicted from IERS data 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.

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

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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 10 9 ) But: latency and incompleteness

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 2 Relativistic precessions of the rotating Earth: (Not observable by astronomical measurements ) “Frame-dragging”, gravitomagnetism Ω B = GI/(c 2 R 3 ) (3sin 2 (lat) -1) Ω Ω B /Ω = 0.98 x 10 -10 at Cashmere A purely Special Relativistic effect Ω T = -(v dv/dt)/2c 2 Ω T /Ω = 6.3 x 10 -13 at Cashmere Gyro moving through curved space-time Ω G = -2GM/(c 2 R) Ω cos 2 (lat) Ω G /Ω = 7.28 x 10 -10 at Cashmere Thomas precession Geodetic precession Lense-Thirring effect de Sitter precession (Earth orbital motion around Sun) Ω G /Ω = 1.4 x 10 -11

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Perimeter Sagnac frequency Area enclosed Angle between rotation and gyro axes (Earth) rotation rate Can absolute rotation rate be measured (to 1 ppb) with a ring laser? At face value, can’t be done! - Cannot measure A, P, cos to ~1 part in 10 9 However….

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 -Make nominally equal to zero; (i.e. align laser with Earth rotation axis) Then cos = 1+O(Δ ) 2 - F or acceptable accuracy, requires to be < 10 μrad Strategy: 1 Control of geometry: - Make the cavity a nominal equilateral triangle (side L ) (Then A = P 2 /(12√3) + O(ΔL) 2 ) cos : Ratio A:P - 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

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 -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 mHz – (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 10 9 -Note that P = (N + ½) (triangle) : calculate N (exactly!) with N a large whole number (~10 8 ). or Ω = f 4 / N (square) Strategy: 2 Scale factor determination : Then Ω = f 3 3 /(N + ½) (triangle)

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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 m 2 scale approximately as L -2.5 for cavity of linear size L. Δf S / f S scales approximately as L -5 !!! It is extremely important to maximize the size of the laser.

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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

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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

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Is that all there is to it? Well, several more things… - ~ 1 part in 10 6 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 10 7 ) 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 Details of mirror reflections:

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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 10 7 (requires cavity loss to be known to better than 1%) Fresnel drag due to HeNe 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.)

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

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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.

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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.

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

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Sagnac 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 = 4A·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) The fundamental effect: Demonstrated in 1913 by Georges Sagnac, trying to show existence of ether.

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3 rd International Workshop on Rotational Seismology 22-25 Sept 2013 Ring Laser Gyros: ‘Intuitive’ description: Imagine light following circular path in both directions; 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. Detector Perimeter Sagnac frequency Area enclosed Angle between rotation axis and gyro axis (Earth) rotation rate Correct description:

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