Sagnac effect in a proper reference frame Endre Kajari, International Workshop on "Gravitational Waves Detection with Atom Interferometry", Florenze, 23 th February 2009
Page 2 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Drop Tower in Bremen
Page 3 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Outline of the talk: • Sagnac's original experiment • Sagnac effect in general relativity • Definition of a proper reference frame (PRF) • Sagnac time delay in a PRF and the double eight-loop interferometer (DELI) • Comment on gravitational wave detection S. Harris
Page 4 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac's Original Experiment
Page 5 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac's Conclusion: "The observed interference effect is clearly the optical whirling effect due to the movement of the system in relation to the ether and directly manifests the existence of the ether, supporting necessarily the light waves of Huygens and of Fresnel.'' C. R. Acad. Sci. 157 , 708 and 1410 (1913), translated by R. Hazelett
Page 6 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Outline of the talk: Sagnac's original experiment • Sagnac effect in general relativity Definition of a proper reference frame (PRF) Sagnac time delay in a PRF and the double eight-loop interferometer (DELI) Comment on gravitational wave detection S. Harris
Page 7 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in General Relativity for a time independent metric
Page 8 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in General Relativity for a time independent metric
Page 9 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in General Relativity for a time independent metric
Page 10 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in General Relativity for a time independent metric
Page 11 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Outline of the talk: Sagnac's original experiment Sagnac effect in general relativity • Definition of a proper reference frame (PRF) Sagnac time delay in a PRF and the double eight-loop interferometer (DELI) Comment on gravitational wave detection S. Harris
Page 12 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Proper Reference Frame (PRF) four-velocity: four-acceleration:
Page 13 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Proper Reference Frame (PRF) four-velocity: four-acceleration: orthonormal tetrads:
Page 14 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Proper Reference Frame (PRF) four-velocity: four-acceleration: orthonormal tetrads: proper transport: transport matrix:
Page 15 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Proper Reference Frame (PRF) four-velocity: four-acceleration: orthonormal tetrads: proper transport: transport matrix:
Page 16 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Metric Expansion in PRF
Page 17 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Metric Expansion in PRF • red-shift mainly due to acceleration term • spacetime curvature occurs in the second order • local inertial frame for freely falling and non-rotating observer
Page 18 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Outline of the talk: Sagnac's original experiment Sagnac effect in general relativity Definition of a proper reference frame (PRF) • Sagnac time delay in a PRF and the double eight-loop interferometer (DELI) Comment on gravitational wave detection S. Harris
Page 19 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in a PRF general surface
Page 20 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in a PRF planar surface
Page 21 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in a PRF
Page 22 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Sagnac Time Delay in a PRF
Page 23 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 DELI: Measurement mode 1
Page 24 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 DELI: Measurement mode 2
Page 25 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Outline of the talk: Sagnac's original experiment Sagnac effect in general relativity Definition of a proper reference frame (PRF) Sagnac time delay in a PRF and the double eight-loop interferometer (DELI) • Comment on gravitational wave detection S. Harris
Page 26 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Comment on gravitational wave detection general flat background-metric background-metric non-linear regime
Page 27 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 The team (Institute of Quantum Physics, Ulm University) Michael Buser Cornelia Feiler Wolfgang P. Schleich E. Kajari, M. Buser, C. Feiler and W. P. Schleich, Proceedings of the International School of Physics "Enrico Fermi" Course "Atom Optics and Space Physics"
Page 28 Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23 th February 2009 Thank you very much for your attention! S. Harris
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