Sagnac effect in a proper reference frame Endre Kajari, - - PowerPoint PPT Presentation

▶
sagnac effect in a proper reference frame
SMART_READER_LITE
LIVE PREVIEW

Sagnac effect in a proper reference frame Endre Kajari, - - PowerPoint PPT Presentation

Feb 25, 2024 265 likes •561 views

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

slide-1
SLIDE 1

Sagnac effect in a proper reference frame

Endre Kajari, International Workshop on "Gravitational Waves Detection with Atom Interferometry", Florenze, 23th February 2009

slide-2
SLIDE 2

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 2

Drop Tower in Bremen

slide-3
SLIDE 3

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 3

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
slide-4
SLIDE 4

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 4

Sagnac's Original Experiment

slide-5
SLIDE 5

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 5

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

  • f 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
slide-6
SLIDE 6

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 6

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
slide-7
SLIDE 7

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 7

Sagnac Time Delay in General Relativity

for a time independent metric

slide-8
SLIDE 8

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 8

Sagnac Time Delay in General Relativity

for a time independent metric

slide-9
SLIDE 9

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 9

Sagnac Time Delay in General Relativity

for a time independent metric

slide-10
SLIDE 10

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 10

Sagnac Time Delay in General Relativity

for a time independent metric

slide-11
SLIDE 11

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 11

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
slide-12
SLIDE 12

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 12

Proper Reference Frame (PRF)

four-velocity: four-acceleration:

slide-13
SLIDE 13

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 13

Proper Reference Frame (PRF)

four-velocity: four-acceleration:

  • rthonormal tetrads:
slide-14
SLIDE 14

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 14

Proper Reference Frame (PRF)

four-velocity: four-acceleration:

  • rthonormal tetrads:

proper transport: transport matrix:

slide-15
SLIDE 15

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 15

Proper Reference Frame (PRF)

four-velocity: four-acceleration:

  • rthonormal tetrads:

proper transport: transport matrix:

slide-16
SLIDE 16

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 16

Metric Expansion in PRF

slide-17
SLIDE 17

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 17

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
slide-18
SLIDE 18

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 18

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
slide-19
SLIDE 19

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 19

Sagnac Time Delay in a PRF

general surface

slide-20
SLIDE 20

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 20

Sagnac Time Delay in a PRF

planar surface

slide-21
SLIDE 21

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 21

Sagnac Time Delay in a PRF

slide-22
SLIDE 22

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 22

Sagnac Time Delay in a PRF

slide-23
SLIDE 23

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 23

DELI: Measurement mode 1

slide-24
SLIDE 24

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 24

DELI: Measurement mode 2

slide-25
SLIDE 25

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 25

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
slide-26
SLIDE 26

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 26

Comment on gravitational wave detection

non-linear regime flat background-metric general background-metric

slide-27
SLIDE 27

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 27

The team

(Institute of Quantum Physics, Ulm University)

Cornelia Feiler Wolfgang P. Schleich Michael Buser

  • 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"

slide-28
SLIDE 28

Sagnac effect in a proper reference frame | Galileo Galilei Institute for Theoretical Physics, Florenze | 23th February 2009 Page 28

Thank you very much for your attention!

  • S. Harris