The Sagnac Effect and the Chirality of Space Time

1. The Sagnac Effect and the Chirality of Space Time Prof. R. M. Kiehn, Emeritus Physics, Univ. of Houston www.cartan.pair.com rkiehn2352@aol.com SPIE, San Diego Aug 25-30, 2007

2. This presentation consists of several parts 1. Fringes vs. Beats

3. This presentation consists of several parts 1. Fringes vs. Beats 2. The Sagnac effect and the dual Polarized Ring Laser

4. This presentation consists of several parts 1. Fringes vs. Beats 2. The Sagnac effect and the dual Polarized Ring Laser 3. The Chirality of the Cosmos

5. (And if there is time – a bit of heresy) 4. Compact domains of Constitutive properties that lead to non-radiating “Electromagnetic Molecules”

6. (And if there is time – a bit of heresy) 4. Compact domains of Constitutive properties that lead to non-radiating “Electromagnetic Molecules” with infinite Radiation Impedance ?!

7. (And if there is time – a bit of heresy) 4. Compact domains of Constitutive properties that lead to non-radiating “Electromagnetic Molecules” with infinite Radiation Impedance ?! Or why an orbiting electron does not radiate

8. 1a. Fringes vs. Beats 1 = e i(k1• r - 1 t)2 = e i(k2• r - 2 t) Superpose two outbound waves k1  k2, 1  2

9. 1a. Fringes vs. Beats 1 = e i(k1• r - 1 t)2 = e i(k2• r - 2 t) Two outbound waves superposed: k = k1 - k2 = 1 - 2 1 + 2~2 cos(k•r/2 - ω•t/2)1

10. Fringes vs. Beats 1 = e i(k1• r - 1 t)2 = e i(k2• r - 2 t) Two outbound waves superposed: k = k1 - k2 = 1 - 2 1 + 2=2 cos(k•r/2 - ω•t/2)1 Fringes are measurements of wave vector variations k(t = constant, r varies)

11. Fringes vs. Beats 1 = e i(k1• r - 1 t)2 = e i(k1• r - 2 t) Two outbound waves superposed: k = k1 - k2 = 1 - 2 1 + 2=2 cos(k•r/2 - ω•t/2)1 Fringes are measurements of wave vector variations k(t = constant, r varies) Beats are measurements of frequency variations: ω(r = constant, t varies)

12. Phase vs. Group velocity Phase Velocity = /k = C/n C = Lorentz Speed n = index of refraction

13. Phase vs. Group velocity Phase Velocity = /k = C/n C = Lorentz Speed n = index of refraction Group Velocity = d/dk ~ /k C/n  /k

14. 4 Propagation Modes Outbound Phase 1 = e i(k1• r - 1 t)2 = e i(- k2• r + 2 t) k = k =

15. 4 Propagation Modes Outbound Phase 1 = e i(k1• r - 1 t)2 = e i(- k2• r + 2 t) k = k = Note opposite orientations of Wave and phase vectors

16. 4 Propagation Modes Outbound Phase 1 = e i(k1• r - 1 t)2 = e i(- k2• r + 2 t) k = k = Inbound Phase 3 = e i(k3• r + 3 t)4 = e i(- k4• r - 4 t) k = k = Note opposite orientations of wave and phase vectors

17. 4 Propagation Modes Mix Outbound phase pairs or Inbound phase pairs for Fringes and Beats.

18. 4 Propagation Modes Mix Outbound phase pairs or Inbound phase pairs for Fringes and Beats. Mix Outbound with Inbound phase pairs to produce Standing Waves.

19. 4 Propagation Modes Mix all 4 modes for “Phase Entanglement” Each of the phase modes has a 4 component isotropic spinor representation!

20. 1b. The Michelson Morley interferometer. The measurement of Fringes

21. Most people with training in Optics know about the Michelson-Morley interferometer.

22. Viewing Fringes.

23. The fringes require that the optical paths are equal to within a coherence length of the photons. L = C • decay time ~ 3 meters for Na light

24. Many are not familiar with the use of multiple path optics (1887).

25. 1c. The Sagnac interferometer. With the measurement of fringes (old)

26. The Sagnac interferometer encloses a finite area, The M-M interferometer encloses ~ zero area.

27. The Sagnac interferometer responds to rotation The M-M interferometer does not.

28. 1d. The Sagnac Ring Laser interferometer. With the measurement of Beats (modern) Has any one measured beats in a M M interferometer ??

29. Two beam (CW and CCW linearly polarized) Sagnac Ring with internal laser light source Linear Polarized Ring Laser Polarization fixed by Brewster windows

30. Dual Polarized Ring Laser Dual Polarized Polarization beam splitters 4 Polarized beams –CWLH, CCWLH, CWRH, CCWRH Sagnac Ring with internal laser light source

31. Ring laser - Early design Brewster windows for single linear polarization state Rotation rate of the earth produces a beat signal of about 2-10 kHz depending on enclosed area.

32. More modern design of Ring Laser

33. Hogged out Quartz monolithic design

34. Ring Laser gyro built from 2-beam Ring lasers on 3 axes

35. These aircraft use (or will use) Ring Laser gyros

36. These missiles use Ring Laser gyros

37. Aerospace devices use ring Laser gyros

38. Under water devices use ring Laser gyros

39. 2. The Sagnac effect and Dual polarized Ring lasers.

40. Dual Polarized Ring Lasers Non-reciprocal measurements with a Q = ~ 1018 Better than Mossbauer

41. Dual Polarized Ring Lasers Non-reciprocal measurements with a Q = ~ 1018 Better than Mossbauer This technology has had little exploitation !!!

42. Non-Reciprocal Media. As this is a conference for Optical Engineers, who know that the speed of light can be different for different states of polarization, let me start out with the first, little appreciated, heretical statement:

43. Non-Reciprocal Media. As this is a conference for Optical Engineers, who know that the speed of light can be different for different states of polarization, let me start out with the first, little appreciated, heretical statement: In Non-Reciprocal media, the Speed of light not only depends upon polarization, but also depends upon the direction of propagation.

44. Non-reciprocal Media Faraday rotation or Fresnel-Fizeau Consider Linearly polarized light passing through Faraday or Optical Active media

45. Non-reciprocal Media Faraday rotation or Fresnel-Fizeau Consider Linearly polarized light passing through Faraday or Optical Active media Exact Solutions given by E. J. Post 1962

46. These concepts stimulated a search for apparatus which could measure the effects of gravity on the polarization of an EM wave,

47. These concepts stimulated a search for apparatus which could measure the effects of gravity on the polarization of an EM wave,and ultimately to practical applications of a dual polarized ring laser. Every one should read E. J. Post “The Formal Structure of Electromagnetics” North Holland 1962 or Dover 1997

48. The Faraday Ratchet can accumulate tiny phase shifts from multiple to-fro reflections. The hope was that such a device could capture the tiny effect of gravity on the polarization of the PHOTON.

49. The Faraday Ratchet can accumulate tiny phase shifts from multiple to-fro reflections. The hope was that such a device could capture the tiny effect of gravity on the polarization of the PHOTON. It was soon determined that classical EM theory would not give an answer to EM - gravity polarization interactions.

50. More modern design of dual polarized Ring Laser