Sorry, Maraner and Zendri derived the Sagnac effect! Read what they say:What they say is one thing, the formula they provide is the CORIOLIS EFFECT formula.
Please read.
Here is the formula provided by Maraner and Zendri:
The main term of the phase shift is this:
4AΩ/c^2
But this is the CORIOLIS EFFECT formula, they add higher relativistic terms to it.
You can't have A SINGLE FORMULA FOR TWO DIFFERENT EFFECTS, CAN YOU?
If they say it is the SAGNAC EFFECT and the formula they provide is the CORIOLIS EFFECT, something is very wrong isn't it?
4AΩ/c^2.
THIS IS THE CORIOLIS EFFECT FORMULA.
Here is the precise proof, peer-reviewed in an IOP article.
THIS IS AN IOP ARTICLE, one of the most comprehensive papers on the Sagnac effect ever published.
Here is reference #27:
http://www.conspiracyoflight.com/Michelson-Gale/Silberstein.pdfThe formula derived by Dr. Silberstein, peer reviewed in the IOP article, and described by the author as the "effect of the Coriolis forces" is this:
dt = 4ωA/c^2
Now, here is a direct derivation of the same formula using only the Coriolis force:
https://www.ias.ac.in/article/fulltext/pram/087/05/0071A beautiful direct derivation using undergraduate level mathematics, very simple.
THE FINAL FORMULA DERIVED BY S. HAJRA IS THIS:
dt = 4ωA/c^2
He derived this formula using ONLY the Coriolis force as a guide.
Same formula as that derived by Sagnac and by Silberstein.
"TWO LOOPS" are not "required by the definition of the Sagnac effect"! That is just something you dreamed up that nobody else agrees with.But they are required.
This plainly shows your cognitive dissonance: you are willing to MODIFY the currently accepted definition of the SAGNAC EFFECT to satisfy your whimsical heliocentrical world.
Please read.
Here are the DEFINITIONS USED BY MODERN SCIENCE TO DESCRIBE THE SAGNAC EFFECT:
https://www.mathpages.com/rr/s2-07/2-07.htmIf two pulses of light are sent in opposite directions around a stationary circular loop of radius R, they will travel the same inertial distance at the same speed, so they will arrive at the end point simultaneously.
http://www.cleonis.nl/physics/phys256/sagnac.phpEssential in the Sagnac effect is that a loop is closed.
http://www.einsteins-theory-of-relativity-4engineers.com/sagnac-effect.htmlThe Sagnac effect is observed when coherent light travels around a closed loop in opposite directions and the phases of the two signals are compared at a detector.
This shows you haven't the foggiest idea of what you are talking about.
Michelson and Gale COMPARED TWO SIDES ONLY, not any loops at all:
http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..137M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdfThe final formula used by Michelson features an AREA: it is the CORIOLIS EFFECT formula.
Using a phase-conjugate mirror, for the first time in 1986, Professor Yeh was able to derive the TRUE SAGNAC FORMULA which is proportional to the velocity of the light beams.
page 152 of the pdf document, section Recent Advances in Photorefractive Nonlinear Optics page 4
The MPPC acts like a normal mirror and Sagnac interferometry is obtained. Here is the derivation of my formula, using TWO LOOPS:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351Here is the final formula:
2(V1L1 + V2L2)/c2My formula is confirmed at the highest possible scientific level, having been published in the best OPTICS journal in the world, Journal of Optics Letters, and it is used by the US NAVAL RESEARCH OFFICE, Physics Division.
A second reference which confirms my global/generalized Sagnac effect formula.
https://apps.dtic.mil/dtic/tr/fulltext/u2/a206219.pdfStudies of phase-conjugate optical devices concepts
US OF NAVAL RESEARCH, Physics Division
Dr. P. Yeh
PhD, Caltech, Nonlinear Optics
Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB
"Engineer of the Year," at Rockwell Science Center
Leonardo da Vinci Award in 1985
Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers
page 152 of the pdf document, section Recent Advances in Photorefractive Nonlinear Optics page 4
The MPPC acts like a normal mirror and Sagnac interferometry is obtained. Phase-Conjugate Multimode Fiber Gyro
Published in the Journal of Optics Letters, vol. 12, page 1023, 1987
page 69 of the pdf document, page 1 of the article
A second confirmation of the fact that my formula is correct.
Here is the first confirmation:
Self-pumped phase-conjugate fiber-optic gyro, I. McMichael, P. Yeh, Optics Letters 11(10):686-8 · November 1986
http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (appendix 5.1)
Exactly the formula obtained by Professor Yeh:
φ = -2(φ
2 - φ
1) = 4π(R
1L
1 + R
2L
2)Ω/λc = 4π(V
1L
1 + V
2L
2)/λc
Since Δφ = 2πc/λ x Δt, Δt = 2(R1L1 + R2L2)Ω/c2 = 2(V1L1 + V2L2)/c2CORRECT SAGNAC FORMULA:
2(V1L1 + V2L2)/c2The very same formula obtained for a Sagnac interferometer which features two different lengths and two different velocities.
http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdfANNUAL TECHNICAL REPORT PREPARED FOR THE US OF NAVAL RESEARCH.
Page 18 of the pdf document, Section 3.0 Progress:
Our first objective was to demonstrate that the phase-conjugate fiberoptic gyro (PCFOG) described in Section 2.3 is sensitive to rotation. This phase shift plays an important role in the detection of the Sagnac phase shift due to rotation. Page 38 of the pdf document, page 6 of Appendix 3.1
it does demonstrate the measurement of the Sagnac phase shift Eq. (3)HERE IS EQUATION (3) OF THE PAPER, PAGE 3 OF APPENDIX 3.1:
φ = -2(φ
2 - φ
1) = 4π(R
1L
1 + R
2L
2)Ω/λc = 4π(V
1L
1 + V
2L
2)/λc
Since Δφ = 2πc/λ x Δt, Δt = 2(R1L1 + R2L2)Ω/c2 = 2(V1L1 + V2L2)/c2CORRECT SAGNAC FORMULA:
2(V1L1 + V2L2)/c2The Coriolis effect is a physical effect upon the light beams: it is proportional to the area of the interferometer. It is a comparison of two sides.
The Sagnac effect is an electromagnetic effect upon the velocities of the light beams: it is proportional to the radius of rotation. It is a comparison of two loops.
Two different phenomena require two very different formulas.
My SAGNAC EFFECT formula proven and experimentally fully established at the highest possible level of science.Let us now compare the two derivations, using two loops (Sagnac effect) and two sides (Coriolis effect):
Point A is located at the detector
Point B is in the bottom right corner
Point C is in the upper right corner
Point D is in the upper left corner
l
1 is the upper arm.
l
2 is the lower arm.
Here is the most important part of the derivation of the full/global Sagnac effect for an interferometer located away from the center of rotation.
A > B > C > D > A is a continuous counterclockwise path, a negative sign -
A > D > C > B > A is a continuous clockwise path, a positive sign +
The Sagnac phase difference for the clockwise path has a positive sign.
The Sagnac phase difference for the counterclockwise has a negative sign.
Sagnac phase components for the A > D > C > B > A path (clockwise path):
l
1/(c - v
1)
-l
2/(c + v
2)
Sagnac phase components for the A > B > C > D > A path (counterclockwise path):
l
2/(c - v
2)
-l
1/(c + v
1)
For the single continuous clockwise path we add the components:
l
1/(c - v
1) - l
2/(c + v
2)
For the single continuous counterclockwise path we add the components:
l
2/(c - v
2) - l
1/(c + v
1)
The net phase difference will be (let us remember that the counterclockwise phase difference has a negative sign attached to it, that is why the substraction of the phase differences becomes an addition):
{l
1/(c - v
1) - l
2/(c + v
2)} - (-){l
2/(c - v
2) - l
1/(c + v
1)} = {l
1/(c - v
1) - l
2/(c + v
2)}
+ {l
2/(c - v
2) - l
1/(c + v
1)}
Rearranging terms:
l
1/(c - v
1) - l
1/(c + v
1)
+ {l
2/(c - v
2) - l
2/(c + v
2)} =
2(v
1l
1 + v
2l
2)/c
2Exactly the formula obtained by Professor Yeh:
φ = -2(φ
2 - φ
1) = 4π(R
1L
1 + R
2L
2)Ω/λc = 4π(V
1L
1 + V
2L
2)/λc
Since Δφ = 2πc/λ x Δt, Δt = 2(R
1L
1 + R
2L
2)Ω/c
2 = 2(V
1L
1 + V
2L
2)/c
2CORRECT SAGNAC FORMULA:
2(V1L1 + V2L2)/c2Self-pumped phase-conjugate fiber-optic gyro, I. McMichael, P. Yeh, Optics Letters 11(10):686-8 · November 1986
http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (appendix 5.1)
This is how the correct Sagnac formula is derived: we have single continuous clockwise path, and a single continuous counterclockwise path.
If we desire the Coriolis effect, we simply substract as follows:
dt = l
1/(c - v
1) - l
1/(c + v
1) - (l
2/(c - v
2) - l
2/(c + v
2))
Of course, by proceeding as in the usual manner for a Sagnac phase shift formula for an interferometer whose center of rotation coincides with its geometrical center, we obtain:
2v
1l
1/(c
2 - v
21) - 2v
2l
2/(c
2 - v
22)
l = l
1 = l
22l[(v
1 - v
2)]/c
22lΩ[(R
1 - R
2)]/c
2R
1 - R
2 = h
2lhΩ/c
2By having substracted two different Sagnac phase shifts, valid for the two different segments, we obtain the CORIOLIS EFFECT formula.
However, for the SAGNAC EFFECT, we have a single CONTINUOUS CLOCKWISE PATH, and a single CONTINUOUS COUNTERCLOCKWISE PATH, as the definition of the Sagnac effect entails.