The derivation of the Coriolis effect for light beams is undergraduate level.
Very easy to do.
Two papers which prove that the formula derived by Michelson is the Coriolis effect equation:
Full derivation of the above formula using the CORIOLIS FORCE:
https://www.researchgate.net/publication/308921264_Spinning_Earth_and_its_Coriolis_effect_on_the_circuital_light_beams_Verification_of_the_special_relativity_theoryDr. Ludwik Silberstein derived the same formula in 1921:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2068289#msg2068289In 1921, Dr. Silberstein proposed that the Sagnac effect, as it relates to the rotation of the Earth or to the effect of the ether drift, must be explained in terms of the Coriolis effect: the direct action of Coriolis forces on counterpropagating waves.
http://www.conspiracyoflight.com/Michelson-Gale/Silberstein.pdfThe propagation of light in rotating systems, Journal of the Optical Society of America, vol. V, number 4, 1921
ONLY someone who should not be allowed to post in the upper forums, could write something like this:
In other words, rather than the "the Sagnac effect, . . . . , must be explained in terms of the Coriolis effect" the Coriolis effect "would certainly be too small to be measured directly."The quote you provided, pg 298 of the paper, has nothing to do with the Sagnac or the Coriolis effect.
Dr. Silberstein is deriving the equation of the light path in relation to Fermat's principle.
Did you even read the paper?
How then could make such a catastrophic blunder?
He starts the derivation of the Coriolis effect on page 298 at the bottom.
The fact that you CONFUSED and MIXED UP two different situations tells volumes about your miserable training as physicist.
No, Dr. Silberstein did not propose that the Sagnac effect must be explained by "the direct action of Coriolis forces on counterpropagating waves".But he did.
In fact, in three papers.
Remember, the CORIOLIS EFFECT is a physical effect.
It relates directly to the area of the interferometer.
In 1922, Dr. Silberstein published a second paper on the subject, where he generalizes the nature of the rays arriving from the collimator:
http://gsjournal.net/Science-Journals/Historical%20Papers-Mechanics%20/%20Electrodynamics/Download/2645In 1924, one year before the Michelson-Gale experiment, Dr. Silberstein published a third paper, where he again explicitly links the Coriolis effect to the counterpropagating light beams in the interferometer:
https://www.tandfonline.com/doi/abs/10.1080/14786442408634503
Dr. Silberstein reveals the error committed by M. von Laue in the paper published in 1911:
"Laue seems, by the way, to be under the misapprehension that the light rays relative to the rotating table are straight lines, which they are not."
Dr. Silberstein proved that the effect measured by Sagnac is A PHYSICAL EFFECT, a deflection/inflection of the light beams due to the CORIOLIS FORCE.
Dr. Silberstein is describing the Coriolis effect, whether the lines are straight or not, NOT the electromagnetic effect (the Sagnac effect).
HERE IS THE PROOF THAT DR. SILBERSTEIN DERIVED THE CORIOLIS EFFECT:
One of the most in-depth treaties on the ring laser interferometers.
https://books.google.ro/books?id=8c_mBQAAQBAJ&pg=PA15&lpg=PA15&dq=malykin+silberstein+coriolis&source=bl&ots=JrMqF2vmto&sig=xCnMB4hL_J_ESg9Xdfhye1ahVjA&hl=en&sa=X&ved=2ahUKEwiE0ZDWxeXeAhXwkYsKHYxwBMYQ6AEwCXoECAUQAQ#v=onepage&q=malykin%20silberstein%20coriolis&f=falseCAN YOU READ ENGLISH RABINOZ?
Silberstein (798, 799) suggested an explanation for the Sagnac effect based on the direct consideration of the effect of the Coriolis force on the counterpropagating waves.Those two references, 798 and 799 are EXACTLY the ones I provided in my messages.
Make no mistake about it: Dr. Silberstein derives the Coriolis effect, which is directly related to the area of the interferometer.
Dr. Silberstein:
He uses the expression kω for the angular velocity, where k is the aether drag factor.
He proves that the formula for the Coriolis effect on the light beams is:
dt = 2ωσ/c^2
Then, Dr. Silberstein analyzes the area σ and proves that it is actually a SUM of two other areas (page 300 of the paper, page 10 of the pdf document).
The effect of the Coriolis force upon the interferometer will be to create a convex and a concave shape of the areas: σ1 and σ2.
The sum of these two areas is replaced by 2A and this is how the final formula achieves its final form:
dt = 4ωA/c^2
A = σ1 + σ2
That is, the CORIOLIS EFFECT upon the light beams is totally related to the closed contour area.
The fact that Dr. Silberstein deals also with TSR/TGR is outside the scope of our discussion: it is very easy to show the errors inherent in TSR/TGR.
Why would you take SANKAR HAJRA as an authority it being the Coriolis Effect and not the Sagnac Effect above the authority of say Albert Michelson and Dr. Ludwik Silberstein?
S. Hajra is using the STANDARD derivation of the Coriolis effect; as I said, undergraduate work, very simple.
https://www.researchgate.net/publication/308921264_Spinning_Earth_and_its_Coriolis_effect_on_the_circuital_light_beams_Verification_of_the_special_relativity_theoryYou cannot have a single formula for two different effects.
Each effect has its own formula.
Here is the formula derived by Michelson:
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.
Exactly the same formula derived both by Hajra and Silberstein (who used areas to build up/derive the formula).
It is a physical effect.
Here is the formula derived by Professor Yeh, which was peer reviewed, and is currently used by the US OFFICE OF NAVAL RESEARCH:
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)/c2Someone is wondering aloud:
Still no answer to these very simple questions.You derived the CORIOLIS EFFECT formula.
Here are not one, but two derivations of the CORRECT SAGNAC EFFECT FORMULA.
This is what Michelson put forth in front of his readers.
dt = 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) - l
1/(c + v
1) = 2l
1v
1/c
2l
2/(c - v
2) - l
2/(c + v
2) = 2l
2v
2/c
2The phase differences have already been obtained.
Now, if you substract, you are going to get the Coriolis effect.
Been there, done that.
If you want to obtain the Sagnac effect, you must add the components.
Just like Professor Yeh did.
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)/c2Now, we can do it differently, that is, we add first and then we substract.
This way is even more revealing.
HERE IS THE DEFINITION OF THE SAGNAC EFFECT:
Two pulses of light sent in opposite direction, while the interferometer is being rotated.
For each arm of the interferometer we ADD the componets which are in the same direction, two of each.
THEN WE SUBSTRACT THE PHASE DIFFERENCE.
Very simple to follow.
Here is how the phase components work out.
Now, let carefully analyze this equation.
We have the following terms, both have the same direction:
l1/(c - v1)
l2/(c - v2)Then, we have the remaining terms, in the opposite direction:
l1/(c + v1)
l2/(c + v2)To obtain the Sagnac effect, we must ADD the terms in the SAME DIRECTION, and substract the final difference.
This is what the Sagnac effect actually entails: BEAMS IN OPPOSITE DIRECTION, A ROTATION OF THE INTERFEROMETER, AND THE FINAL MEASUREMENT OF THE PHASE DIFFERENCE.
l1/(c - v1) + l2/(c - v2) = (l
1c - l
1v
2 + l
2c - l
2v
1)/(c
2 - cv
1 - cv
2 + v
1v
2)
l1/(c + v1) + l2/(c + v2) = (l
1c + l
1v
2 + l
2c + l
2v
1)/(c
2 + cv
1 + cv
2 + v
1v
2)
Since we have already added the correct Sagnac terms (both sets located in opposite directions), corresponding to the (l
1 + l
2)/(c - v
1 - v
2) and (l
1 + l
2)/(c + v
1 + v
2) terms, now the final phase difference can be correctly derived:
(l
1c - l
1v
2 + l
2c - l
2v
1)/(c
2 - cv
1 - cv
2 + v
1v
2) - (l
1c + l
1v
2 + l
2c + l
2v
1)/(c
2 + cv
1 + cv
2 + v
1v
2) = 2[(l
1v
1 + l
2v
2)]/c
2Either way, we obtain the CORRECT SAGNAC EFFECT FORMULA, derived experimentally by Professor Yeh:
2(V1L1 + V2L2)/c2Get it straight through your heads: there are TWO SEPARATE FORMULAS for two DIFFERENT EFFECTS.
You cannot have one formula for two very different physical phenomena.