You are destroying whatever credibility you had left here, in the upper forums.

You are not able to even read a scientific paper properly.

You are confusing two very different derivations which speaks volumes of your training as a researcher into scientific matters.

http://www.conspiracyoflight.com/Michelson-Gale/Silberstein.pdfOne of them, the first one, ends on page 298, and Dr. Silberstein is deriving the equation of the light path in relation to Fermat's principle.

It is there where he states that: "the difference would certainly be too small to be measured directly".

Next, he takes up another matter, the derivation of the CORIOLIS EFFECT.

*Silberstein takes great pains to show that while the Coriolis effect does cause the light paths to curve very slightly it can have no effect on the Sagnac delay.*He does?

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.

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.

You confused TWO VERY DIFFERENT DERIVATIONS, deviously assigning the conclusion for the first derivation to the second derivation, which really means you are getting very desperate.

I understand your predicament.

The most ingenious experiment performed by Professor Yeh: light from a laser is split into two separate fibers, F1 and F2 which are coiled such that light travels clockwise in F1 and counterclockwise in F2.

https://www.researchgate.net/publication/26797550_Self-pumped_phase-conjugate_fiber-optic_gyro**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)

The first phase-conjugate Sagnac experiment on a segment light path with a self-pumped configuration.

The Sagnac phase shift for the first fiber F1:

+2πR

_{1}L

_{1}Ω/λc

The Sagnac phase shift for the second fiber F2:

-2πR

_{2}L

_{2}Ω/λc

These are two separate Sagnac effects, each valid for the two fibers, F1 and F2.

The use of the phase conjugate mirror permits the revealing of the final formula, the total phase difference:

φ = -2(φ

_{2} - φ

_{1}) = 4π(R

_{1}L

_{1} **+** R

_{2}L

_{2})Ω/λc

2(v

_{1}l

_{1} + v

_{2}l

_{2})/c

^{2}Exactly the formula obtained by Professor Yeh:

φ = -2(φ

_{2} - φ

_{1}) = 4π(R

_{1}L

_{1} **+** R

_{2}L

_{2})Ω/λc = 4π(V

_{1}L

_{1} + V

_{2}L

_{2})/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R

_{1}L

_{1} **+** R

_{2}L

_{2})Ω/c

^{2} = 2(V

_{1}L

_{1} + V

_{2}L

_{2})/c

^{2}CORRECT SAGNAC FORMULA:

**2(V**_{1}L_{1} + V_{2}L_{2})/c^{2}http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..137M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdfThe promise made by A. Michelson, "the difference in time required for the two pencils to return to the starting point will be...", never materialized mathematically.

Instead of applying the correct definition of the Sagnac effect, Michelson compared TWO OPEN SEGMENTS/ARMS of the interferometer, and not the TWO LOOPS, as required by the exact meaning of the Sagnac experiment.

As such, his formula captured the Coriolis effect upon the light beams.

Not even the formal derivation of the Sagnac effect formula is not entirely correct.

This is the correct way to derive the Sagnac formula:

Sagnac phase component for the clockwise path:

2πR(1/(c - v))

Sagnac phase component for the counterclockwise path:

-2πR(1/(c + v))

The continuous clockwise loop has a positive sign +

The continuous counterclockwise loop has a negative sign -

The net phase difference will be (let us remember that the counterclockwise phase difference has a negative sign attached to it):

2πR(1/(c - v)) - (-){-2πR(1/(c + v))} = 2πR(1/(c - v)) - (+)2πR(1/(c + v)) = 2πR(1/(c - v)) - 2πR(1/(c + v)) = 2vL/c

^{2}The definition of the Sagnac effect is applied to a closed loop (either circular or a uniform path).

Loop = a structure, series, or process, the end of which is connected to the beginning.

Thus, from a mathematical point of view, Michelson did not derive the Sagnac effect formula at all, since he compared two open segments, and not two loops.

Using the correct definition, we recover not only the error-free formula, but also the precise velocity addition terms.

Practically, A. Michelson received the Nobel prize (1907) for the wrong formula (published in 1904 and 1887; E.J. Post proved in 1999 that the Michelson-Morley interferometer is actually a Sagnac interferometer).

No other physicist has been able to derive the correct Sagnac formula: for the past 100 years they have been using the wrong formula (the Coriolis effect equation) to describe a very different physical situation.

Here, for the first time, the correct Sagnac formula for an interferometer located away from the center of rotation has been derived in a precise manner.

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

_{1}l

_{1} + v

_{2}l

_{2})/c

^{2}Exactly the formula obtained by Professor Yeh:

φ = -2(φ

_{2} - φ

_{1}) = 4π(R

_{1}L

_{1} **+** R

_{2}L

_{2})Ω/λc = 4π(V

_{1}L

_{1} + V

_{2}L

_{2})/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R

_{1}L

_{1} **+** R

_{2}L

_{2})Ω/c

^{2} = 2(V

_{1}L

_{1} + V

_{2}L

_{2})/c

^{2}CORRECT SAGNAC FORMULA:

**2(V**_{1}L_{1} + V_{2}L_{2})/c^{2}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)

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

_{1}l

_{1}/(c

^{2} - v

^{2}_{1}) - 2v

_{2}l

_{2}/(c

^{2} - v

^{2}_{2})

l = l

_{1} = l

_{2}2l[(v

_{1} - v

_{2})]/c

^{2}2lΩ[(R

_{1} - R

_{2})]/c

^{2}R

_{1} - R

_{2} = h

2lhΩ/c

^{2}By 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.

HERE IS THE DEFINITION OF THE SAGNAC EFFECT:

Two pulses of light sent in opposite direction

**around a closed loop** (either circular or a single uniform path), while the interferometer is being rotated.

Loop = a structure, series, or process, the end of which is connected to the beginning.

A single continuous pulse A > B > C > D > A, while the other one, A > D > C > B > A is in the opposite direction, and has the negative sign.

We can see at a glance each and every important detail.

For the Coriolis effect, one has a formula which is proportional to the area; only the phase differences of EACH SIDE are being compared, and not the continuous paths.

For the Sagnac effect, one has a formula which is proportional to the velocity of the light beam; the entire continuous clockwise path is being compared to the other continuous counterclockwise path exactly as required by the definition of the Sagnac effect.

Experimentally, the Michelson-Gale test was a closed loop,

**but not mathematically**. Michelson treated mathematically each of the longer sides/arms of the interferometer as a separate entity: no closed loop was formed at all. Therefore the mathematical description put forth by Michelson has nothing to do with the correct definition of the Sagnac effect (two pulses of light are sent in opposite direction

**around a closed loop**) (either circular or a single uniform path). By treating each side/arm separately, Michelson was describing and analyzing the Coriolis effect, not the Sagnac effect.

Loop = a structure, series, or process, the end of which is connected to the beginning.

Connecting the two sides through a single mathematical description closes the loop; treating each side separately does not. The Sagnac effect requires, by definition, a structure, the end of which is connected to the beginning.

The derivation used by Dr. Silberstein leads to the same formula derived by Michelson where THERE IS NO LOOP WHATSOEVER in the analysis.

The SAGNAC EFFECT requires two loops, neither Silberstein nor Michelson ever offered at least one loop.

Again, this speaks volumes of your training as a physicist, and of your true motives for trolling the upper forums.