In 1999 E. J. Post showed the equivalence between the Michelson-Morley experiment and the Sagnac experiment.
E. J. Post, A joint description of the Michelson Morley and Sagnac experiments.
Proceedings of the International Conference Galileo Back in Italy II, Bologna 1999,
Andromeda, Bologna 2000, p. 62
E. J. Post is the only person to notice the substantial identity between the 1925 experiment and that of 1887: "To avoid possible confusion, it may be remarked that the beam path in the more well-known Michelson-Morley interferometer, which was mounted on a turntable, does not enclose a finite surface area; therefore no fringe shift can be expected as a result of a uniform rotation of the latter".
E. J. Post, Reviews of Modern Physics. Vol. 39, n. 2, April 1967
A. Michelson and E. Morley SIMPLY MEASURED THE CORIOLIS EFFECT OF THE ETHER DRIFT. Since they did not use a phase-conjugate mirror or a fiber optic equipment, the Coriolis force effects ("attractive" and "repulsive") upon the light offset each other.
The positive (slight deviations) from the null result are due to a residual surface enclosed by the multiple path beam (the Coriolis effect registered by a Sagnac interferometer). Dayton Miller also measured the Coriolis effect of the ether drift in his experiment (Mount Wilson, 1921-1924 and 1925-1926, and Cleveland, 1922-1924).
Michelson repeated his error in the Michelson-Gale experiment, where he used the WRONG formula (Michelson and Gale actually recorded the CORIOLIS EFFECT and not the Sagnac effect). Hammar also committed the same error.
Dr. Patrick Cornille (Essays on the Formal Aspects of Electromagnetic Theory, pg. 141):
http://image.ibb.co/eHyoUn/mmo.jpg
The SAGNAC EFFECT is a superluminal formula (c + v), and is derived by the comparison of TWO LOOPS.
The CORIOLIS EFFECT is a subluminal formula (related to the area and the angular velocity of the interferometer), and is derived by the comparison of two separate segments, leading directly to the KASSNER-IVES time gap/discontinuity paradox, and is not related at all to the SAGNAC EFFECT. Here is the CORIOLIS formula: 4AΩ/c^2 (of course, for the MGX we include the sine of the latitude term as well).
The Sagnac effect is directly related to the velocity of the light beams, light is the laevorotatory string (electromagnetic wave).
In an interferometer whose center of rotation coincides with the geometrical center, BOTH these effects will have equal values.
However, for an interferometer whose center of rotation no longer coincides with its geometrical center, the SAGNAC EFFECT will be much greater than the CORIOLIS EFFECT (since it is directly proportional to the radius of the rotation), while BOTH effects will be recorded/registered by the fringe shifts.
SAGNAC EFFECT: a superluminal effect, the speed of light varies to c + wr in one direction and c – wr in the other direction. It is based on the original superluminal Maxwell equations.
CORIOLIS EFFECT: a subluminal effect, the path of the light beams is slightly modified. It is based wholly on the modified Heaviside-Lorentz equations.
That is why all of the formulas generated using general relativity can only capture the CORIOLIS EFFECT.
CORIOLIS EFFECT
Path 1 - A>B, D>C
Path 2 - C>D, B>A
A comparison of TWO SEGMENTS, a subluminal description based on the static Heaviside-Lorentz equations. It is mechanical effect: a slight deviation of the path of the light beams. It compares the phase shifts of two different segments/sides of the interferometer.
SAGNAC EFFECT
Path 1 - A > B > C > D > A is a continuous counterclockwise path, a negative sign -
Path 2 - A > D > C > B > A is a continuous clockwise path, a positive sign +
A comparison of TWO LOOPS, a superluminal phenomenon based on the original dynamical Maxwell equations. It is an electromagnetic effect: the speed of light varies by c±ωr in one or the other direction. It compares the phase shifts of the two continuous loops of the interferometer.
The CORIOLIS effect for light beams: either the Earth rotates around its own axis, or the ether drift rotates above the surface of the Earth; the deciding factor is the correct SAGNAC EFFECT formula which was never registered by MGX/ring laser gyroscopes.
The calculations performed for LISA (the space antenna) show that there are TWO formulas to deal with: the CORIOLIS effect and the ORBITAL SAGNAC effect.
The Stokes formula also guarantees two formulas for each interferometer: one is proportional to the area, the other one is proportional to the line/path of the light beam: what then is the correct line/path formula for the MGX? Exactly the derivation shown above.
Here is the correct SAGNAC EFFECT formula for the MGX:
Δt = (l1 + l2)/(c - v1 - v2) - (l1 + l2)/(c + v1 + v2)
The velocity terms are immediately identified: c - v1 - v2 and c + v1 + v2.
Δt = (l1 + l2)/(c - v1 - v2) - (l1 + l2)/(c + v1 + v2) = 2[(l1v1 + l2v2)]/c^2
Proof:
http://www.conspiracyoflight.com/Michelson-Gale_webapp/image002.png
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
l1 is the upper arm.
l2 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):
l1/(c - v1)
-l2/(c + v2)
Sagnac phase components for the A > B > C > D > A path (counterclockwise path):
l2/(c - v2)
-l1/(c + v1)
For the single continuous clockwise path we add the components:
l1/(c - v1) - l2/(c + v2)
For the single continuous counterclockwise path we add the components:
l2/(c - v2) - l1/(c + v1)
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):
{l1/(c - v1) - l2/(c + v2)} - (-){l2/(c - v2) - l1/(c + v1)} = {l1/(c - v1) - l2/(c + v2)} + {l2/(c - v2) - l1/(c + v1)}
Rearranging terms:
l1/(c - v1) - l1/(c + v1) + {l2/(c - v2) - l2/(c + v2)} =
2(v1l1 + v2l2)/c^2
reply #1 to fellow traveller
Michelson and Gale measured the CORIOLIS EFFECT, which is proportional to the area of the interferometer, and not the SAGNAC EFFECT, which is proportional to the velocity (and thus to the radius of rotation).
Here is the derivation of the Coriolis effect formula featured in the 1925 paper published by A. Michelson:
https://www.ias.ac.in/article/fulltext/pram/087/05/0071
Spinning Earth and its Coriolis effect on the circuital light beams
The final formula is this:
dt = 4ωA/c^2
The SAGNAC EFFECT for the MGX or for the ring laser gyroscopes is much larger than the CORIOLIS EFFECT, since the Sagnac effect now is proportional to the radius of rotation.
According to Stokes’ rule an integration of angular velocity Ω over an area A is substituted by an integration of tangential component of translational velocity v along the closed line of length L limiting the given area.
That is, the form of the correct Sagnac effect must be: 2VL/c^2
V = angular velocity x radius of the Earth
However, for the MGX we have two velocities, one for each latitude, and two lengths for the each side of the interferometer (large sides).
Here is the correct formula for the SAGNAC EFFECT for the MGX:
dt = 2(V1L1 + V2L2)/c^2
Michelson and Gale measured ONLY the Coriolis effect and NOT the Sagnac effect which is thousands of times larger than the Coriolis formula.
reply #2 to bob j.
E.J. Post's comments and proofs are very clear: the Michelson-Morley interferometer = the SAGNAC interfemeter; as such, MM measured the CORIOLIS EFFECT of the ether drift, but not the SAGNAC EFFECT.
Michelson and Gale and each and every ring laser gyroscope in the world measured/measure the CORIOLIS EFFECT, while the true/correct SAGNAC EFFECT is not being registered at all.
KASSNER-IVES effect
In 1997, Dr. Franco Selleri, one of the top researchers of the Sagnac effect, published the time gap/discontinuity paradox which arises from the application of the Einstein synchronization: the clock on the disk is out of synchronization with itself (equivalently, since time “jumps” a gap between 360° and 0°, one could say time is discontinuous on the rotating disk. Also equivalently, one could say time is multivalued, as a given event has more than one time associated with it).
Actually, the paradox was discovered in 1938 by Dr. Herbert Ives, who proved that ”there are of course not merely two clocks, but an infinity of clocks, where we include those that could be transported at finite speeds, and around other paths. As emphasized previously, the idea of “local time” is untenable, what we have are clock readings. Any number of clock readings at the same place are physically possible, depending on the behaviour and history of the clocks used. More than one “time” at one place is a physical absurdity.“
The only explanation left, is Langevin’s proposition a) that the light speed varies by c±wr in one or the other direction around the disk, consistent with Dufour and Prunier’s experimental results."
Herbert Ives, Light Signals Sent Around a Closed Path:
http://www.conspiracyoflight.com/Ives/Herbert_Ives_Light_Signals_Sent_Around_a_Closed_Path.pdf
The full description of the paradox was presented by Dr. Klaus Kassner (Institut fur Theoretische Physik, Germany) in 2012:
https://arxiv.org/pdf/1302.6888.pdf
"In his Minkowsky analysis of the circular Sagnac effect, Kassner is met with a discontinuity related to the speeds c + v and c−v of Selleri's paradox. Because of it, in order to confirm that the local speed of light is c along the disk circumference, Kassner tries to justify the discontinuity by introducing the unusual concept of a ‘time gap’ and states that ‘the speed of light is c everywhere except at the point on the circle where we put the time gap."
In order to make sense of the entire situation, the modified Lorentz transformation is used (Einstein synchronization) so that the CORIOLIS EFFECT formula is derived, which features the area and the angular velocity.
None of these authors has realized that by having derived the CORIOLIS EFFECT formula using STR/GTR, there will ALWAYS be a time gap/discontinuity paradox.
That is, the CORIOLIS EFFECT formula does not compare TWO LOOPS, but only TWO SEPARATE SEGMENTS. This fact was discovered, here on this thread, for the very first time, and proven to be true for the Michelson-Gale interferometer. Now, we have the full proof which also addresses interferometers whose center of rotation coincides with their geometrical center: only by introducing the TIME GAP/DISCONTINUITY can the CORIOLIS EFFECT formula be derived. In this case, we have a comparison of two separate segments, and not the comparison of two loops, as required by the definition of the SAGNAC EFFECT.
Dr. Gianfranco Spavieri has also examined the Kassner time gap/discontinuity and has debunked Dr. Kassner's second attempt to explain the paradox (by means of the absolute synchronization):
https://medcraveonline.com/PAIJ/testing-einsteinrsquos-second-postulate-with-an-experiment-of-the-sagnac-type.html
After his Minkowsky analysis, Kassner concludes by acknowledging that “Einstein synchronization fails when performed along a path around a full circle”, i.e., on a closed path on the rotating disk, a failure that has also been observed by Weber and earlier by Anandan.
Thus, in order to account for the resulting unphysical time discontinuity arising from the speeds c + v and c − v and solve Selleri’s paradox, Kassner introduces the unusual concept of a “time gap” on the rotating disk and states, “the speed of light is c everywhere except at the point on the circle where we put the time gap. The position of this point is arbitrary but there must inevitably be such a point.”
The best analysis of the Kassner time gap paradox belongs to Dr. Stephan J.G. Gift:
https://pdfs.semanticscholar.org/66fe/0dc3683bca9f1be34923ac8e47c2870e16f7.pdf
On the Selleri Transformations: Analysis of Recent Attempts by Kassner to Resolve Selleri’s Paradox
Kassner’s first approach employed Einstein synchronization and failed as it led to an unphysical time discontinuity. His second approach ironically involved the introduction of the Inertial (or Selleri) transformations which explain the associated Sagnac effect using light speed anisotropy but preserve the paradox. His core methodology based on his belief that a clock synchronization procedure can be freely chosen is shown to be without foundation and therefore the paradox stands unresolved.
Kassner continued in his effort to explain the Sagnac effect in the frame of the commoving observer by utilizing Minkowski analysis. He concluded by acknowledging that “Einstein synchronization fails when performed along a path around a full circle” i.e. on a closed path on the rotating disc. This failure has also been observed by Weber (1997) and earlier by Anandan (1981).
Dr. Wolfgang Engelhardt (Max-Planck-Institut fur Plasmaphysik) has proven, using the full Lorentz transformation (the Einstein synchronization adopted by Post, Malykin, Ashby and every other relativist), that when STR is correctly applied to the Sagnac interferometer, it will NOT predict the Sagnac effect.
Dr. Engelhardt points out that all of the relativists are using a modified Lorentz transformation, which then directly leads to the Kassner time gap/discontinuity paradox.
http://www.espenhaug.com/SagnacEffectFavorsAbsolute.pdf
Dr. Gianfranco Spavieri
In both the outward and return paths, the one-way speed is c (in agreement with Einstein’s second postulate) if the length L of the outward path covered by the signal is reduced to L(1 - 2v/c) < L in Eq. (3).
CORIOLIS EFFECT = a path measuring L(1 - 2v/c), a comparison of two separate/different segments
SAGNAC EFFECT = a path measuring L, a comparison of two continuous loops
Therefore, Michelson and Gale, Silberstein, Langevin, Post, Bilger, Anderson, Steadman, Rizzi, Targaglia, Ruggiero, have been measuring ONLY the CORIOLIS EFFECT formula (area and angular velocity), nothing else. The formulas features on the wikipedia and mathpages websites are the CORIOLIS EFFECT equations, not the correct SAGNAC EFFECT formulas.
Here is the crown jewel of all the SAGNAC EFFECT formulas:
Δt = (l1 + l2)/(c - v1 - v2) - (l1 + l2)/(c + v1 + v2)
The velocity terms are immediately identified: c - v1 - v2 and c + v1 + v2.
Δt = (l1 + l2)/(c - v1 - v2) - (l1 + l2)/(c + v1 + v2) = 2[(l1v1 + l2v2)]/c^2
