Global/Generalized Sagnac Effect Formula

[sandokhan]

In this thread the new, global/generalized Sagnac effect formula will be derived.

Sagnac formula for an interferometer whose center of rotation coincides with its geometrical center:

Δt = l/(c - v) - l/(c + v) = 2lv/c²

Sagnac formula for an interferometer located away from the center of rotation (different radii, different velocities):

Δt = (l₁ + l₂)/(c - v₁ - v₂) - (l₁ + l₂)/(c + v₁ + v₂) = 2[(l₁v₁ + l₂v₂)]/c²

The Sagnac effect formula for an interferometer whose center of rotation coincides with its geometrical center is well known: 2vL/c^2. The Sagnac effect involves two continuous loops for which we find the difference in travel times: it is an electromagnetic effect upon the velocities of the light beams, and is directly proportional to the radius of rotation (v = RΩ). By contrast, the Coriolis effect formula for the same interferometer is 4AΩ/c^2: it is a comparison of the two arms of the interferometer; it is a physical effect upon the light beams, and is directly proportional to the angular velocity and the area of the interferometer.

The derivation of the Coriolis effect formula:

https://www.ias.ac.in/article/fulltext/pram/087/05/0071

Spinning Earth and its Coriolis effect on the circuital light beams

http://www.conspiracyoflight.com/Michelson-Gale/Silberstein.pdf

The propagation of light in rotating systems, Journal of the Optical Society of America, vol. V, number 4, 1921

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/2645

In 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

 

Thus, the Sagnac interferometer can register/record BOTH the Coriolis effect and the Sagnac effect; the Coriolis effect is much smaller in magnitude than the Sagnac effect (one is proportional to the area of the interferometer, the other one is directly proportional to the radius of rotation).

 

If the interferometer is located away from the center of rotation, a new global/generalized Sagnac effect formula must be derived.

Here are some illustrations of these cases (which include the Michelson-Gale interferometer, and all ring laser gyroscope interferometers).

http://image.ibb.co/fjSJy7/ahasag2.jpg
http://image.ibb.co/iQWfJ7/cir2.jpg

http://image.ibb.co/j7Q3hc/kel12.jpg

http://earthmeasured.com/wp-content/uploads/2018/05/michelson-gale-1.png

 

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)/c²

 Exactly the formula obtained by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

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 = l₁/(c - v₁) - l₁/(c + v₁) - (l₂/(c - v₂) - l₂/(c + v₂))
 

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.

A second reference which confirms my global/generalized Sagnac effect formula.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a206219.pdf

Studies 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

https://i.ibb.co/MsS5Bb5/yeh4.jpg

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

 

As an example, for the square ring laser interfermeter at Gran Sasso, Italy (GINGERino) experiment, the correct SAGNAC EFFECT formula is:

https://i.ibb.co/bXJDkV1/sqrlg.jpg

Let us now rotate the square interferometer by 135° in the clockwise direction: point A will be located in the uppermost position (the source of light will be placed at point A as well).

Distance from the center of rotation to point C is k₂, while the distance from the center of rotation to point A is k₁.

v₁ = k₁ x ω

v₂ = k₂ x ω

Proceeding exactly as in the case of the interferometer in the shape of a rectangle, we have two loops, one counterclockwise, one clockwise.

A > B > C > D > A is the clockwise path

A > D > C > B > A is the counterclockwise path

Sagnac phase components for the counterclockwise path (only the v_x components of the velocity vector are subject to a different time phase difference in rotation, not the v_y components):

L/(c - v₁)

-L/(c + v₂)

-L/(c + v₂)

L/(c - v₁)

Sagnac phase components for the clockwise path:

-L/(c + v₁)

L/(c - v₂)

L/(c - v₂)

-L/(c + v₁)

For the single continuous counterclockwise path we add the components:

L/(c - v₁) - L/(c + v₂) - L/(c + v₂) + L/(c - v₁) = 2L/(c - v₁) - 2L/(c + v₂)

For the single continuous clockwise path we add the components:

-L/(c + v₁) + L/(c - v₂) + L/(c - v₂) - L/(c + v₁) = -2L/(c + v₁) + 2L/(c - v₂)

The net time 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):

2L/(c - v₁) - 2L/(c + v₂) -(-)[-2L/(c + v₁) + 2L/(c - v₂)] = 2L(2v₁/c²) + 2L(2v₂/c²) = 4L(v₁ + v₂)/c²

This is the correct global/generalized SAGNAC EFFECT formula for a square shaped ring laser interferometer:

4L(v₁ + v₂)/c²

For the same interferometer, the CORIOLIS EFFECT formula is:

4Aω/c²


The phase difference for the SAGNAC EFFECT is:

Δφ = Δt x c/λ = [4L(v₁ + v₂)]/c² x c/λ = [4L(v₁ + v₂)]/cλ

The frequency formula for the SAGNAC EFFECT is:

Δf = Δφ x c/P = [4L(v₁ + v₂)]/λP

 

 

[swansont]

You should identify what the variables mean. Interferometers come in multiple shapes, so it’s not clear what you mean.

Does “new” imply some difference from what the textbooks say?

[sandokhan]

Virtually all textbooks present the Coriolis effect formula substituted for the correct Sagnac effect formula. Even E.J. Post committed the same error in his famous 1967 article on the Sagnac effect.

The same formula presented in this thread was also derived by Professor P. Yeh, and it is used by the US Naval Research Office and was peer reviewed in the Journal of Optics Letters, so no speculations here: that is why I posted this message, originally, in the physics section.

As an example, for the Michelson-Gale experiment, the correct Sagnac effect formula is some 21,000 times greater than the Coriolis effect formula published by Albert Michelson.

FULL CORIOLIS EFFECT FOR THE MGX, using the latitude:

4AΩsinΦ/c²

FULL SAGNAC EFFECT FOR THE MGX, using the latitudes:

4Lv(cos²Φ₁ + cos²Φ₂)/c²


Sagnac effect/Coriolis effect ratio:

R((cos²Φ₁ + cos²Φ₂)/hsinΦ 

R = 4,250 km

h = 0.33924 km

The rotational Sagnac effect is much greater than the Coriolis effect for the MGX.

Φ₁ = Φ = 41°46' = 41.76667°

Φ₂ = 41°45' = 41.75°

R((cos²Φ₁ + cos²Φ₂) = 4729.885

hsinΦ = 0.225967

4729.885/0.225967 = 20,931.72

 

[swansont]

You should identify what the variables mean. 

[sandokhan]

The variables are identified as required by the use of an interferometer which is located away from the center of rotation (as in, for example, the Michelson-Gale experiment, or the ring laser gyroscopes at Gran Sasso, Italy). If the interferometer is located away from the center of rotation, one will encounter two different lengths (of the arms of the interferometers) and two different velocities for the light beams.

This situation, of course, is different from the context where one has an interferometer whose center of rotation coincides with its geometrical center: same lengths and the same velocities.

So, for the interferometer located away from the center of rotation, the variables are as follows:

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.

v₁ 

v₂

are the velocities of the rotation of the Earth at the corresponding latitudes (since there are two latitudes, one will have two velocities, one for each latitude)

c = speed of light

Here are the variables used by Michelson:

 

Edited March 24, 2019 by sandokhan

[sandokhan]

Now, we can finally solve the mystery of the Michelson-Morley experiment.

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. The Coriolis effect can be registered/recorded either due to the rotation of the Earth or due to the rotation of the ether drift (Whittaker's potential scalar waves). The deciding factor is of course the Sagnac effect, which is much greater than the Coriolis effect, and was never registered.

Since MM did not use a phase-conjugate mirror or a fiber optic equipment, the Coriolis force effects 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).

Dr. Patrick Cornille (Essays on the Formal Aspects of Electromagnetic Theory, pg. 141):

 

Let us examine now the Sagnac interferometer using topology.

https://www.researchgate.net/publication/288491190_SAGNAC_EFFECT_A_consequence_of_conservation_of_action_due_to_gauge_field_global_conformal_invariance_in_a_multiply-joined_topology_of_coherent_fields

Dr. Terence W. Barrett (Stanford University)

Just like the Aharonov-Bohm experiment, the Sagnac interferometer is a multiply-connected domain in the presence of a topological obstruction.

The Heaviside-Lorentz equations (the modified Maxwell set of equations) can only partially describe the rotating interferometer.

Upon rotation, the Sagnac interferometer will exhibit a patch condition.

Dr. Terence W. Barrett:

Stated differently, with the rotation of the platform, the gauge symmetry is SU(2)/Z2 = SO(3), and on the stabilization of the platform the gauge symmetry is U(1).

When rotated, a patch condition exists in the multiply-connected topology.

 

To put it differently, the Sagnac interferometer experiment cannot be described by vector fields (the usual Heaviside-Lorentz equations): they required the use of the quaternions, the mathematical language developed by Maxwell to describe his original set of EM equations.

"Maxwell's original EM theory was written in quaternions, which are an extension to the complex number theory and an independent system of mathematics. In short, since the quaternion is a hypernumber, Maxwell's theory was a hyperspatial theory -- not just the limited three-dimensional subset that was extracted and expressed by Heaviside and Gibbs in terms of an abbreviated, incomplete vector mathematics."

Quaternions have a vector and a scalar part and have a higher topology than vector and tensor analysis.

 

 

[sandokhan]

Gran Sasso, Italy - GINGERino experiment

Latitude: 42.4166° 

λ_He:Ne = 632 nm

L = 3.6 m

The formula for the square ring laser interferometer located away from the center of rotation derived in the previous message, could have been obtained directly from the global/generalized Sagnac formula, by letting l₁ = l₂ = 2L:

2(V₁L₁ + V₂L₂)/c²

Frequency formula for the CORIOLIS EFFECT at Gran Sasso, Italy, ring laser gyroscope:

4Aω/λP = Lω/λ

(A = L², P = 4L)

Frequency formula for the SAGNAC EFFECT at Gran Sasso, Italy, ring laser gyroscope:

[4L(v₁ + v₂)]/λP = 2v/λ

(v = Rω, since the sides of the square interferometer measure 3.6 meters in length, v₁ practically equals v₂)

2v/λ / Lω/λ = 2R/L

At the Gran Sasso latitude, R = 4,710 km = 4,710,000 meters

L = 3.6 meters

2R/L = 2,616,666.666

The SAGNAC EFFECT frequency is larger by a factor of 2,616,666.666 times than the CORIOLIS EFFECT frequency.

As we have seen earlier, for the Michelson-Gale experiment, the SAGNAC EFFECT time phase difference is 21,000 times greater than the CORIOLIS EFFECT phase difference.

The CORIOLIS EFFECT frequency formula is not always written in its full form, which must include the conversion factor from rad/s to Hz:

https://pos.sissa.it/318/181/pdf (the 2π factor is featured in the formula)

https://www.scitepress.org/papers/2015/54380/54380.pdf (the authors do not include the 2π conversion factor)

https://bura.brunel.ac.uk/bitstream/2438/7277/1/FulltextThesis.pdf (it includes the correct derivation for the CORIOLIS EFFECT frequency formula, pg. 39-40  and 60)

The huge error introduced by Albert Michelson in 1925 has not been observed by all of the distinguished physicists who have published works on the SAGNAC EFFECT, including E.J. Post who had no idea in 1967 that he was deriving and describing the CORIOLIS EFFECT formula.

http://www.orgonelab.org/EtherDrift/Post1967.pdf

http://signallake.com/innovation/andersonNov94.pdf

https://phys.org/news/2017-03-deep-earth-rotational-effects.html

https://agenda.infn.it/event/7524/contributions/68390/attachments/49528/58554/Schreiber.pdf

https://pdfs.semanticscholar.org/47ea/33bdc7d0247772658b1e29c3e9e2a4578d17.pdf

http://inspirehep.net/record/1468904/files/JPCS_718_7_072003.pdf

 

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..137M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

 

The 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.

 

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.

[Ghideon]

What is this trying to prove? Some kind of luminiferous ether theory?

 

[Ghideon]

I tried to look into the math of this, starting with references to the Coriolis formula [math] \frac{4A \Omega}{c^{2} } [/math]. I didn't find it connected to Coriolis but rather Sagnac, exception was for instance some references with content of questionable scientific quality. Example: www.theflatearthsociety.org

It doesn't look like the Global/Generalized Sagnac Effect Formula is backed up by scientific evidence.

 

Edited April 11, 2019 by Ghideon
missing line

[sandokhan]

You haven't done your homework on the subject at all.

But I have.

Please read the copious references posted earlier: right from the start, on the CORIOLIS effect formula.

Then, you need to read Professor Yeh's papers, published by the US NAVAL RESEARCH OFFICE, and having been peer-reviewed in the Journal of Optics Letters: SAME formula as that derived by me.

My derivation is flawless.

The SAGNAC EFFECT is directly proportional to the RADIUS of rotation, and thus to the VELOCITY (v = R x ω).

The CORIOLIS EFFECT is directly proportional to the AREA of the interferometer, thus this effect is much smaller in magnitude than the SAGNAC EFFECT.

The SAGNAC EFFECT is an electromagnetic effect upon the velocities of the light beams.

The CORIOLIS EFFECT is a physical effect upon the light beams.

A light interferometer CAN detect and register/record BOTH the Sagnac effect and the Coriolis effect.

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

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) 

Look seriously into this subject, and you will discover/see that my formula is perfectly derived and thus is correct.

 

You mentioned the ether.

Ether = longitudinal waves (telluric currents) of subquarks = potential/scalar Whittaker waves

Aether = medium through which these waves propagate/travel

E.T. Whittaker, in 1904, showed that all EM fields and waves can be decomposed into differential functions of two scalar potentials.

Each of these two base scalar potentials can be decomposed by Whittaker's earlier 1903 paper into a set of longitudinal EM waves. All EM fields, potentials, and waves are comprised of longitudinal EM waves and their internal dynamics.

E.T. Whittaker, "On the Partial Differential Equations of Mathematical Physics," Math. Ann., Vol. 57, 1903, p. 333-355 (W-1903)

http://www.cheniere.org/misc/Whittak/ORIw1903.pdf

E.T. Whittaker, "On an Expression of the Electromagnetic Field Due to Electrons by Means of Two Scalar Potential Functions," Proc. Lond. Math. Soc., Series 2, Vol.1, 1904, p. 367-372 (W-1904)

http://hemingway.softwarelivre.org/ttsoares/books_papers_patents/books%20papers%20patents%20(scientis/whittaker/whittaker%20et%20-%20on%20an%20expre.pdf

 

The seminal Aharonov-Bohm paper:
https://journals.aps.org/pr/pdf/10.1103/PhysRev.115.485

The Aharonov-Bohm effect, where potentials alone can interfere, even  in the absence of EM force fields, and produce real force effects in  charged particle systems. That is, the sole agent of the interference  of scalar potentials can induce EM changes, according to the  experimentally proven Aharonov-Bohm effect, even in the total absence  of EM force fields. 

“What? Do you mean to tell me that I can tell you how
much magnetic field there is inside of here by measuring
currents through here and here – through wires which
are entirely outside – through wires in which there is no
magnetic field... In quantum mechanical interference experiments
there can be situations in which classically there
would be no expected influence whatever. But nevertheless
there is an influence. Is it action at distance? No, A is
as real as B-realer, whatever that means.” 

R. Feynman


“throughout most of 20th century the Heaviside-Hertz form of Maxwell’s equations were taught to college students all over the world. The reason is quite obvious: the Heaviside-Hertz form is simpler, and exhibits an appealing near symmetry between E and H. With the widespread use of this vector-potential-less version of Maxwell’s equations, there arouse what amounted to a dogma: that the electromagnetic field resides in E and H. Where both of them vanish, there cannot be any electromagnetic effects on a charged particle. This dogma explains why when the Aharonov-Bohm article was published it met with general disbelief. . . E and H together do not completely describe the electromagnetic field, and. . . the vector potential cannot be totally eliminated in quantum mechanics. . . the field strengths underdescribe electromagnetism.”

C.N. Yang, Nobel prize laureate

 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4323049/

The Aharonov-Bohm effect and its applications to electron phase microscopy, A. Tonomura (state of the art proofs of the Aharonov-Bohm effect)

 

So, the Heaviside-Lorentz equations apply ONLY TO VECTOR FIELDS.

But J.C. Maxwell published his original set of dynamical equations WHICH ARE INVARIANT UNDER GALILEAN TRANSFORMATIONS.

https://www.omicsonline.org/open-access/back-to-galilean-transformation-and-newtonian-physics-refuting-thetheory-of-relativity-2090-0902-1000198.php?aid=80761

"Maxwell's original EM theory was written in quaternions, which are an extension to the complex number theory and an independent system of mathematics. In short, since the quaternion is a hypernumber, Maxwell's theory was a hyperspatial theory -- not just the limited three-dimensional subset that was extracted and expressed by Heaviside and Gibbs in terms of an abbreviated, incomplete vector mathematics.

Maxwell's quaternion theory was in fact a unified theory of electromagnetics and gravitation, and that the scalar component of the quaternion was the electrogravitational part. That part was discarded by Heaviside and Gibbs, and so electrogravitation no longer appears in the electromagnetics that resulted from Heaviside's and Gibbs' surgery on Maxwell's quaternion theory.”

“It appears that the union of gravitation and Maxwell’s theory is achieved in a completely satisfactory way by the five-dimensional theory (Kaluza-Klein).” 

(Einstein to H. A. Lorentz, 16 February 1927)

“Kaluza's roundabout way of introducing the five dimensional continuum allows us to regard the gravitational and electromagnetic fields as a unitary space structure”

Einstein, A. & Bergman, P., On a Generalization of Kaluza's Theory of Electricity. In: Modern Kaluza-Klein Theories. Menlo Park: Addison-Wesley, p. 93.


"Hamilton's algebra of quaternions, unlike Heaviside's algebra of vectors, is not a mere abbreviated mode of expressing Cartesian analysis, but is an independent branch of mathematics with its own rules of operation and its own special theorems. A quaternion is, in fact, a generalized or hypercomplex number ..."

H.J. Josephs ("The Heaviside Papers found at Paignton in 1957," Electromagnetic Theory by Oliver Heaviside)


T. Kaluza, Zum Unitatsproblem der Physik, Sitz. Preuss. Akad. Wiss. Phys.
Math. K1 (1921) 966

O. Klein, Quantentheorie und funfdimensionale Relativitatstheorie, Zeits.
Phys. 37 (1926) 895

In 1921, T. Kaluza showed that the gravitational and electromagnetic fields stem from a single universal tensor and such an intimate combination of the two interactions is possible in principle, with the introduction of an additional spacial dimension.

In 1926, Oscar Klein provided an explanation for Kaluza’s fifth dimension by proposing it to have a circular topology so that the coordinate y is periodic i.e., 0 ≤ y ≤ 2πR, where R is the radius of the circle S¹. Thus the global space has topology R⁴× S¹.

Kaluza-Klein compactification: although there are four space dimensions, one of the space dimensions is compact with a small radius.

Theodor Kaluza and Oscar Klein were able to recover four dimensional gravity as well as Maxwell’s equations for a vector field.

The extra space dimension somehow had collapsed down to a tiny circle "smaller than the smallest atom".

"Klein theorized that Kaluza's new dimension likely had somehow collapsed down to the "Planck length" itself -- supposedly the smallest possible size allowed by these fundamental interactions: 10^-33 cm."

"Kaluza and Klein showed that this extra dimension would still have an effect on the space around us. In particular they showed that the effect of gravity in that very small fifth dimension would actually appear to us, from our larger-scale perspective, as electromagnetism."
 

"The scalar portion of the original Maxwell equations expressed in quaternions was discarded (by Oliver Heaviside) to form "modern" EM theory; thus also the unified field interaction between electromagnetics and gravitation was discarded as well.

The quaternion scalar expression has, in fact, captured the local stress due to the forces acting one on the other. It is focused on the local stress, and the abstract vector space, adding a higher dimension to it.

One sees that, if we would capture gravitation in a vector mathematics theory of EM, we must again restore the scalar term and convert the vector to a quaternion, so that one captures the quaternionically infolded stresses. These infolded stresses actually represent curvature effects in the abstract vector space itself. Changing to quaternions changes the abstract vector space, adding higher dimensions to it.

Quaternions have a vector and a scalar part and have a higher topology than vector and tensor analysis."

 

 

Edited April 12, 2019 by sandokhan

[Ghideon]

 

22 minutes ago, sandokhan said:

Please read the copious references posted earlier

 

22 minutes ago, sandokhan said:

My derivation is flawless.

 

22 minutes ago, sandokhan said:

Look seriously into this subject, and you will discover/see that my formula is perfectly derived and thus is correct.

I don't think your style of discussion works well on this forum. It may be successful in other contexts.

 

bold by me:

28 minutes ago, sandokhan said:

Ether = longitudinal waves (telluric currents) of subquarks = potential/scalar Whittaker waves

Aether = medium through which these waves propagate/travel

E.T. Whittaker, in 1904, showed that all EM fields and waves can be decomposed into differential functions of two scalar potentials.

I don't think the concept of quarks was introduced until much later.

 

[sandokhan]

Here is the derivation of the correct SAGNAC EFFECT formula for an interferometer which is located away from the center of rotation (Michelson-Gale experiment, any and all ring laser gyroscopes), once again, so that you can study it carefully:

Sagnac formula for an interferometer whose center of rotation coincides with its geometrical center:

Δt = l/(c - v) - l/(c + v) = 2lv/c²

Sagnac formula for an interferometer located away from the center of rotation (different radii, different velocities):

Δt = (l₁ + l₂)/(c - v₁ - v₂) - (l₁ + l₂)/(c + v₁ + v₂) = 2[(l₁v₁ + l₂v₂)]/c²

The Sagnac effect formula for an interferometer whose center of rotation coincides with its geometrical center is well known: 2vL/c^2. The Sagnac effect involves two continuous loops for which we find the difference in travel times: it is an electromagnetic effect upon the velocities of the light beams, and is directly proportional to the radius of rotation (v = RΩ). By contrast, the Coriolis effect formula for the same interferometer is 4AΩ/c^2: it is a comparison of the two arms of the interferometer; it is a physical effect upon the light beams, and is directly proportional to the angular velocity and the area of the interferometer.

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)/c²

 Exactly the formula obtained by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

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) 

A second reference which confirms my global/generalized Sagnac effect formula.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a206219.pdf

Studies 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

https://i.ibb.co/MsS5Bb5/yeh4.jpg

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

 

So, as far as the subject of this thread is concerned, my formula coincides perfectly with the formula derived by Professor Yeh. Rest assured, it is correct. That is why I posted this thread, initially, in the Physics section, and not here, since there are no speculations whatsoever involved.

19 minutes ago, Ghideon said:

I don't think the concept of quarks was introduced until much later.

This is not the subject of this thread. What if I were to tell you that the concept of quarks was introduced in 1908, and also much more than that, including antimatter, bosons, Higgs field, neutrinos, and yes subquarks (subdivision of a quark, discovered at FermiLab). 

Now, it is incumbent upon you to do your homework, and read the references on the CORIOLIS effect formula, Professor Yeh's seminal papers, and then verify that my global Sagnac effect formula is indeed correct.

[Strange]

4 minutes ago, sandokhan said:

That is why I posted this thread, initially, in the Physics section, and not here, since there are no speculations whatsoever involved.

Ahem.

Quote

Ether = longitudinal waves (telluric currents) of subquarks = potential/scalar Whittaker waves

Aether = medium through which these waves propagate/travel

 

[sandokhan]

E.T. Whittaker has already proven the existence of the scalar longitudinal waves: we can call them the POTENTIAL, not necessarily use the word ether, just like Aharonov and Bohm did.

You might look up the Galaev experiments on ether drift.

Would you like me to open a new thread on subquarks? I would be very much pleased to do so.

 

[Strange]

2 minutes ago, sandokhan said:

Would you like me to open a new thread on subquarks? I would be very much pleased to do so.

Please don't.

[studiot]

18 minutes ago, sandokhan said:

So, as far as the subject of this thread is concerned, my formula coincides perfectly with the formula derived by Professor Yeh. Rest assured, it is correct. That is why I posted this thread, initially, in the Physics section, and not here, since there are no speculations whatsoever involved.

You claim this is Physics - at a high level.

Yet you talk repeatedly of proof.

 

Surely you know that there is no such thing as 'proof' in Physics?

[sandokhan]

Let us not bring metaphysics into our technical discussions. It is unfortunate that a new age concept (no proof in physics) has found its way into the scientific mainstream.

All physics is based on experiments. They either work or they don't.

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
Richard P. Feynman

Then, using the language of mathematics we derive formulas which are correct.

What is needed in physics is a new impetus, knowledge of the original equations published by Maxwell.

"...the failure of the world's physicists to find such a (satisfactory) theory, after many years of intensive research," says Dirac, "leads me to think that the aetherless basis of physical theory may have reached the end of its capabilities and to see in the Aether a new hope for the future".

Paul Dirac, the Nobel Prize winner in physics in 1933
Scientific American, The Evolution of Physicists Picture of Nature, May 1963

[Bufofrog]

2 minutes ago, sandokhan said:

Let us not bring metaphysics into our technical discussions. It is unfortunate that a new age concept (no proof in physics) has found its way into the scientific mainstream.

Metaphysics?  You can disprove a hypothesis with experimentation, but you can't prove a hypothesis with experimentation.  An experiment can certainly support a hypothesis, but it cannot prove it.  This is not new age metaphysics, it just logic and regular old normal physics.

[studiot]

1 hour ago, sandokhan said:

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
Richard P. Feynman

 

 

Yes exactly so.

 

So if another experiment comes along with a different result what does that 'prove'

 

The experiment is always 'right' but until we have carried out every possible experiment we have to admit the possibility that a different experiment will yield different results, perhaps extending our knowledge, perhaps providing the basis for yet more 'Principles' - but it does not prove them.

 

And you still haven't replied to my first post.

Edited April 12, 2019 by studiot

[sandokhan]

The greatest experimental physicist of all time, Nikola Tesla, would certainly disagree with the second statement.

Now, let us analyze what has happened, from a philosophical point of view, to modern physics.

Science (physics) is an undertaking based on reason, on a rational epistemology.

However, Kantian skepticism has found its way into physics (and mathematics): Heisenberg and Bohr and Godel. It seems that physics is no longer sought to advance man's confidence or make reality intelligible, but to achieve the opposite. Quantum mechanics refutes causality, light refutes logic, relativity refutes common sense, thermodynamics refute hope, electrons are a myth, mathematics is a game.

One of the most influential physicists of the 20th century P.W. Bridgman (Harvard), wrote in the Bulletin of the American Academy of Arts and Sciences:

"We are now approaching a bound beyond which we are forever stopped from pushing our inquiries... The very concept of existence becomes meaningless. It is literally true that the only way of reacting  to this is to shut up. We are confronted with something truly ineffable. We have reached the limit of the vision of the great pioneers of science, the vision, namely, that we live in a sympathetic world, in that it is comprehensible by our minds."

A truly avant-garde answer.

9 minutes ago, studiot said:

So if another experiment comes along with a different result what does that 'prove'

It means that perhaps the hypotheses of the experiment were not met in full. This has happened, as an example, to the physicists who tried to replicate Dr. Podkletnov's experiments. Or to the physicists who tried to measure the Allais effect, and at the same time did not adhere to Dr. Maurice Allais' stringent requirements for the experiment.

There are however, definite experiments, such the SAGNAC EFFECT.

1 hour ago, studiot said:

Surely you know that there is no such thing as 'proof' in Physics?

I have tried to point out that this new age concept "no proofs in physics" must be replaced by certainty, by definite and wonderful demonstrations. 

Edited April 12, 2019 by sandokhan

[Strange]

25 minutes ago, sandokhan said:

The greatest experimental physicist of all time, Nikola Tesla

LOL

25 minutes ago, sandokhan said:

I have tried to point out that this new age concept "no proofs in physics" must be replaced by certainty, by definite and wonderful demonstrations. 

And failed.

Your simplistic approach doesn't work.

For example, gravity. Newton's theory was "proved" by all the evidence. Until it wasn't. But does that mean Newtonian gravity is "wrong"? Then how come we keep using it. GR is a more accurate model, but it will also fail at some point. We will need a new model.

[sandokhan]

The SAGNAC EFFECT experiment does not involve an area.

Professor Yeh's interferometer features NO AREA at all, just TWO SINGLE SEGMENTS OF LIGHT traveling in OPEN LOOPS consisting of different lengths, which connect the the mirrors of the interferometer: there is no area enclosed at all.

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(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

The very same formula obtained for a Sagnac interferometer which features two different lengths and two different velocities.

 

Only the CORIOLIS EFFECT involves an area.

 

15 minutes ago, Strange said:

For example, gravity. Newton's theory was "proved" by all the evidence. Until it wasn't. But does that mean Newtonian gravity is "wrong"? Then how come we keep using it. GR is a more accurate model, but it will also fail at some point. We will need a new model.

Newton's theory is woefully incomplete. Just as are the other theories proposed including QFT, or the modified Newton theory.

A new, correct model must define PRECISELY the notion of mass.

“What we call mass would seem to be nothing but an appearance, and all inertia to be of electromagnetic origin”

Henri Poincare

“Light cannot be anything else but a longitudinal disturbance in the ether, involving alternate compressions and rarefactions. In other words, light can be nothing else than a sound wave in the ether”

“It being a fact that radio waves are essentially like sound waves in the air"

Nikola Tesla

"The limiting velocity is c, but a limit has two sides"

Gerald Feinberg

“If a special geometry has to be invented in order to account for a falling apple, even Newton might be appalled at the complications which would ensue when really difficult problems are tackled”

"If we could understand the structure of the particle, in terms of the medium of which it is composed, and if we knew the structure of the rest of the medium also, so as to account for the potential stress at every point—that would be a splendid step, beyond anything accomplished yet”

Oliver Lodge

“We are about to enter the 21st century but our understanding of the origin of inertia, mass, and gravitation still remains what has been for centuries – an outstanding puzzle”

Vesselin Petkov

“The more we study gravitation, the more there grows upon us the feeling that there is something peculiarly fundamental about this phenomenon to a degree that is unequalled among other natural phenomena. Its independence of the factors that affect other phenomena and its dependence only upon mass and distance suggest that its roots avoid things superficial and go down deep into the unseen, to the very essence of matter and space”

Paul Heyl

”Mass is a very important property of matter, and we have nothing in our current theory that says even a word about it”

Claude Detraz, one of the two research directors at CERN

"Instead of asking himself what caused the apple to fall to the ground, Sir Isaac Newton should have asked how it got up there in the first place! What else if not levitation enables a tree to grow upwards against the action of gravity?"

Viktor Schauberger

 

 

Edited April 12, 2019 by sandokhan

[Strange]

8 minutes ago, sandokhan said:

Newton's theory is woefully incomplete.

It works.

[swansont]

2 minutes ago, sandokhan said:

The SAGNAC EFFECT experiment does not involve an area.

Professor Yeh's interferometer features NO AREA at all, just TWO SINGLE SEGMENTS OF LIGHT traveling in OPEN LOOPS consisting of different lengths, which connect the the mirrors of the interferometer: there is no area enclosed at all.

Loops have an area

2 minutes ago, sandokhan said:

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) 

 

RL gives an area

L = 2*pi*R*n where n is the number of loops

RL = 2*Pi*R^2*n

pi*R^2 is the area of a circle.

2 minutes ago, sandokhan said:

Exactly the formula obtained by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

 

Where does this equation show up in the paper? Page and equation number, please.

2 minutes ago, sandokhan said:

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

The very same formula obtained for a Sagnac interferometer which features two different lengths and two different velocities.

What is the velocity referring to? Sagnac depends on rotation.

 

[studiot]

Firstly let me say that I realise I owe you an apology, when I said this

50 minutes ago, studiot said:

And you still haven't replied to my first post.

I was confusing this thread with the current thread about Special Relativity and the MM experiment.

 

However my points still remain and I hope you will not follow the trend established in that other thread of attempting to invert history.

By this I mean this comment here

44 minutes ago, sandokhan said:

Science (physics) is an undertaking based on reason, on a rational epistemology.

 

Historically Science was founded in and generally restricted to classification and cataloging of observations.

No rational epistemology was possible before this stage although there there were plenty of guesses, some of them far wilder and less justifiable than others.

The science of Physics has progressed further away from this than most other sciences, some of which have not moved very far at all.