sandokhan

It cannot be any poorer than Michelson's, who derived the WRONG equation (Coriolis effect) while claiming all the while it was the Sagnac effect formula. It cannot be any poorer than Einstein's, who made this statement in 1905: "The principle of the constancy of the velocity of light is of course contained in Maxwell's equations” However, those are the HEAVISIDE-LORENTZ equations, NOT the original J.C. MAXWELL equations which are invariant under galilean transformations. Dr. A.G. Kelly discovered the humongous fudging of the data in the Hafele-Keating experiment: http://www.cartesio-episteme.net/h%26kpaper.htm His credibility is as good as any of the top researchers in the field. Certainly he will include the CORIOLIS EFFECT formula as a substitution for the SAGNAC EFFECT formula, since this subject was not thoroughly investigated/researched at all in the 20th century. However, now there is no reason to do so anymore: we have a generalized/global SAGNAC EFFECT formula which essentially and beautifully captures the entire phenomenon. E.J. Post made the same comments as did Dr. Kelly. Sagnac Effect, E.J. Post, Reviews of Modern Physics, April 1967 "The search for a physically meaningful transformation is not aided in any way whatever by the principle of general space-time covariance, nor is it true that the space-time theory of gravitation plays any direct role in establishing physically correct transformations." Post (1967) shows that the two (Sagnac and STR) are of very different orders of magnitude. He says that the dilation factor to be applied under SR is “indistinguishable with presently available equipment” and “is still one order smaller than the Doppler correction, which occurs when observing fringe shifts” in the Sagnac tests. He also points out that the Doppler effect “is v/c times smaller than the effect one wants to observe." Here Post states that the effect forecast by SR, for the time dilation aboard a moving object, is far smaller than the effect to be observed in a Sagnac test. It is essential to understand that the SAGNAC EFFECT requires the use of the original MAXWELL equations to be properly described since the SAGNAC interferometer represents A TOPOLOGICAL OBSTRUCTION, hence requiring a higher topology. https://books.google.ro/books?id=qsOBhKVM1qYC&pg=PA85&dq=Lakhtakia+Barrett,+T.W.+electromagnetism&hl=ro&sa=X&ved=0ahUKEwiV3IXAmbnZAhXKJVAKHeebCnUQ6AEIJjAA#v=onepage&q=Lakhtakia%20Barrett%2C%20T.W.%20electromagnetism&f=falseDr. T.W. Barrett, "Electromagnetic Phenomena Not Explained by Maxwell's Equations" pg 6 - 85 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 Univ., Princeton Univ., U.S. Naval Research Laboratory, Univ. of Edinburgh, author of over 200 papers on advanced electromagnetism):Topology has been used to provide answers to questions concerning what is most fundamental in physical explanation. That question itself implies the question concerning what mathematical structures one uses with confidence to adequately “paint” or describe physical models built from empirical facts. For example, differential equations of motion cannot be fundamental, because they are dependent on boundary conditions which must be justified—usually by group theoretical considerations. Perhaps, then, group theory is fundamental.Group theory certainly offers an austere shorthand for fundamental transformation rules. But it appears to the present writer that the final judge of whether a mathematical group structure can, or cannot, be applied to a physical situation is the topology of that physical situation. Topology dictates and justifies the group transformations. So for the present writer, the answer to the question of what is the most fundamental physical description is that it is a description of the topology of the situation. With the topology known, the group theory description is justified and equations of motion can then be justified and defined in specific differential equation form. If there is a requirement for an understanding more basic than the topology of the situation, then all that is left is verbal description of visual images. So we commence an examination of electromagnetism under the assumption that topology defines group transformations and the group transformation rules justify the algebra underlying the differential equations of motion.Those situations in which the Aμ potentials are measurable possess a topology, the transformation rules of which are describable by the SU(2) group; and those situations in which the Aμ potentials are not measurable possess a topology, the transformation rules of which are describable by the U(1) group.https://pdfs.semanticscholar.org/a9bc/aee223173c4fef38a36623c550a05c584801.pdfTopology and the Physical Properties of Electromagnetic Fields

That article is available elsewhere for full reading. It is also discussed in several other works on the subject. It is fundamental in understanding the subject of the first part of your message. Here is Carl Ockert's analysis of the Fizeau experiment: http://adsabs.harvard.edu/abs/1968AmJPh..36..158O http://adsabs.harvard.edu/abs/1969AmJPh..37..335O

You haven't done your homework on this one. Sagnac Effect, E.J. Post, Reviews of Modern Physics, April 1967 "The search for a physically meaningfull transformation is not aided in any way whatever by the principle of general space-time covariance, nor is it true that the space-time theory of gravitation plays any direct role in establishing physically correct transformations." The Sagnac effect is a non-relativistic effect. COMPARISON OF THE SAGNAC EFFECT WITH SPECIAL RELATIVITY, starts on page 7, calculations/formulas on page 8http://www.naturalphilosophy.org/pdf/ebooks/Kelly-TimeandtheSpeedofLight.pdfpage 8Because many investigators claim that theSagnac effect is made explicable by using theTheory of Special Relativity, a comparison ofthat theory with the actual test results is givenbelow. It will be shown that the effectscalculated under these two theories are of verydifferent orders of magnitude, and thattherefore the Special Theory is of no value intrying to explain the effect. COMPARISON OF THE SAGNAC EFFECT WITH STRSTR stipulates that the time t' recorded by an observer moving at velocity v is slower than the time to recorded by a stationary observer, according to:to = t'γwhere γ = (1 - v2/c2)-1/2 = 1 + v2/2c2 + O(v/c)4...to = t'(1 + v2/2c2)dtR = (to - t')/to = v2/(v2 + 2c2)dtR = relativity time ratioNow, to - t' = 2πr/c - 2πr/(c + v) = 2πrv/(c + v)cdt' = to - t' = tov/(c + v)dtS = (to - t')/to = v/(v + c)dtS = Sagnac ratiodtS/dtR = (2c2 + v2)/v(v + c)When v is small as compared to c, as is the case in all practical experiments, this ratioreduces to 2c/v.Thus the Sagnac effect is far larger than anypurely Relativistic effect. For example,considering the data in the Pogany test (8 ),where the rim of the disc was moving with avelocity of 25 m/s, the ratio dtS/dtR is about1.5 x 10^7. Any attempt to explain the Sagnacas a Relativistic effect is thus useless, as it issmaller by a factor of 10^7. Referring back to equation (I), consider a discof radius one kilometre. In this case a fringeshift of one fringe is achieved with a velocityat the perimeter of the disc of 0.013m/s. Thisis an extremely low velocity, being less thanlm per minute. In this case the Sagnac effectwould be 50 billion times larger than thecalculated effect under the Relativity Theory.Post (1967) shows that the two (Sagnac and STR) are of very different orders of magnitude. He says that the dilation factor to be applied under SR is “indistinguishable with presently available equipment” and “is still one order smaller than the Doppler correction, which occurs when observing fringe shifts” in the Sagnac tests. He also points out that the Doppler effect “is v/c times smaller than the effect one wants to observe." Here Post states that the effect forecast by SR, for the time dilation aboard a moving object, is far smaller than the effect to be observed in a Sagnac test. By the way, Post proved in 1999 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. 62E. 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): https://www.osapublishing.org/ol/abstract.cfm?uri=ol-6-8-401 Sagnac effect in fiber gyroscopes H.J. Arditty and H.C. Lefevre Optics Letters, vol. 6, 1981 We review the kinematic explanation of the Sagnac effect in fiber gyroscopes and recall that the index of the dielectric medium does not have any influence. Your explanation/"theory" is based on the conventional approach to optics (the Heaviside-Lorentz equations). You need to upgrade your understanding, and use the original Maxwell equations, written in quaternion form, and which are invariant under galilean transformations. As for the Fizeau experiment (and the Fresnel drag factor) you need to study Ockert's analysis (1968 and 1969).

Fig 11 refers to the Selecting Proper PCMs, NOT to Section 3, entitled Phase Conjugate Sagnac Experiment. In section 3, we have this caption: This experiment shows us two important points. First, it confirms the phase reversal of a PCM and demonstrates the Sagnac effect in an arc segment AB, not a closed path. Second, it gives us important implications: The result, φ = 4πRΩL/cλ, can be re-written as φ = 4πvL/cλ where v is the speed of the moving arc segment AB (where R is the radius of the circular motion, Ω is the rotational rate).If we increase the radius of the circular motion as shown in Fig. 6, the arc segment AB will approach a linear segment AB, the circular motion will approach the linear motion, the phase-conjugate Sagnac experiment will approach the phase-conjugate first-order experiment as shown in Fig. 4, and the phase shift is always φ = 4πvL/cλ. Take a look at the derivation, ONLY A CONTINUOUS PATH OF LIGHT. No area is present in the final formula. You have a single line/segment. The words used by the authors: "No enclosed area appears in this expression." The Sagnac effect is distributed along a line, not an enclosed area.

Try again. Figure 11 refers to the section called Selecting proper PCMs. Figures 5 and 6 refer to the phase conjugate single segment of light Sagnac experiment. You have an OPEN LOOP. You cannot get to point B from point A unless the beam of light travels in the OPEN LOOP. Very simple. There is no enclosed area. The beam of light travels ONLY THROUGH THE SINGLE SEGMENT AB. Please read. This experiment shows us two important points. First, it confirms the phase reversal of a PCM and demonstrates the Sagnac effect in an arc segment AB, not a closed path. Second, it gives us important implications: The result, φ = 4πRΩL/cλ, can be re-written as φ = 4πvL/cλ where v is the speed of the moving arc segment AB (where R is the radius of the circular motion, Ω is the rotational rate).If we increase the radius of the circular motion as shown in Fig. 6, the arc segment AB will approach a linear segment AB, the circular motion will approach the linear motion, the phase-conjugate Sagnac experiment will approach the phase-conjugate first-order experiment as shown in Fig. 4, and the phase shift is always φ = 4πvL/cλ. NOT A CLOSED PATH! NO AREA. Yet, you drew, again, an area where none exists, the figure referenced is figure 6, not figure 11: the beam of light travels ONLY within segment AB. Another reference: SAGNAC effect without an area. https://arxiv.org/pdf/gr-qc/0401005.pdf

I won't accuse you of trolling this thread. But I have made it clear that this subject (which was referenced while mentioning the potential) requires a different thread. These are open loops. Just like the interferometer created by Professor Yeh. A closed loop? RLGs and the MGX. The phase conjugate mirror has revolutionized the field of optics. Please study this subject a little bit more, starting here: Here is a paper written by Professor Ruyong Wang, in which the Sagnac effect is being derived without an area (what Dr. Wang calls "closed path"): https://arxiv.org/ftp/physics/papers/0609/0609202.pdf But it does not cross itself. To get from point A to point B requires an OPEN LOOP. It does matter, if there is no area enclosed. It has already been done. Here is the derivation for the SAGNAC without an area: https://arxiv.org/ftp/physics/papers/0609/0609202.pdf Here is the formula: The Sagnac effect for a ROTATING LINEAR SEGMENT interferometer IS: 2vL/c^2, where v=RΩ. No area involved at all. Just like the interferometer featured in Professor Yeh's papers.

Surely you can differentiate between an OPEN LOOP and a CLOSED LOOP. The reason I brought up Professor Yeh's first paper is because in that article the OPEN LOOP is displayed right in front of reader. In fact... Starting point A An OPEN LOOP Then we arrive at point B Very clearly and precisely defined. You drew red circles over the two OPEN LOOPS. Now, if you want them to be closed at any cost, you can draw even more circles over them, but the facts won't change. There is no area whatsoever in Professor Yeh's interferometer. 2(v1l1 + v2l2)/c2Since v1 = R1 x Ω, and v2 = R2 x Ω, the formula becomes: 2(R1L1 + R2L2)Ω/c2 Since Δφ = 2πc/λ x Δt, we obtain: 4π(R1L1 + R2L2)Ω/λc which is of course Professor Yeh's formula.

For the Coriolis effect derivation, one needs an area. This was proven in 1921 by Dr. Ludwik Silberstein: 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 For the Sagnac effect derivation, without an area, one needs to employ the use of a phase conjugate mirror. The formulas have already been derived: you have already read Professor Yeh's papers, here is another paper written by Professor Ruyong Wang, in which the Sagnac effect is being derived without an area (what Dr. Wang calls "closed path"): https://arxiv.org/ftp/physics/papers/0609/0609202.pdf You do have an open loop and closed path. Let me clarify matters even further by using Professor Yeh's first paper on the subject, where the Sagnac effect was recorded using only one arm (segment of light/open loop), as opposed to the second experiment, where two arms (open loops with different lengths/different radii) were employed. https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (page 71 of the pdf document, appendix 5.4, Phase-Conjugate Fiber Optic Gyro) To get from point A to point B and from point B to point A you need a continuous path and an open loop. This is the first experiment carried out by Professor Yeh, using only one open loop/arm. Then, we have the second experiment which uses TWO OPEN LOOPS, instead of just one. https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (page 31 of the pdf document), appendix 5.1) Two continuous paths: BS to PCM, PCM to M using two OPEN LOOPS, just like in the first experiment. No area involved at all. One does not need to use an interferometer with an area, while utilizing the phase conjugate mirror.

No. The Sagnac effect is a non-relativistic effect. COMPARISON OF THE SAGNAC EFFECT WITH SPECIAL RELATIVITY, starts on page 7, calculations/formulas on page 8http://www.naturalphilosophy.org/pdf/ebooks/Kelly-TimeandtheSpeedofLight.pdfpage 8Because many investigators claim that theSagnac effect is made explicable by using theTheory of Special Relativity, a comparison ofthat theory with the actual test results is givenbelow. It will be shown that the effectscalculated under these two theories are of verydifferent orders of magnitude, and thattherefore the Special Theory is of no value intrying to explain the effect. COMPARISON OF THE SAGNAC EFFECT WITH STRSTR stipulates that the time t' recorded by an observer moving at velocity v is slower than the time to recorded by a stationary observer, according to:to = t'γwhere γ = (1 - v2/c2)-1/2 = 1 + v2/2c2 + O(v/c)4...to = t'(1 + v2/2c2)dtR = (to - t')/to = v2/(v2 + 2c2)dtR = relativity time ratioNow, to - t' = 2πr/c - 2πr/(c + v) = 2πrv/(c + v)cdt' = to - t' = tov/(c + v)dtS = (to - t')/to = v/(v + c)dtS = Sagnac ratiodtS/dtR = (2c2 + v2)/v(v + c)When v is small as compared to c, as is the case in all practical experiments, this ratioreduces to 2c/v.Thus the Sagnac effect is far larger than anypurely Relativistic effect. For example,considering the data in the Pogany test (8 ),where the rim of the disc was moving with avelocity of 25 m/s, the ratio dtS/dtR is about1.5 x 10^7. Any attempt to explain the Sagnacas a Relativistic effect is thus useless, as it issmaller by a factor of 10^7. Referring back to equation (I), consider a discof radius one kilometre. In this case a fringeshift of one fringe is achieved with a velocityat the perimeter of the disc of 0.013m/s. Thisis an extremely low velocity, being less thanlm per minute. In this case the Sagnac effectwould be 50 billion times larger than thecalculated effect under the Relativity Theory.Post (1967) shows that the two (Sagnac and STR) are of very different orders of magnitude. He says that the dilation factor to be applied under SR is “indistinguishable with presently available equipment” and “is still one order smaller than the Doppler correction, which occurs when observing fringe shifts” in the Sagnac tests. He also points out that the Doppler effect “is v/c times smaller than the effect one wants to observe." Here Post states that the effect forecast by SR, for the time dilation aboard a moving object, is far smaller than the effect to be observed in a Sagnac test.

I am going to derive both the SAGNAC EFFECT and the CORIOLIS EFFECT formulas for the MGX interferometer, so that everyone will be able to see at a glance the difference. Point A is located at the detectorPoint B is in the bottom right cornerPoint C is in the upper right cornerPoint D is in the upper left cornerl1 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 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))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:2v1l1/(c2 - v21) - 2v2l2/(c2 - v22)l = l1 = l22l[(v1 - v2)]/c22lΩ[(R1 - R2)]/c2R1 - R2 = h2lhΩ/c2By 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. This is exactly what Professor Yeh's ingenious experiment entailed: the use of the phase conjugate mirror permitted, for the first time, to actually separate the clockwise/counterclockwise paths, while at the same time the open loops have different radii and thus different linear velocities. Again, let us compare the derivations for both cases: SAGNAC and CORIOLIS. CORIOLIS EFFECT derivation dt=l1/(c - v1)+l2/(c + v2)-l1/(c + v1)-l2/(c - v2)=l1/(c - v1)-l1/(c + v1)+l2/(c + v2)-l2/(c - v2)=l1(c + v1-c + v1)/(c2 - v12)+l2(c - v2-c - v2)/(c2 - v22)=2*l1v1/(c2 - v12)-2*l2v2/(c2 - v22) dt=2*l1v1/c2-2*l2v2/c2=(2*l1v1-2*l2v2)/c2=2*(l1v1-l2v2)/c2 We are comparing two OPEN SEGMENTS: defying the very definition of the Sagnac effect.Path 1 - A>B, D>C. Path 2 - C>D, B>A By comparison, the 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) 2(v1l1 + v2l2)/c2Since v1 = R1 x Ω, and v2 = R2 x Ω, the formula becomes: 2(R1L1 + R2L2)Ω/c2 Since Δφ = 2πc/λ x Δt, we obtain: 4π(R1L1 + R2L2)Ω/λc which is of course Professor Yeh's formula. FULL CORIOLIS EFFECT FOR THE MGX:4AΩsinΦ/c2FULL SAGNAC EFFECT FOR THE MGX:4Lv(cos2Φ1 + cos2Φ2)/c2Sagnac effect/Coriolis effect ratio:R((cos2Φ1 + cos2Φ2)/hsinΦ R = 4,250 kmh = 0.33924 kmThe 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) = 4729.885hsinΦ = 0.2259674729.885/0.225967 = 20,931.72 A Sagnac light interferometer (MGX, RLGs) can detect BOTH EFFECTS: one is a physical effect proportional to the area - the CORIOLIS EFFECT; the other one is an electromagnetic effect proportional to the radius of rotation - the SAGNAC EFFECT.

Those are open loops, and you know this fact very well. Not closed loops. No area. No enclosure whatsoever. (Open-ended (non-closed) loops: a single segment from end to end) Loop = a structure, series, or process, the end of which is connected to the beginning. The use of the phase conjugate mirror means that you have an interferometer where there is no need to actually have an enclosed area. The paths of light in the figure are the two segments of light which connect BS and M with PCM, back and forth. The path of the light is described as follows: 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. Both of you already know these very simple facts. You have TWO CLOSED PATHS and TWO OPEN LOOPS. Did you even read the paper? The description is very clear: https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (page 34 of the pdf document) where R1,2 and L1,2 are the radii and lengths of the fiber loops, and Ω is the rotation rate. You have two OPEN LOOPS of radii R1,2. The lengths of the paths of light are L1,2, and they are different for each open loop. Very simple. But it is. φ = -2(φ2 - φ1) = 4π(R1L1 + R2L2)Ω/λc V1 = R1 x Ω V2 = R2 x Ω Do you understand this very easy substitution? 4π(V1L1 + V2L2)/λcSince Δφ = 2πc/λ x Δt, Δt = 2(R1L1 + R2L2)Ω/c2 = 2(V1L1 + V2L2)/c2CORRECT SAGNAC FORMULA:2(V1L1 + V2L2)/c2 But it is the same. You have two different radii, thus two different linear velocities. Exactly the same case as in the Michelson-Gale experiment, or the ring laser gyroscopes interferometers. This is why the experiment carried out by Dr. Yeh is so ingenious. It is the same. φ = -2(φ2 - φ1) = 4π(R1L1 + R2L2)Ω/λc V1 = R1 x Ω V2 = R2 x Ω 4π(V1L1 + V2L2)/λc You have two different velocities, for each latitude, in the Michelson-Gale experiment. Each open loop has a different linear velocity, since both open loops have different radii, in the figure shown by Professor Yeh. Remember, we are dealing with a Sagnac interferometer which is located away from the center of rotation (as in the case of all ring laser gyroscopes or the MGX). Then, you will automatically have two different linear velocities, for each arm, and two different lengths of the arms. The Sagnac effect is an electromagnetic effect. https://www.researchgate.net/publication/253792325_Sagnac_Effect What S.A. Werner measured in 1979 is the CORIOLIS EFFECT upon the neutron phase: https://arxiv.org/pdf/1701.00259.pdf Once the area of the interferometer is mentioned you get the CORIOLIS EFFECT. If you want the SAGNAC EFFECT, you must derive a formula which is proportional to the RADIUS OF ROTATION, just like I did, just like Professor Yeh did. The derivation I provided obeys the RULES of the Sagnac effect, while Michelson's derivation did not. He compared two open arms of the interferometer, thus obtaining the Coriolis effect formula. I compared two loops, one counterclockwise, one clockwise, thus I obtained the correct Sagnac effect formula.

No speculation at all. Just a straightforward and direct derivation, using the correct definition of the Sagnac effect. Remember this: the CORIOLIS EFFECT is a physical effect upon the light beams. It is directly proportional to the area of the interferometer. The SAGNAC EFFECT is an electromagnetic effect upon the velocities of the light beams, as such it must be directly proportional to the RADIUS of rotation. A huge difference. As for the subquarks, I should open a new thread, where we will investigate the nature of the potential, which, as R. Feynman stated, is much more important than the vector field.

Don't you want to know what the potential consists of? What exactly causes the Aharonov-Bohm effect? How do subquarks relate to this very important branch of physics? Perhaps I will open a new thread, in the Speculations section of course, devoted to this subject. For now, please study the topological implications of the Aharonov-Bohm effect: http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf (Dr. Terence W. Barrett, Stanford University) None of my assertions have been contradicted. Do you understand how a phase conjugate mirror functions? There is no area at all featured in Professor Yeh's interferometer, just two segments of light. Please show to your readers where the area is in the following diagram: But it is. Surely you know that v = R x Ω. This is the formula published by Professor Yeh: φ = -2(φ2 - φ1) = 4π(R1L1 + R2L2)Ω/λc V1 = R1 x Ω V2 = R2 x Ω Do you understand this very easy substitution? 4π(V1L1 + V2L2)/λcSince 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.

Here is more "voodoo" for you: the Maxwell-Lodge effect. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.726.6101&rep=rep1&type=pdfThe Maxwell-Lodge effect: significance of electromagnetic potentials in the classical theoryG. Rousseaux, R. Kofman, and O. MinazzoliThe Aharonov-Bohm effect has been the starting point of the reconsideration of the reality of the vector potential within quantum physics. We argue that the Maxwell-Lodge effect is its classical equivalent: what is the origin of the electromotive force induced in a coil surrounding a (finite) solenoid fed by an alternative current? We demonstrate theoretically, experimentally and numerically that the effect can be understood using the vector potential while it cannot using only the fields. http://www.ccsenet.org/journal/index.php/apr/article/view/26623/17220The Physical Entity of Vector Potential in ElectromagnetismVladimir A. Leus, Ray T. Smith and Simon Maher “...the vector potential appears to give the most direct description of the physics. This becomes more apparent the more deeply we go into quantum theory. In the general theory of quantum electrodynamics, one takes the vector and scalar potentials as the fundamental quantities in a set of equations that replace the Maxwell equations: E and B are slowly disappearing from the modern expression of physical laws; they are being replaced by A and φ” (Feynman et al, 1989, chapter 15, section 5, The Feynman Lecture on Physics (Vol. 2), 1989) Did you know that there is also a Gravitational Aharonov-Bohm effect? But you haven't done your homework here. You treated the entire subject matter superficially; hopefully, the attention you devote to your other areas of interest will be more focused.

I made no such suggestion. I did not even mention photons. I mentioned scalar waves, not scalar fields (aether). Are you going to call the Aharonov-Bohm voodoo physics? It is being caused by the POTENTIAL, in the absence of vector fields. Are you going to call Whittaker's proofs as voodoo physics? He proved, mathematically, the existence of scalar/longitudinal waves. Are you going to call Maxwell's original set of equations, which are invariant under galilean transformations voodoo physics? You better not. Now, for those interested in the correct model of the atom, which does include the subquark, I can open a new thread, again with definite proofs. You will find out about Martin Ruderfer's celebrated experiment (1960), the first null result in the history of ether drift analysis, how the Riemann zeta function is related to the mass of a boson, and much more. But this would be the subject of a different thread. Here we are concerned with the Sagnac effect formula for an interferometer which features different velocities for each arm, and different lengths for each arm. Go ahead and make my day: prove that my derivation is wrong. If you cannot, then you must replace the word speculations with proofs.

Isn't it strange (no pun intended) to ask where is the work published, when you have the full derivation at your disposal and certainly by now you'd have been able to find any possible errors in it? I have not submitted the derivation to a journal, if that is what you are asking. However, the very same formula has been peer reviewed at the highest possible scientific level (Journal of Optics Letters) and is being used by the US Naval Research Office. Take a look at the final formula, it is a generalization of the Sagnac formula which features a single velocity. Remember, the MGX and the RLGs feature TWO different velocities (one for each latitude) and two different lengths.

Sure it is Dr. Yeh's publication. The correct SAGNAC formula was derived for an interferometer which features two different velocities and two different lengths. The interferometers in the Michelson-Gale experiment/ring laser gyroscope experiments also feature two different velocities and two different lengths. This is how the correct Sagnac formula is derived: we have single continuous clockwise path, and a single continuous counterclockwise path. 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. 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. A beautiful generalization of the SAGNAC effect formula for an interferometer whose center of rotation coincides with its geometrical center.

See the previous message for the exact page numbers where the formula appears in the Journal of Optics Letters. The derivation is not difficult at all, all we have to do is to respect the definition of the SAGNAC EFFECT, which involves TWO LOOPS. The CORIOLIS EFFECT formula involves a comparison of TWO SIDES, no loops at all present there.

It is wonderful to have you comment here, again, in this thread swansontea. No closed loop, no area.L is the entire length of the fiber, Professor Yeh specifies that quite clearly. (Open-ended (non-closed) loops: a single segment from end to end) There is no closed LOOP in the experiment, therefore no area of a circle. https://apps.dtic.mil/dtic/tr/fulltext/u2/a206219.pdf Phase-Conjugate Multimode Fiber GyroPublished in the Journal of Optics Letters, vol. 12, page 1023, 1987page 69 of the pdf document, page 1 of the article second reference https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf page 35 of the pdf document page 3 of appendix 5.1 Self-Pumped Phase-Conjugate Fiber-Optic Gyro Exactly the formula obtained by Professor Yeh:φ = -2(φ2 - φ1) = 4π(R1L1 + R2L2)Ω/λc = 4π(V1L1 + V2L2)/λcSince 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. 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) Here are the variables used by Michelson: The science of Physics will progress much further once it realizes that in a magnet there are TWO STREAMS OF PARTICLES, not only a South - North flux of lines, but also a North-South flux of lines.

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)/λcSince 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. Only the CORIOLIS EFFECT involves an area. 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

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. 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. 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.

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 1933Scientific American, The Evolution of Physicists Picture of Nature, May 1963

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.

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/c2Sagnac 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 detectorPoint B is in the bottom right cornerPoint C is in the upper right cornerPoint D is in the upper left cornerl1 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)/λcSince Δφ = 2πc/λ x Δt, Δt = 2(R1L1 + R2L2)Ω/c2 = 2(V1L1 + V2L2)/c2CORRECT 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) 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 conceptsUS OF NAVAL RESEARCH, Physics DivisionDr. P. YehPhD, Caltech, Nonlinear OpticsPrincipal Scientist of the Optics Department at Rockwell International Science CenterProfessor, UCSB https://i.ibb.co/MsS5Bb5/yeh4.jpg Phase-Conjugate Multimode Fiber GyroPublished in the Journal of Optics Letters, vol. 12, page 1023, 1987page 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. 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.

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)/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) 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.pdfE.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 howmuch magnetic field there is inside of here by measuringcurrents through here and here – through wires whichare entirely outside – through wires in which there is nomagnetic field... In quantum mechanical interference experimentsthere can be situations in which classically therewould be no expected influence whatever. But neverthelessthere is an influence. Is it action at distance? No, A isas 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) 966O. Klein, Quantentheorie und funfdimensionale Relativitatstheorie, Zeits.Phys. 37 (1926) 895In 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."