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Michou Interferometer July 21st 2016 Michou interferometer Costel Munteanu Montreal, QC, Canada [email protected] Abstract: The speed of light c defined as a constant of nature is in fact the “two­way speed of light” ​ ​ calculated from the measured time of travel of light from a light source to a reflector and back to a detector situated next to the source. In a “two­way” experiment (like Fizeau­Foucault apparatus) the constant c is the harmonic mean of “forward” and “backward” speeds [13]. A simple ​ ​ ​ ​ Michelson­Morley interferometer with equal length arms detects a difference between the time of travel of light along its two perpendicular arms in certain frames of reference in motion or in gravitational field and this is interpreted as Lorentz–FitzGerald contraction of length in the direction of motion or along the gradient of gravitational field [5]. While no experiment seemed to allow the ​ ​ precise “one­way” measurement of speed of light, Lorentz­FitzGerald length contraction interpretation is preferred. In this article I present an interferometer that determines the difference between “forward” and “backward” speed of light in certain frames of reference ­ the anisotropy of speed of light along one direction ­ showing a flow of electromagnetic medium through the frame of reference of the device contradicting the Lorentz­FitzGerald length contraction hypothesis and bring proof for the first time of (local) preferred frame effects. The device determines the direction of the flow and allows to calculate the velocity of that flow using the measured (or calculated) value of canonical “two­way” speed of light c in that particular frame of reference and the anisotropy measured by the ​ ​ device presented herein. Experiments carried on with this device allow to bring clarifications on the nature of light, physical “vacuum”, inertia and gravitational field. Encouraging results seem to favor the concept of a dynamic massive “dark fluid” (a generalized Chaplygin gas model) [14], [15] that could replace the ​ ​ ​ ​ concept of “luminiferous aether” promoted by Hendrik Lorentz and narrow the direction of research for dark matter. This interferometer allows to bring direct experimental proof of equivalence principle between inertial and gravitational forces. According to Thanu Padmanabhan and Erik Verlinde, gravity might be emergent as hypothesized in “entropic gravity” theory [16] opening a new perspective on the thermodynamic ​ ​ aspect of gravity. The thermodynamic description of gravity has a history that goes back to the research on black hole thermodynamics by Bekenstein and Hawking in the mid­1970s. Thermodynamic analysis of gravitational field leads to the conclusion that on an arbitrary surface enclosing a certain mass we can define a temperature that is proportional to the mass enclosed. That means the surface radiates outwards as much power as the inwards power of gravitational field establishing a thermodynamic equilibrium for masses remaining constant inside a surface. That inward flow of energy of the gravitational field might be a flow of a “dark fluid” (as discussed above) having a certain mass density (energy density), flowing (inwards) through the reference surface with a velocity equal to the “escape velocity” corresponding to the strength of the gravitational field (g) calculated at a point on the reference surface. In this case, the equivalence principle is demonstrated experimentally by measuring with the device presented herein the anisotropy of the speed of light along the gravitational field gradient (“on the vertical”) and comparing it with the anisotropy measured for a frame in constant motion (with the velocity equal to the corresponding “escape velocity”) in the absence of any gravitational field. A century old controversy In 1851, Hippolyte Fizeau carried on an experiment which proved that the medium of propagation of light is dragged by matter in motion somehow in accord with the theory of aether widespread at that time but only partially [1] . ​ ​ In 1881 and 1887, Albert A. Michelson and Edward W. Morley, carried on experiments to test the Lorentz hypothesis of the “luminiferous aether” according which the Earth moving through space should “feel” an “aether wind” [2] . ​ ​ The negative results of Michelson­Morley experiment lead on one side to the hypothesis of total drag of the “aether” by the moving Earth which was in contradiction with Fizeau’s experiment (showing only a partial drag), and on the other side lead to the concept of length contraction postulated by George FitzGerald in 1889 [3] and adopted by Hendrik Antoon Lorentz (1892) to ​ ​ explain the negative outcome of Michelson­Morley experiment [4], [5]. ​ ​ ​ ​ According to Lorentz, the “luminiferous aether” wind was not dragged by the Earth in motion and through the arm of the interferometer the “aether wind” effect was cancelled by the length contraction of the arm (in the direction of motion). Lorentz’s solution seemed to favor a static aether fixed in a “universal frame of reference” through which all massive bodies move without dragging it. But this contradicts the result of Fizeau experiment which proved that there is a drag. None of the three hypotheses related to aether (no­drag, complete drag or partial drag) seemed to fit the experimental data and this represented a conundrum in the new domain of electromagnetism. Electromagnetic phenomena seemed to prove an aether that is always static in the frame of the laboratory even when that frame is in motion. In 1905 Albert Einstein gave a solution to avoid this conundrum by proposing a simple algorithm and demonstrating that by taking into account only the relative motion between frames of reference and applying Lorentz transform between those frames, the effects of an eventual “aether flow” cancel out [6]. ​ ​ Still Einstein never gave up the idea of an “aether flow” through certain frames of reference but he never found a way to prove it. In one of lectures on general relativity and aether theory, an address delivered on May 5th, 1920, at the University of Leyden ­ "Aether and the theory of relativity" [7] , Einstein said that general relativity's gravitational field parameters could be said to ​ ​ ​ ​ have all the usual properties of an aether except one: it was not composed of particulate bodies that could be tracked over time, and so it could not be said to have the property of motion. In Einstein’s opinion, the FitzGerald length contraction was an artefact even if it made work the mathematical framework he proposed. But the time dilation, even if it has only a geometric meaning in the Relativity theory seemed to be a well real fact and it was only later proved by Ives­Stilwell (1938, 1941)[8], [9], Robert Pound and Glen A. Rebka (1959) [10] and Hafele­ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Keating (1971) experiments [11] . Time dilation (or more precise”the slowing of the clock rate” in ​ ​ ​ certain frames of reference) has more profound causes being related to the “clocks” (like a pendulum or the “quantum harmonic oscillators”) submitted to stresses generated by fields (inertial, gravitational and electromagnetic) ­ and those stresses shift the natural frequency of oscillation (the “clock rate”) to a lower frequency. A simple solution older than the problem In this article I present a simple interferometer that is a cross hybrid between the Michelson interferometer and an interferometer experimented by Martin Hoek in 1868 [12]. The interferometer ​ ​ I present ends a debate more than a century old by demonstrating “preferred frame” effects without equivoca. Michelson interferometer [2] uses isotropic refringent media (air or vacuum) through which ​ ​ light travels from a light source to a mirror and back towards the source on two equal length perpendicular arms. The difference in time of travel of light along the two perpendicular depends on the direction of motion of the reference frame of the device but not on the sense of motion. The device moving along the direction of one arm “forward” (for example) generates the same interference pattern as in the case it moves in opposite direction (backwards). Even if there is a difference between the speed of light traveling in one sense and the opposite sense (anisotropy of speed of light) the device could not measure it. Michelson interferometer seems to agree with FitzGerald length contraction hypothesis [5]. ​ ​ As long as no experiment could determine any anisotropy, the use of Lorentz transform(which is a symmetrical transform between inertial frames of reference) seemed to be safe and Lorentz symmetry largely accepted as a symmetry of nature. Even if Lorentz symmetry leads to paradoxes like “the twins paradox”, as long as there is no proof of light speed anisotropy the prefered way to deal with those paradoxes is to find even more complicated solutions [6] implying ​ ​ that the time dilation depends on the acceleration of the the frame of reference although everything indicates that it depends only on the instant value of the velocity. The interferometer described herein sheds light on all these controversies being able to measure the anisotropy of speed of light and brings the proof that Lorentz symmetry is broken in certain situations. More yet, this device is more efficient than Michelson interferometer, generating a difference in the travel time of the split beams of light proportional to the ratio v/c (ratio between the ​ ​ velocity of the device and the speed of light in vacuum) which for low velocities is many orders of magnitude larger than that generated by Michelson interferometer (which is proportional to the ratio 2 2 v /​ c )​ ​ ​ By measuring the anisotropy of the speed of light in the frame of the device, this interferometer demonstrates that the FitzGerald length contraction hypothesis is false and helps validate the equivalence principle ­ that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo­force experienced by an observer in a non­inertial (accelerated) frame of reference (or that the inertial mass is equivalent to the gravitational mass).
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