c Allerton Press, Inc., 2010. ISSN 1541-308X, Physics of Wave Phenomena, 2010, Vol. 18, No. 3, pp. 164–166.
OPTICAL MEASUREMENTS
First-Order Ether Drift Experiment with a Mach−Zehnder Fiber Interferometer V. de Haan* BonPhysics Research and Investigations B.V., Laan van Heemstede 38, 3297 AJ Puttershoek, The Netherlands Received April 16, 2010
Abstract—The recently proposed first-order ether drift experiment with an asymmetrix Mach−Zehnder interferometer could be used to detect anisotropy in the speed of light. The experiment has been performed, and no effect was detected within the measurement accuracy. DOI: 10.3103/S1541308X10030039
Recently Spavieri et al. [1] proposed a first-order ether drift experiment to test Consoli’s suggestion about the speed of light and the preferred frame velocity. Consoli’s argument [2] is that up to now all experimental results leave the possibility open that light is dragged according to the Fizeau drag formula in transparant solids and liquids but differently in gaseous substances like air or helium at atmospheric pressure. This would be supported by the renewed interpretation of the results of the Michelson−Morley experiments [2−4]. A test experiment is proposed: to let light pass through two arms of a Mach−Zehnder interferometer, the arms having different refractive indices. Such an experiment with an atmospheric air path has been performed recently by de Haan [5]. With such an asymmetric fiber Mach−Zehnder interferometer (Fig. 1), the laser beam injected into the fiber is split into two equal in-phase beams by a 2×2 directional coupler. These two light beams travel through the two (parallel) fiber arms of the interferometer and are rejoined by the second 2×2 directional coupler. Depending on the mutual phase, the light beams interfere constructively in one output fiber and destructively in the other one. The two output beams from the second 2×2 directional coupler are fed into two detectors, where their intensities I1 and I2 are measured. The sum of the intensities is proportional to the laser output power. The ratio of the intensity difference to the intensity sum is called the visibility, V . The visibility of an ideal interferometer changes between −1 and +1, depending on the phase difference φ of the light beams in the second directional coupler: *
V =
I1 − I2 = cos φ. I1 + I2
(1)
The phase difference is determined by the optical path of the light traveling along the fibers from the first directional coupler to the second one. This optical path depends on the length of the arms and the wavelength λ of the light traveling through the fibers. The light wavelength depends on the speed of light in the fibers and, hence, on the refractive index n of the fibers and (possibly) on the velocity and motion direction (v) of the Earth relative to the preferred rest frame. Hence,
Fig. 1. Configuration of the asymmetric Mach−Zehnder interferometer.
E-mail:
[email protected]
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φ=
FIRST-ORDER ETHER DRIFT EXPERIMENT
2π dl − λ(n, v)
1
2π dl, λ(n, v)
(2)
2
where i is the line integral along arm i from the first directional coupler to the second one. The aim of this experiment is to determine the change in the phase difference due to the motion of the Earth. Therefore, the entire interferometer is put on a rotation table to make it possible to change the interferometer azimuth. In this way the direction of the Earth motion relative to the arm orientation changes during rotation. While tracking the changes in the phase difference during interferometer rotation, one can determine the direction in which the projection of the Earth velocity on the preferred rest frame is maximum and find the magnitude of this maximum projection. These characteristics, relative to the local North, change with the time of year and the sidereal day. If there is any effect due to the rotation of the Earth, this signal should change depending on sidereal time (see [3] for details). Obviously, a perfect interferometer does not need to be rotated because the Earth rotates around its axis every 24 h. However, for a real-time fiber interferometer it is very difficult to get a stable signal for more than several hours, even more difficult for several days, and barely possible for a year. One of the problems with Eq. (1) is that the visibility is determined by the cosine of the phase difference between the light beams. There is an ambiguity in the sign and exact value of Δφ when only the visibility is determined. To overcome this problem, an optical phase shifter is inserted in the interferometer arms to introduce an extra phase shift. This additional phase shift is controlled in such a way that the visibility remains zero and, accordingly, the argument of the cosine remains π/2. The details of the measurement method can be found in [5, 6]. To test Consoli’s suggestion, a 175-mm atmospheric air path was inserted in one of the arms. The detailed analysis was reported in [5, 6]. The results are shown in Fig. 2. The average amplitude of the firstorder effect is 0.20(1). The results indicate clearly the absence of any sidereal dependence. The measurement error was about 0.05 rad per rotation, which corresponds to 0.01 fringes. The amplitude of the phase difference upon rotation due to the air path is Δφ =
165
2πL(1 − 1/n2a )v , cλ
where na is the refractive index of air. The maximum first-order effect under these conditions is 64(6) km s−1 , about twice the velocity of the Earth in its orbit around the Sun. However, the azimuth of the first-order effect maximum is constant and corresponds approximately to the North−South diPHYSICS OF WAVE PHENOMENA
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Fig. 2. (a) First-order amplitude of the interferometer signal as a function of sidereal time with 175-mm atmospheric air path. (b) First-order azimuth of the maximum of the same signal. For clarity error bars are omitted. Their length is approximately the same as the spread of points.
rection. Since it does not depend on the sidereal time, Consoli’s explanation can be valid for the magnitude but fails to yield the direction in the experiment. This can be due to the large velocity component oriented perpendicularly to the Earth’s orbit plane. Consoli’s hypothesis was further tested by replacing the atmospheric air in the 100-mm path with atmospheric helium to reduce the effect of the signal amplitude by a factor of about two. However, no change in the firstorder amplitude larger than 0.01(1) rad was observed. Thus, Consoli’s hypothesis can be rejected. Nevertheless, it is remarkable that all the measurements show a first-order effect, directed almost parallel to the Earth axis. If this effect is not due to the stresses in the fibers or other instrumental artifacts, it can be caused by the rotation of the Earth. The sensitivity of the method used could be enhanced by increasing the air path length or the setup stability.
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REFERENCES 1. G. Spavieri, V. Guerra, R. De Abreu, and G. T. Gillies, “Ether Drift Experiments and Electromagnetic Momentum,” Eur. Phys. J. D. 47(3), 457 (2008). 2. M. Consoli and E. Costanzo, “From Classical to Modern Ether-Drift Experiments: the Narrow Window for a Preferred Frame,” Phys. Lett. A. 333, 355 (2004). 3. H. A. Munera, “Michelson−Morley Experiments Revisited: Systematic Errors, Consistency Among Different Experiments, and Compatibility with Absolute Space,” Apeiron. 5(1−2), 37 (1998).
4. R. T. Cahill and K. Kitto, “Re-Analysis of Michelson−Morley Experiments Reveals Agreement with COBE Cosmic Background Radiation Preferred Frame so Impacting on Interpretation of General Relativity,” Apeiron. 10(2), 104 (2003). 5. V. de Haan, “Asymmetric Mach−Zehnder Fiber Interferometer Test of the Anisotropy of the Speed of Light,” Can. J. Phys. 87(10), 1073 (2009). 6. V. de Haan, “Mach−Zehnder Fiber Interferometer Test of the Anisotropy of the Speed of Light,” Can. J. Phys. 87(9), 999 (2009).
PHYSICS OF WAVE PHENOMENA
Vol. 18 No. 3
2010
