Marinov's Toothed-Wheels Measurement of Absolute Velocity of Solar System. J.P.Wesley. Weiherdammstrasse 24, 7712 Blumberg, West Germany. Abstract: Marinov reports measuring the absolute velocity of the closed laboratory using two toothed wheels mounted on the ends of a rotating shaft. Light incident on the first toothed wheel is chopped. As it arrives at the second toothed wheel later, due to the finite time it takes light to travel down the shaft, it is again chopped by the second toothed wheel. The amount of light that gets through measures the oneway time-of-flight velocity of light in the direction of the shaft. By directly comparing the results for beams travelling in opposite directions the absolute velocity is directly measured, v = ((c+v)-(c-v))/2. He reports the absolute velocity of the solar system as v = 360 +- 40 km/s, alfa = 12 +- 1 h, delta = - 24 +- 7 deg, in agreement with the results from the 2.7K cosmic background anisotropy and Marinov's coupled mirrors experiment. The errors he reports are consistent with his experimental setup and procedure. 1. INTRODUCTION It is of considerable importance to examine Marinov's claim(1): i) It contradicts SPECIAL RELATIVITY, which assumes the velocity of light is uniquely c fixed relative to the moving observer. ii) It provides an additional independent measurement of the absolute velocity of the solar system. Considering point i) above there exists considerable dissatisfaction with SPECIAL RELATIVITY already (2-7). It would also seem that the observations of Roemer and Bradley(8,9), the Sagnac experiment(10), the 2.7K cosmic background anisotropy(11), and the Marinov coupled mirrors experiment(12) give firm evidence that the velocity of energy propagation of light is, in fact, c fixed relative to absolute space. In addition, assuming absolute space exists, it would appear that a moving observer must see two wave velocities for light, the phase velocity and the velocity of energy propagation, and not simply a single unique wave velocity of light as is usually assumed(13). These two wave velocities need not have the same magnitude nor direction. It is, thus, very impotant to know if more independent experimental evidence is now available that can confirm the fact that the velocity of energy propagation of light is c fixed relative to absolute space. Considering point ii) above, presently the only two reliable determinations of the absolute velocity of the solar system are 1) the anisotropy of the 2.7K cosmic background radiation 2) the Marinov coupled mirrors experiment. (12).The 2.7K background anisotropy provides one place accuracy. The Marinov coupled mirrors experiment provides slightly better accuracy; although with little difficulty it can be readily improved to give two, three or even four place accuracy(14). The Marinov toothed wheel experiment provides still a third independent method for determining the absolute velocity of the solar system. He reports one place accuracy; but it would appear that with some minor improvements that two place accuracy might easily be obtained. It is of some interest to know the absolute velocity of the solar system to as great an accuracy as possible; as three place accuracy might provide the chance of detecting dark neighbours to the solar system. The primary purpose of this paper is to provide a short understandable and readily available description and critique of Marinov's toothed wheel experiment, Marinov's own account(1) being neither clear nor readily available. It is hoped that this presentation might encourage an independent repetition of this important experiment. 2. MARINOV'S EXPERIMENTAL ARRANGEMENT (1) Two toothed wheels consisting of 40 round holes of diameter b = 6 millimeters drilled equi-angular distance from each other at a radial distance R = 12 cm from the center of two circular steel plates were mounted on a common shaft d = 120 cm from each other as indicated in Fig. 1. The shaft was driven at the center by a variable speed motor, N revolutions per second. An Argon laser illuminated the holes on the entrance wheel. A silicon photocell detected the light passing out of the exit wheel. The entire apparatus was enclosed in a vacuum. Fig.1. A diagram of the Marinov toothed-wheel experiment to measure the absolute velocity of the closed laboratory. 3.THEORY FOR ONEWAY TIME-OF-FLIGHT VELOCITY OF LIGHT Although the present paper is concerned with the direct measurement of the absolute velocity of the closed laboratory; and it is not concerned with the measurement of the oneway time-of-flight velocity of light; in order to develop the theory and to indicate how possible errors may be estimated it is convenient to first present the hypothetical example of how one might measure the oneway time-of-flight velocity of light. It might be thought that one need merely measure the oneway time-of-flight velocity of light in two opposite directions and by subtracting them obtain the absolute velocity of the laboratory. This is in principle possible; but in practice the experimental errors for the measurement of the one-way time-of-flight velocity in either direction are too large.It is only by balancing the two results directly in a Wheatstone bridge that significance can be obtained; and the absolute velocity of the laboratory can be measured. The rotating entrance wheel chops the light beam. The rotating exit wheel chops this signal again but at a later time dt, the time for a pulse of light to travel down the length of the shaft d. If the observed time-of-flight velocity of light in the direction of the shaft is c*, then dt = d / c* (1) If the time-of-flight velocity of light is fixed as c relative to absolute space, then c* = c - vd (2) where vd is the component of the absolute velocity of the laboratory in the direction of the shaft. The two wheels, being rigidly mounted to the same shaft, can be optically aligned by simply altering the inclination of the light beam relative to the axis of rotation. If the beam is aligned to achieve a certain intensity Io (chosen as one half of maximum intensity, Io = Imax/2, to optimize the sensitivity) when N = 0, then the intensity must change as N increases and as the alignment of the entrance and exit holes changes relative to the chopped light pulse. Ideally for square holes of width b that can be perfectly aligned the fractional change in intensity is simply proportional to the fractional mismatch created by the time it takes the light to travel between the two toothed wheels; thus, dI/Io = 2 db/b (3) where db = 2 pi R N dt (4) It may be readily appreciated that for round holes and including possible effects from diffraction and vibrations dI/Io, will be simply a linear function of 2 db / b, if dI / Io is small, as is the case. In general then Eq. (3) may be replaced by dI/Io = 2 K db / b (5) where K is some konstant of proportionality. If this constant of proportionality were desired, it could be measured directly or it could be estimated theoretically. Combining Eqs. (1), (4), and (5) then gives the oneway time-of-flight velocity of light as (15) c* = (K Io / dI) ( 4 pi R N d / b) (6) 4. THEORY TO FIND THE ABSOLUTE VELOCITY OF THE LABORATORY Marinov sent simultaneously laser beams in opposite directions through his toothed wheel apparatus which were detected by two independent photocells, as shown in Fig. 1. He measured the difference ddI in the intensities registered by the two photocells directly using a Wheatstone bridge for the outputs. Letting the two light velocities involved be c-* = c + vd and c+* = c - vd (7) Eq. (6) yields the component of the absolute velocity in the direction of the shaft as vd = (c-* - c+*)/2 = (ddI / dI- dI+)(4 pi K Io R N d / b) (8) where 2 ddI = I- - I+ = |dI-| - |dI+| and dI- and dI+ are the intensity differences registered in the two directions. It may be readily appreciated that to within a negligible second order error of the order of (ddI / dI)^2 or (vd / c)^2 that dI- dI+ = (dI)^2 (9) where dI may be taken as the intensity when vd = 0 or as 2 dI = |dI-| + |dI+|. Combining Eqs. (8), (9) and (6) (for the case vd = 0) then gives the desired result vd = (ddI / dI) c (10) To double his sensitivity and to obviate certain possible errors in alignment of his apparatus Marinov employed the stratagem of measuring the change in intensity dI when the shaft was rotated in both senses. Because when N = 0 the intensity Io was chosen as 1/2 the maximum intensity, Imax; the change in intensity was positive for one sense of rotation, and negative in the opposite sense. The effective intensity change that could be measured was, thus, doubled. The intensity change dI was then taken as 2 dI = |dI(clockwise)| + |dI(counter clockwise)| (11) Marinov used the same stratagem when measuring ddI, averaging the results for the shaft rotating in the two possible senses. If the intensities are broken down into Io, a part dI that depends merely upon the average velocity of light c(where vd may be regarded as zero), and a part that depends upon the absolute velocity of the laboratory ddI, then the four possible situations considered by Marinov experimentally are listed in Table 1. The observed intensity difference was thus Table 1. Four intensities involved in Marinov's toothed-wheel experiment. case direction a c + vd Ia = Io + dI + ddI b c + vd Ib = Io - dI - ddI c c - vd Ic = Io + dI - ddI d c - vd Id = Io - dI + ddI 4 ddI = (Ia - Ic) - (Ib - Id) (12) It was found to be impossible to align the apparatus so that the two beams in opposite directions were precisely equivalent. Thus in fact (Io + dI)a - (Io + dI)c = I' and (Io - dI)b - (Io - dI)d = I'' were not precisely zero. A residual constant error (I' + I'')/2 remained in the determination of ddI. It is clear that this assymetry could have been easily taken into account if the apparatus had been mounted on a turn table and turned through 180 deg to repeat the observations. Averaging the two results would have then removed this constant error. Since Marinov's equipment was righidly fixed to the earth and could not be rotated; he resorted to the following strategem: 5 TWELVE HOUR OBSERVATIONS TO DETERMINE THE ABSOLUTE VELOCITY OF THE LABORATORY Marinov placed his shaft in the north-south direction horizontal to the earth's surface. At the latitude of Graz, Austria, where the experiment was performed, as the earth rotated, the shaft moved on the surface of a cone making an angle of 47 deg with respect to the axis of the cone, which was parallel to the axis of the earth's rotation. Thus, Marinov had to merely wait 12 hours for the earth to rotate his equipment through 180 deg as far as the component projected onto the earth's equatorial plane is concerned. It was, therefore an easy matter to subtract off the constant error (I' + I'')/2, mentioned above, by making observations over 12 or more hours without changing any alignments. 6. DETERMINATION OF THE DIRECTION OF THE ABSOLUTE VELOCITY OF THE SOLAR SYSTEM Because the component of Marinov's shaft projected onto the earth's equitorial plane sampled all possible directions in this plane after 12 hours of observation, and because the component of the shaft projected onto the earth's rotational axis provided the remaining direction to be sampled; straight forward trigonometry provided the direction of the absolute velocity of the earth on the day observations were made. The absolute velocity of the solar system (ie the sun) was then obtained by simply subtracting off the earth's orbital velocity with respect to the sun (which was, in fact, only of the order of the error that he reports for his observations). The tangential velocity of the earth's rotation, which is less than the error Marinov reports, did not enter in due to the north-south orientation of the shaft of his apparatus. 7. DISCUSSION The final formula(10) for vd involves only the intensity differences ddI and dI. Only these two quantities need be examined to determine the random or experimental error. Is the error of 11% reported by Marinov reasonable? This can be best estimated by considering 4 dI/I, and 4 ddI / Io. The factor 4 arises from the increased sensitivity due to two senses of rotation being used and due to the two directions of light travel being used. From Qu. (6), setting c* = c, the fractional value 4 dI / Io, according to the numbers provided by Marinov, where he estimated the value of K theoretically for round holes as 9/2, is 4 dI/Io = K 16 pi R N d / c b = 5E-3 (13) To obtain dI it was necessary to subtract separate readings on a galvanometer. Separate large readings on a galvanometer can be usually made to about 1% accuracy. Thus, the theoretical and the experimental estimate of the fractional error are roughly the same. The determination of ddI was quite different. Here the difference was measured directly on a Wheatstone bridge. Differences of the order of ddI = 1E-3 dI = 5E-6 milliamps could be measured. Since ddI/dI ,varying as vd/c, Eq. (10), is in fact, about 1E-3, as known from the 2.7K anisotropy(11) and the Marinov coupled mirrors experiment; the fractional errors to determine 4 ddI / Io and 4 dI / Io are comparable. The highest current Marinov recorded for Io was 21 milliamp; and the maximum difference associated with the difference ddI was about 6E-5 milliamps. This means a fractional intensity difference of 4 ddI/Io = 1E-5 was recorded. Others have also reported being able to measure such intensity differences down to a level of 1E-5 using electronic comparisons. From Eq. (10)the fractional error for vd / c is the sum of the fractional errors of 4 dI / Io and 4 ddI / Io. As estimated above each of these fractional errors are of the order of 1%; so Marinov's experimentally determined experimental error of 11% seems quite reasonable. It has been speculated that mechanical vibrations would make it impossible for Marinov to have obtained a positive result. Although it may be true that instantaneous mechanical distortions produced misalignments resulting in an instantaneous error of the order of 1E-5 in fractional intensity; observations were not taken instantaneously. Observations were averaged over a time span long in comparison to the period of any mechanical vibrations of interest. Even if vibrations of the order of 1E-3cm existed, the fractional error produced by holes of 0.6 cm would be much less than Marinov's reported error. It seems clear taht vibrations could not possibly have affected the results. And Marinov reports, consistent with this estimate, no difficulty with vibrations. It is difficult to imagine systematic errors that might have distorted Marinov's results. Since the apparatus was evacuated, no atmospheric effects could enter in. 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After correcting some computational errors Marinov now reports for his coupled mirrors experiment the value of the absolute velocity of the solar system v = 303 +- 20 km/sec, alfa = 13.3 +- 0.3 h, delta = -21 +- 4 deg. 13.J.P.Wesley, Found.Phys.,16,817(1986) 14.J.P.Wesley, Found.Phys.,11,945 (1981) 15.S.Marinov measured the oneway velocity of light to one place accuracy using a terrestrial light source, Spec.Sci.Tech.,3,57 (1980)