False and correct fringe-shift expectations in the Michelson- Morley experiment.

Transcription

1 False and correct fringe-shift expectations in the Michelson- Morley experiment. Gyula Korom Mail: Summary In the original papers of Michelson and Morley, erroneous, seriously misleading calculations were used. Since then, the physical literature have been using that incorrect method in the experiments, in the textbooks and in the teaching materials used for the students. Author has been analyzed the reasons of the errors and shows the correct calculus. Furthermore, the correct way of calculations were performed and plotted by a computer program in different ether-wind intervals, before and after the turning of the Michelson-Morley interferometer. The author also tested three different ether models by the computer program. The results show that observable phase-shifts (interference ring displacements) can be expected only, if the speed of the supposed ether wind is much faster than 3 km/sec. Around and below of this limit, the Michelson-Morley interferometer is insensitive for determining the phase shifts of the ether wind. The reason is, the phase-displacement due to the blue shift of the light on the route from the F semi permeable mirror to the M reflexive mirror along the arm of the interferometer laying in the direction of the ether-wind is superimposed by the red shift of the light while turning back to the F mirror. Below 3 km/sec ether speed, the interferometer is practically insensitive for the ether wind, no observable ring shifts are expected in the -3 km/sec speed interval, neither before nor during nor after turning the instrument. Key words: Michelson-Morley experiments, supersonic Jets, wave-theory of light, ether models, ether wind, the false Michelson-calculus, light route and optical distance, phasorcalculus, speed-dependent superposition of the blue- and red shifts. I. Introduction At the end of the XIX th and at the beginning of the XX th centuries, the null-effects of the Michelson-Morley experimental series were extremely surprising, because large amount of interference-line shifts were expected based on the incorrect calculations used by Michelson and Morley []. II. The original erroneous calculation used by Michelson and Morley (The Michelsoncalculus) The optical way-differences of the two light-waves have turned back form the reflexive mirrors of the MM interferometer to the F semi permeable mirror and reunited, were calculated as the lines,, and shows on Figure. This method of determining the optical way-differences is false due to the reasons as follows. a.) When semi permeable mirror F is at the left position, and the two separated wave-crests leave F to the directions M and M 2, one and only one wave-crest will run along route and

2 to the reflexive mirrors, because F will move to the right. The next wave-front will run on a parallel line to. b.) Having turned back to F, the two separate wave-crests never will meet, because + is shorter than +. Consequently, interference rings will never build up on this way. c.) When arrives at F, the angle of the incoming light wave is such, that will not always enter the registration area, and it will pass F with small changes of the angular direction, like it can be seen on Figure. d.) When arrives at F, another light wave-crest (e.g. /a) will arrive from M 2, and never that one ( ), with which left F. As a result, the phase constant of /a is not the same as that of. e) The optical way-difference, must and can only be calculated, when the light source and the observer is in the same moment. Obviously three light sources produce wave-fronts in the MM-interferometer as it follows: F, M and M 2 mirrors. These three optical elements are the observers as well. The optical distances of these three elements are constants. The optical distance between F and M is L, and that between F and M 2 is L 2. In the calculus used by Michelson and Morley, the light source F emanates a wave front that goes to M on in a while, and arrives at M at a different moment. As a result, is not an optical distance, but a light rout instead. Consequently the phasor-calculus cannot be applicable. Nevertheless, Michelson and Morley incorrectly applied the phasor-method in determining the phase difference between the two end of light route. This calculus erroneous because at that very moment, when light wave arrives at M, light source F is not at the starting point of. Observer Ether Wind (v) Figure. f) The optical distance of cannot be calculated as Michelson did, because when lives M, F was not in that place, where it will be, when arrives at F. Optical distance must be determined at the very same moment. Page 2/

3 Summarizing the results of these cumulated errors, the Michelson-calculus erroneously enhances the calculated blue phase shift (longer optical way difference), and erroneously decreases the calculated red shift. As a result, the MM-interferometer looks much more sensitive, as it really is. III. The correct calculus Based on the wave-theory of light, and on the ether-hypothesis, the moving light sources are generating expanding Doppler-shifted light-wave balls around themselves. As the MMinterferometer consists of three light sources as parts of the calculations, we have to take into account three independent Doppler-shifted, spherical wave-spaces, as it is seen on Figure. Having switched on the primary light source, first the F Doppler-space will be built up. Waiting for a while, light coming from F riches the M 2 mirror, that will start constructing its own Doppler-space. Little bit later, blue-shifted light waves riches also mirror M that now will start pulsing as well. When enough time has gone by, the distances along L and L 2 will be full of Doppler-shifted waves in both directions. Now, let us take an imagined photograph at that very moment, when the top of a wave-crest leaves F. As L 2 is perpendicular to the ether wind, wave-lengths between F and M 2 will be the same in both directions, and equal with the original wave-length of the primary source (Figure 2). Éterszél l (V) L 2 M 2 M L Copyright Korom Gy. Figure 2. Page 3/

4 On the route from F to M (along L ), blue-shifted wave fronts, from M back to F, redshifted wave fronts are. As all light sources and observers are photographed at the very same moment, the phasor-calculus can be applied. We can simply calculate the wave-lengths in all directions to and back (Figure 3), then we have only to calculate, how many full and partial wave-lengths have space along the given arm, considering each phase constants as well. Now we calculate the phasedifferences between the two arms. What is very important, the optical distances are the same during the course of the movement of the instrument. The optical distance is independent from the speed of the ether wind. Only the wave-lengths are subjects to change, if the speed of the instrument in the ether changes, or when we rotate the double armed interferometer. IV. Testing the different ether models Using the above mentioned V V correct method of phase-shift λ t = λ + cosα λ k = λ cosα c c calculations, a computer program Figure 3. was developed to calculate the expected phase shifts, if an ether wind does exist. Several tests were performed with different arm lengths, and wavelengths. On the figures showed in this article, the following standards were used: the length of L 2 was m, the arm difference was o,5 cm, the amplitude of the light waves was a unit, the phase constant of the primary light source was, the wave-lengths of the light sources are shown on the figures below. Three different ether models were tested. ) Ether at absolute rest According to the Very Long Baseline Array, the speed of the Sun around the center of the Milky way is 268 km/sec. Let us suppose that the Milky way is resting in the ether. In that very improbable case, the ether wind on the Sun is also 268 km/sec. As the Earth is revolving around the Sun, and the angle of the orbital plane is 6,2 degrees, the relative speed between the Earth and the ether will change in a year according to a cycloid curve. The speed interval of the ether wind on the surface of the Earth according to the model will be cca km/sec. Page 4/

5 The correlation was calculated and plotted between the speed of the ether wind and the expected phase shift in the MM-interferometer, when arm L is in the direction of the wind, and the laser was λ=458 nm argon ion. (Figure 4). Differences in the number of waves along the two arms of the MM-interferometer (Rotation angle: zero, wave length: 458 nm) 34 The speed of the ether wind (km/sec) ,6 2828,8 2829, 2829,2 2829,4 2829,6 2829,8 283, 283,2 283,4 283,6 283,8 Figure 4. Let us now rotate the instrument by 9, the changes are shown on Figure 5. Differences in the number of waves along the two arms of the MM-interferometer (Rotation angle: 9 degrees, wave length: 458 nm) 34 The speed of the ether wind (km/sec) ,4 2837,6 2837,8 2838, 2838,2 2838,4 2838,6 2838,8 2839, 2839,2 2839,4 2839,6 Figure 5 Comparing Figure 4 and 5, several number of wave-differences occurs after the rotation. For example at the speed of 3 km/sec, the difference is approximately 9 wave lengths. Interestingly enough, when the ether-wind speed is decreasing, the differences in the wavenumbers are decreasing. Page 5/

6 This result means that the null-effect of the MM-experiments is convincing, the absolute resting ether model really cannot be accepted. 2) If the ether rotates around the center of the Milky way with the speed of the Sun. According to some galactic model, in the center of the Milky way is a black hole, that swallows the stars, and possibly the ether as well. In this model the matter of the stars and the matter of the ether is moving along a spiral route towards the black hole just like in e whirlpool. In this model, the Sun and the ether is moving approximately at the same speed, and the Earth is revolving in the whirling ether-pond at a constant 3 km/sec speed. Plottings between the -3 km/sec ether-wind interval can be shown on figure 6 and 7. Differences in the number of waves along the two arms of the MM-interferometer (Rotation angle: degrees, wave length: 458 nm) 4 3 Ether wind (km/sec) ,5 2834,2 2834, ,3 2834, ,4 2834, ,5 2834, ,6 2834, Differences in the number of the wave-fronts Figure 6 On Figure 6 one can see that at speed 3 km/sec, the expected wave-front difference is 2834,7. After a 9 degree rotation, the expected phase shift is minimal, only,88. Similar results are, when we use different wave-lengths. This shift is under, or around the minimum sensitivity of the best MM interferometers. Generally speaking, these instruments are able to register not less than,5 weave length. Smaller shifts are non-observables by this method. Page 6/

7 Differences in the number of waves along the two arms of the MM-interferometer (Rotation angle: 9 degrees, wave length: 458 nm) 4 3 Ether wind (km/sec) , ,6 2834, ,7 2834, ,8 2834, ,9 2834, , 2834,5 2834, Differences in the number of the wave-fronts Figure 7 3) If the light is the vibration of the electromagnetic and gravitational fields of the celestial bodies G.G. Stokes supposed, that the Earth has an ether atmosphere. This model was refuted for several reasons. Much more reasonable model is, when we suppose, that the conductive medium of the light-waves are the electromagnetic and gravitational fields of the heavenly bodies (see Figure 8). Figure 8 There is no expected fringe (phase) shift according to the correct phasorcalculus, as it can be shown on Figures 9 to 4. The so called double Doppler effect produces a null fringe-shift effect. Page 7/

8 (Rotation angle: degrees, wave length: 458 nm),5 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 -,5 - - Figure 9 (Rotation angle: 9 degrees, wave length: 458 nm),5 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 2834,6 -,5 - - Figure Page 8/

9 (Rotation angle: degrees, wave length: 694 nm),5 449, , , , , , ,222 -,5 - - Figure (Rotation angle: 9 degrees, wave length: 694 nm),5 449, , , , , , , ,222 -,5 - - Figure 2 Page 9/

10 (Rotation angle: degrees, wave length: nm),5 7,958 7,958 7,958 7,958 7,958 7,958 7,958 7,958 -,5 - - Figure 3 (Rotation angle: degrees, wave length: nm),5 7,958 7,958 7,958 7,958 7,958 7,958 7,958 7,958 -,5 - - Figure 4 On the Figures above is shown, that there is no expected fringe (phase) shift in the Michelson- Morley instrument, if the speed of the ether-wind is much lower than 3 km/sec. Page /

11 V. Discussion and consequences Michelson and Morley [] used light routes (incorrectly), instead of optical distances in their calculations. Between the starting point and the end of a light route, the time is passing, as the light needs time to reach the endpoint. The optical distance means the distance of two bodies in the ever-changing wave-space at the very same moment. In the Michelson-Morley interferometer, the expected phase-shifts can only be calculated by the optical distance of the mirrors, which are the lengths of the two arms of the interferometer. The Michelson-calculus and the correct phasor-calculus give different results, because the light route from F semi permeable mirror to the reflexive M mirror is much longer than the light route back to the F. As a result, in the Michelson-calculus, the differences of the phaseshifts caused by the Doppler blue-shift are much more, than the shift differences caused by the red shifts. Furthermore, the rotation of the instrument expects much more phase-shifts on the basis of the erroneous Michelson-calculus. The correct phasor-calculus uses the optical distances, instead of the light routes. The optical distance of F and M is the same and constant, while the instrument moves in the ether. Within the same optical distance, the phase-shift differences between the blue-shifted and redshifted phases are speed-dependent. At low ether-wind speeds ( 3 km/sec), these phase shifts practically extinct each other, and phase-shift changes caused by the rotation of the instrument are also under the sensitivity of the interferometer. At higher ether-wind speeds (> 3 km/sec) the phase-shift differences increase proportionally with the increase of the speed, and the effect of the rotation is also increasing. The correctly calculated (expected) phase-shifts show that the double-armed interferometer is not able to measure the ether wind, if the speed of the wind is lower than 3 km/sec. Consequently, the axiom of the absolute constant speed of light in the Special Relativity Theory is only an experimentally not proved, bizarre hypothesis. Furthermore, the wave theory of light, and the ether model is not falsified experimentally. VI. Reference [] Albert A. Michelson, Edward W. Morley: On the Relative Motion of the Earth and the Luminiferous Ether, Am. J. Sci., N 23, Vol. 3., pp (887) Page /