MODERNIZED MICHELSON’S INTERFEROMETER
Uzhgorod National University, 88 000, Pidhirna Str., 46, Uzhgorod, Ukraine
It is shown that Fizeau’s experiments on the investigation of photons dragging by the environment moving with respect to the device can be explained through the assumption that analogous dragging of photons also takes place, when optical environment is moving with respect to the ether. Scheme of modernization of Michelson’s interferometer, supposedly capable of registering the fact of a device motion with respect to the light-carrying environment, is proposed. The appropriate estimating calculations are made.
It is known that experiments with Michelson’s interferometer were tried in order to discover the Earth’s motion with respect to the light-carrying environment – ether. It was supposed, that in mutually perpendicular arms of the device, photons as the ether wave formations will undergo the influence of the Earth’s motion with respect to the environment in a different way. However, the experiment did not demonstrate the expected phenomenon. For explaining the reason of the independence of the interferential pattern on the device orientation, three assumptions were made:
(1) All moving bodies decrease their dimensions in the direction of motion, in accordance with (Fitzgerald–Lorentz’s hypothesis),
where l0 is the body’s length in the resting state, l is the body’s length during its motion with the velocity of ^ with respect to the resting frame, C is the light velocity. All quantities are measured with the devices of the resting frame.
(2) Bodies do not change their dimensions, but the velocity of the photons having corpuscular properties is summed with the source velocity (Ritz’s ballistic hypothesis).
(3) Photons’ velocity does not depend on the velocity of the frame, in which the light velocity is measured. This assumption forms one of the bases of the Special Relativity Theory (SRT), but goes beyond the limits of the common sense.
Lately in the literature one can quite often come across the assumption that all elementary particles are soliton formations of the light-carrying environment. On the basis of this supposition, one can propose the fourth variant of explaining the results of Michelson’s experiments, and also make up a relativity theory, not only well-agreed with all corresponding experiments, but also free from the well-known paradoxes of the SRT [1, 2]. This hypothesis raises in a new way the question of its experimental testing, since almost all conclusions, which can be obtained from the relativity theory, are already made and tested experimentally. In the present work, we will represent the scheme of the experiment, which supposedly will allow fixing the fact of motion with respect to the light-carrying ether with the devices of the isolated laboratory.
As it is known, in Fizeau’s experiments, there was quite effectively registered the fact of the dependence of the photons’ velocity with respect to the coordinate frame, connected with the device, on the velocity of the water stream with respect to the device. In these experiments, the ray of the light source S was divided by the light-dividing plate into two parts, which were directed in opposite directions at the same contour, passed through two cuvettes with moving water, came back to the dividing plate and interfered, Fig. 1. In this case, the water in the cuvettes moved in such a way that promoted the motion of photons on the first ray and prevented the motion of photons on the second ray. This asymmetry in the action of moving optical environment upon the photons led to the shift of the observed interferential stripes.
First it was supposed that the moving water would completely drag the photons. Since photons moved at one and the same contour, it was possible to influence the interferential pattern only by the water motion in the cuvettes. In this case, the difference t in the times of the photons propagation in opposite directions determines the shift degree of the interferential stripes.
S – light source; 1 and 2 – interfering beams of photons, from which ray 1 is propagated along the water stream, and ray 2 – opposite the stream.
We assume that the device is resting with respect to the light-carrying environment. Velocity ^ 1 of the photons in the water for ray 1 is summed with the water motion velocity U. Since the photons’ velocity in the environment is reversely proportional to the refraction quotient n, the resulting velocity for complete dragging of the photons by the water in ray 1 is equal to
For the photons of ray 2:
The time of the photons’ motion along the water motion in both cuvettes, each of which has length l:
The time of the photons’ motion opposite the water motion in both cuvettes:
The difference t0 in the times of the cuvette passing by the photons is equal to
In Fizeau’s experiments, the water velocity U was equal to 7 m/s, the cuvette length l is equal to 1.5 m, the refraction quotient is n=1.333. For С=3108 m/s, in accordance with (2.5), we have
t0= 8.2921510–16 sec. (2.5*)
This difference in the times of the photons motion through the cuvettes had to lead to the stripes shift at the half of the photons’ wavelength, i.e. the light stripes had to occupy the place of the black ones. However, the experiment showed that the phenomenon occurs in such a way as if only partial dragging of photons by the water takes place – approximately a half of the calculated degree, with some dragging coefficient , .
With taking into consideration the photons dragging by the water stream, the expression (2.5) acquires the following form:
Numerically, in case of the above-mentioned conditions of Fizeau’s experiment:
t1= 3.6254810–16 sec (2.6*)
The result (2.6*) is well agreed with the experiment. In this case, the relation t1/t0 is quantitatively equal to the dragging coefficient for water, =0.437.
If all bodies, including transparent ones, consist of soliton formations of the light-carrying environment, and photons are specific oscillations of this environment, then there must be observed the effect of partial dragging the photons by the bodies moving with respect to the ether, by analogy with Fizeau’s experiments. Moreover, Fizeau’s experiment itself must be analyzed from this viewpoint.
Assume that in this case the dragging coefficient is the same as in case of the photons’ motion in the moving environments, i.e. . Thus, the expression (2.6) for the time differences should be analyzed, since one should take into consideration not only the water motion with respect to the device, but also the motion of the device together with the Earth with respect to the ether. Let V be the velocity of the Earth motion with respect to the ether and its direction coincide with the direction of the photons’ motion in ray 1, Fig. 1. In this case, the photons’ velocity in cuvette A is summed not only with the velocity of the water motion U with respect to the device, but also with the velocity V of the water motion with respect to the immovable ether, therefore, the photons move with respect to the ether with the following velocity:
During the time t1 of the photon’s motion in cuvette A with the length of l, the end of this cuvette will be transmitted at the value Vt1, therefore
In cuvette B the time of the photons’ motion (in the same ray) is determined from the following balance:
Thus, we have the time t2 of motion of ray 1 in cuvette B:
Analogously, ray 2 in cuvette B is dragged by the cuvette in the direction of the Earth’s motion and transmitted back a little by the water stream:
The photon of ray 2 will catch up the end of cuvette B during the time t3, therefore
Photons of ray 2 will pass through cuvette A during the time:
Difference t in the times of motion of rays 1 and 2 in the cuvettes, taking into account the Earth’s motion, is equal to:
It is easy to see, that if V0, expression (3.12) turns into expression (2.6), as it must be. For the velocity V = 37104 m/s (determined through Doppler’s effect for relict radiation), for Fizeau’s experiment conditions, the calculations through (3.12) give the following result:
t3=3.6254910–16 sec (3.12*)
and it coincides with the results of Fizeau’s calculations through (2.6*) up till the sixth digit. These calculations are made with taking partial dragging of the photons by the moving water into consideration, but without taking the motion of the device itself into account (t1= 3.6254810–16 sec). Physically this result means that the Earth’s motion with tremendous velocity with respect to the light-carrying environment practically does not influence the results of Fizeau’s experiments (for example, if one changes the orientation of Fizeau’s device when trying the experiments), since the influence of the velocity V upon the photons’ motion in one cuvette is almost completely compensated by analogous influence in the other cuvette. As a result, only the influence of the moving water upon the interferential pattern is left.
The result obtained above gives us some reason to hope that partial dragging of the photons by moving transparent bodies is, however, available in the nature, and if the experiment is organized properly, it can be discovered experimentally. The modernized Michelson’s interferometer, in which the light ray (in case of direct motion from the dividing plate to the mirror) propagates through an optically dense substance, and comes back to the plate in the air, can serve as the first candidate for being such a device, Fig. 2.
Fig. 2. Modernized Michelson’s interferometer.
The radiation of the source S is diffracted by the plate P into two rays. Ray 1 in the direct direction passes through the rod L, is reflected from the mirrors M1 and M2 and comes back to the plate P in the air. Ray 2 passes the way to the mirrors M3 and M4 in the air, and then interferes with ray 1.
If such a device is turned at 180o, the conditions for the ray passing in perpendicular direction will not change, however, now the Earth’s motion will not promote the propagation of the photons in the rod, but will prevent. Thus, there must appear the asymmetry in the degree of the moving rod’s action upon the photons’ motion with respect to the ether, and it should be manifested in the change of the interferential pattern. The scheme of this experiment was already raised earlier by the author and D. Samoilov , and, probably, by other authors, but the turn to quantitative estimations did not come. The necessary estimative calculations can be made according to the methods given above.
a) When the device is oriented in the direction of the Earth’s motion, the photons are partially dragged by the rod L, therefore, the time of their motion towards the mirrors M1, M2 decreases (in comparison with the motion time in the immovable rod), but also the time of the photons’ returning to the plate P decreases, due to the plate’s meeting motion.
b) When the device is turned at 180о, the motion of the rod L prevents the photons’ motion.
(1) Let the interferometer arm with the rod made of an optical material be oriented in the direction of the Earth’s motion, whose velocity with respect to the ether is equal to V, Fig. 3, a). In the optically transparent rod with length L and the refraction quotient n, the photon moves with the velocity С1.
where, as before,
During the time t1, the photon will catch up the escaping end of the rod, which will be transmitted at the value Vt1 during this time. Therefore:
(2) The photon will go backwards in the air (we will neglect the difference between L and the distance from the plate P to the mirror) with the velocity С2=С (ballistic hypothesis is not carried out).
(3) After turning the rod at 180о, the rod’s motion with respect to the ether will prevent the photons from motion:
(4) The photon moves backwards in the air with the velocity С4=С, therefore:
The difference in the motion times is equal to:
It is not difficult to see, that if n1, we have 0, therefore, t0, and also if is not equal to zero, but V 0, we have t0 again.
The maximal velocity, which we can expect, is the velocity of the Earth’s motion with respect to the relict radiation in the direction of the Lion constellation, V = 37104 m/s. Nowadays the real refraction quotient can be equal to n=1.9 (modern glasses for spectacles), or n=2.2 (fianite), or even more, n=3.0 [5, 6]. For the mentioned conditions, if n=1.9 as a really available material, for some values of L, expression (4.12) gives the result, see Table 1:
Table 1. The calculated values of the difference t between the times of passing the arm of the modernized Michelson’s interferometer by the photons.
L t C t C t /
m 10–18 s Е %
1 9.04 27.1 0.54
2 18.08 54.3 1.09
5 45.22 135.6 2.71
10 90.42 271.3 5.43
20 180.85 542.5 10.85
40 361.70 1085.1 21.70
50 452.12 1356.4 27.13
100 904.24 2712.7 54.25
(n=1.9, =5000 Е)
The last column represents the ratio of the difference in the ways of the photons to the ray’s wavelength, assumed for the definiteness that =5000 Е. As seen from the table, beginning with L=40 m, the modernized interferometer will promote the stripe shift at 1085 angstroms, which will be equal to 21.7% of the stripe width. In case of higher values of the refraction quotient, the shift will be still larger. It means that the presence of the light-carrying environment, if it exists, can be discovered certainly enough. If one uses a material with the refraction quotient n=3, the stripe shift will increase, in comparison with that given in the table, approximately at 20%. It is noticeable that the results of the experiment should not depend on the presence of Fitzgerald–Lorentz’s shortening, since the device is turned not at 90о, but at 180о.
One should give the modernized interferometer the possibility of rotation at three coordinate axes, better in telescopic equipment. The largest change of the interferential pattern must be observed, when the device is rotated in the plane passing through the axis “Earth – Lion constellation”. When it is rotated in the plane perpendicular to the mentioned axis, the interferential pattern must change little.
In reality, it is problematic to provide L=100 m. If one supposes that it will be technically possible to provide the length of an optically dense and transparent body (a rod) approximately up to 2-3 meters, and by means of mirrors system make the ray pass through the rods at least 10-15 times, then finally one can obtain L=20-45 m. In accordance with the calculations table, it means that the expected stripe shift can be up to 25%. Certainly, similar experiments require experimentalists’ high qualification, and quite serious financing, but in case of luck, the success would be mire than simply serious.
On the other hand, it is affirmed in the literature, that the shift of interferential stripes can be registered with the exactness of about 0.2 per cent . If it is so, then even for L=10 (which is quite real), where effect is expected at the level of 5 per cent, the fact of motion with respect to the light-carrying environment can be certainly registered. Moreover, there exists information, that the Earth’s absolute motion was fixed through the shift of interferential stripes in Miller’s experiments at the level of 8%, and also in the experiments with electromagnetic signals in the coaxial cable .
Fig. 4. Scheme of the interferometer with optically dense rods in both arms of the device.
The sensitivity of the proposed interferometer, Fig. 2, can be doubled, if in the arm of mirrors M3-M6 one also locates an optically dense body in such a way as it is shown in Fig. 4. In accordance with (4.12), the time of the photons’ motion in this arm for the mentioned orientation is larger than after turning the device at 180o, since now the photons begin their motion from the mirror M3 in the air, and come back through an optically dense body. Therefore, the effect, influencing the shift of the interferential stripes in different arms of the device, must be summed up. Such a scheme not only increases the device’s sensitivity, but also equalizes the interfering rays in their intensiveness. Obviously, in reality, instead of one rod, in the device’s arm one should understand their series, moreover, in two layers.
Note that the proposed interferometer can be complicated, if instead of solid rods one uses pipes with a liquid moving with the velocity U. In this case, formula (4.12) will acquire the following form:
In conditions of Fizeau’s experiments, the velocity of water motion is approximately equal to 10 m/s. If in the arm of the mirrors M1–M2 one makes up two rows of pipes with water (each of which is 2 m long, 10 pipes in each row), totally we will obtain L=40 m. Formula (4.13) for these conditions gives the result 2.3210–16 sec. The effect will be almost doubled, due to the photons’ motion in the arms of mirrors M3–M6. Therefore, in accordance with Table 1, the stripe shift is expected at the level of 25%, which is quite essential.
It is not difficult to make sure that the usage of a moving liquid with the mentioned velocity influences the results of the experiment not strongly, i.e. without essential harm for sensitivity, instead of solid rods, one can also use a liquid immovable with respect to the device. Usage of a liquid (especially with a large refraction quotient) will in reality make the experiment significantly cheaper, and its trying will become accessible for a laboratory having a medium level of technical equipment.
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3. Landsberg G.S. Optics. – M.: Nauka, 1976. – 928 p.
5. Shelikh A.I, Gurin V.N., Nikanorov S.P. Refraction Quotient of Aluminum Boron-Carbide Al3C2B48 // Letters in JTP, 2008, Vol. 34, Issue 13. – P. 21–24.
6. Zaimidoroga O.A., Samoilov V.N., Protsenko I.E. Problem of Obtaining High Refraction Quotient and Optical Properties of Heterogeneous Environments // Physics of Elementary Particles and Atomic Nucleus. – 2002, V. 33, Issue 1. – P. 101–157.
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