9. Propagation of electromagnetic waves in the ether medium
A motion in the ether medium may occur as a travel of physical bodies in it and transfer (propagation) of energy. The transfer of disturbances (energy) occurs as electromagnetic oscillations (waves). Types of these oscillations have long been known. They are light, electromagnetic, X-ray etc. types of oscillations that have common electromagnetic nature. The basis for propagation of such oscillations is the ether medium. The wave velocity is equal to the light velocity Ñ.
An analysis of propagation of an electromagnetic wave front from a moving point source is rather interesting. Imagine the most common case when a source radiates a spherical wave. Let us consider that the space (ether) in which the wave is radiated is free from physical bodies (solid, gaseous, plasma etc.) and electromagnetic fields. In this case the space has isotropic properties. The wave amplitude at the front from the source will be the same in all directions and the wave front will be ball-shaped, F = 4p r2, where r – is the ball's radius. Consider that the source moves along the straight line. In this case, theoretically, three versions of the relation between the source movement velocity V and the light velocity C may appear.
1. The source velocity V is less than the light velocity C, V < C. In this case, the wave radiated at some initial moment and all the subsequent moments, forms a spherical front. This spherical front will propagate with the velocity C that is larger than V. The subsequent fronts arising at the points which the source passes through will lag behind the spherical front formed at the initial moment of radiation. Thus, the initial front of an electromagnetic wave from the source moving with the velocity that is less than the velocity of light will always be the spherical front from the initial moment of the source radiation. This can be easily demonstrated with the diagram in Fig. 21. We consider that at the moment to the source was at the point Î and the front of its wave occupied the Nfo position. The source moved to the point P over the distance PO with the velocity V < C for the time t1 and its front occupied the position Nfp. The front will travel LK = PO = V× t1 in the direction of the source movement. The front Nfo will travel the distance SK = Ñ× t1 and occupy the position Nfñ for the same time t1. Division of SK by PO yields SK/PO = C/V > 1. This means that the fronts arising from the source position that differs from the initial one, will always be within the front propagating from the point at which the source was at the initial moment.
Figure 21 allows one to note that the energy density Àf (a number of spherical fronts from various positions of the source per the length unit) in the direction of the source movement will be higher than in other directions. It is easy to show that the change in this energy will be proportional to
Àf = f[(p -a)C/(C-V)p + Ca/(C+V)p]2, (38)
where a is the angle between the direction of the source movement and direction in which the energy flow is assessed at the wave front.
2. Consider the type of the light wave front with the source moving with the velocity equal to the light velocity V = C. As the source moves it will create spherical fronts, Fig. 22. For instance, when it is at the point k it will produce the front Nfk. At the point n the front Nfn will be formed. In the movement direction the source travels with the velocity C. In the same direction (as in all others) the fronts Nfk and Nfn expand also with the velocity C. Thus, the source will always be at the wave front created by the front. The wave front created at all the preceding points of the source presence along the line of its propagation, will pass through the point S where the source is at the moment, Fig. 22. Since we consider that the radiating source moves infinitely long along the strait line, the wave front created infinitely long ago will also move through the point S. The crookedness of the spherical front with the indefinitely large radius of the sphere is equal to zero. Hence, the general front Nfc of the light or electromagnetic wave in the direction of the radiating source movement, with V = C, will be a plane perpendicular to the movement line and extensively propagating into infinity from the source.
This conclusion can suggest that this source should possess infinitely great energy, so that the area of its front will be infinitely large. This conclusion is corroborated when analysing the expression (38), since with V = C, the first item of this expression turns into infinity. But this conclusion will be invalid if the source does not move infinitely long.
Note that at point S, all the amplitudes of the whole set of fronts that, accordingly, had arisen at all points of time before the source reached point S, will be summed up.
3. Theoretically, one can imagine a source that will move faster than light, i.e. V > C. In this case the source will be at the top of the bodily cone that will form the wave front Nfc, Fig. 23. The front Nfc will be formed by the sequence of the spherical fronts of every preceding position of the source. For instance, the front Nfo is formed by the source at point O. During the same time t, the source will move from point O to point N and the spherical front Nfo of the wave will reach point K with the light velocity C.
Let us determine angle a between the front Nfñ and the symmetry axis of this front cone. Since the triangle formed by points NOK has a right angle, by the Pythagorean theorem, we can write down (NO)2 = (NK)2 + (KO)2. Angle a lying opposite the side KO will be equal
a = arccos(NK/NO) = . (39)
The distance NO will be travelled with the V velocity for the time t and the distance KO with the C velocity for the same time t. Accordingly, NO = Vt, KO = Ct. Putting these equalities in Eq. (39) we get
a = . (40)
The wave amplitude on the movement line at point N will be equal to the amplitude of the source. At other points, for instance at point K, it will be inversely proportional to the squared distance KO. Note that by formula (39) the greater is the velocity of the source in relation to the light velocity, the less is the angle a . The last-mentioned formula also corroborates the following feature of the wave front: if the source moves with the light velocity, V = C, then the front will be flat and extend at infinity.
On the whole, the possibility of some physical bodies to propagate faster than the light should be considered to be only a hypothetical one, since no movements exceeding the light velocity are known with assurance so far, at least when observing the processes of microinteractions.
Note that since the electromagnetic wave velocity in the free space is determined only by the characteristics of the ether medium, it is equal to the light velocity in spite of the velocity of the source movement.
Now it is necessary to consider the effects arising in the motion of the observer or device (receiver) that will move and register the waves (radiation) from the source. The velocity of the receiver movement is also restricted by the light velocity. Thus, the extreme mutual velocity (VSR) of the source (S) and receiver (R) approach may be thought of as being always less than the double light velocity, VSR < 2C.
Oscillation frequency in the source located in the free (from physical bodies and electromagnetic fields) space is determined by the oscillatory process in the source. If the source is immovable, the receivers located motionlessly at some distance and in any directions will register the same frequency of the electromagnetic waves as in the source. But if the source moves, then, according to the Doppler effect, immovable receivers located along the trajectory and in the moving direction will register the frequency increased over the wave frequency in the source. Immovable receivers located along the trajectory but in the direction opposite to the moving direction of the source, will register the decrease in the wave frequency proportional to the source movement velocity.
Such changes will be observed as the wave receiver (observer) moves relative to the immovable source. If the receiver moves in the source direction, then it will register an increased wave frequency over the frequency in the source. The receiver moving away from the source registers a decrease in the wave frequency proportional to the velocity of the source motion. The manifestation of the Doppler effect prevents distinguishing whether the receiver moves relative to the source or, vice versa, the source moves relative to the receiver.
The presence of the ether medium allows returning to the tenets stated by H. Lorentz. For instance, one may find an explanation why the mass of an accelerated particle (physical body) increases by the law :
where mo is the particle mass at rest, m is the particle mass in motion relative to the ether medium, V is the particle velocity, C is the light velocity.
This law shows that as the particle velocity approaches the light velocity, phenomena similar to those observed as the body velocity approaches the sound velocity in gases occur. But there is a fundamental difference between these phenomena. When a body moves in gas, the gas flows around it. As a body moves in the ether medium, as is shown by H. Fizeau's experiments and some other ones, the ether medium moves through the physical body. In this case the ether medium directly interacts with every elementary particle composing the physical body and possessing a mass - with electrons, protons, neutrons etc.
Formulas (38) and (41) show that the motion in relation to the ether medium is possible with any small difference between V and C, since in the case V = C the energy and mass of the particle will be infinitely great. The laws of conservation of mass and energy impose a ban on infinitely great masses of any bodies. Thus, physical bodies cannot move through the ether medium with the light velocity.
The last conclusion has an interesting consequence - photons, light quanta, that always propagate with the C velocity, cannot have a mass and therefore they are waves that disturb the ether medium and propagate in it. As is known, photons (quanta) have a large spectrum of different frequencies from a thermal range to X-rays. An infinite number of photons (quanta) of different frequency propagate in the ether in all directions and are received by devices as electromagnetic waves, light and X-radiation.
On the basis of the accepted concept, below is given an interpretation of the known experiment of H. Fizeau. To our mind, this experiment allowed determining an interaction of the ether medium with the substance on the Earth's surface.