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From THE EVOLUTION OF PHYSICS by Einstein and Infeld (Chapter III, Section “Ether and Motion”):
We are sitting in a closed room so isolated from the external world that no air can enter or escape. If we sit still and talk we are, from the physical point of view, creating sound waves, which spread from their resting source with the velocity of sound in air. If there were no air or other material medium between the mouth and the ear, we could not detect a sound. Experiment has shown that the velocity of sound in air is the same in all directions, if there is no wind and the air is at rest in the chosen c.s. [coordinate system.]
Let us now imagine that our room moves uniformly through space. A man outside sees, through the glass walls of the moving room (or train if you prefer), everything which is going on inside. From the measurements of the inside observer he can deduce the velocity of sound relative to his c.s. connected with his surroundings, relative to which the room moves. Here again is the old, much discussed, problem of determining the velocity in one c.s. if it is already known in another.
The observer in the room claims: the velocity of sound is, for me, the same in all directions.
The outside observer claims : the velocity of sound, spreading in the moving room and determined in my c.s., is not the same in all directions. It is greater than the standard velocity of sound in the direction of the motion of the room and smaller in the opposite direction… In the case of the sound wave in the room moving uniformly, relative to the outside observer, the following intermediate steps are very essential for our conclusion:
The moving room carries the air in which the sound wave is propagated.
The velocities observed in two c.s. moving uniformly, relative to each other, are connected by the classical transformation.
The corresponding problem for light must be formulated a little differently. The observers in the room are no longer talking, but are sending light signals, or light waves in every direction. Let us further assume that the sources emitting the light signals are permanently resting in the room. The light waves move through the ether just as the sound waves moved through the air.
Is the ether carried with the room as the air was? Since we have no mechanical picture of the ether, it is extremely difficult to answer this question. If the room is closed, the air inside is forced to move with it. There is obviously no sense in thinking of ether in this way, since all matter is immersed in it and it penetrates everywhere. No doors are closed to ether… There is not the slightest doubt as to the clarity of this verdict, although it is obtained through rather indirect experiments in view of the great technical difficulties caused by the enormous value of the velocity of light. The velocity of light is always the same in all c.s. independent of whether or not the emitting source moves, or how it moves.
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In case of sound, the vibration of the object creates displacement in the medium that is at the same macro level.
In case of light, the “vibration” is occurring at a subatomic level, and so is the “displacement” of the “medium”. It is a whole different level.
Motion at macro level may be compared to another motion at macro level in a meaningful way. Similarly, motion at subatomic level may be compared to another motion at subatomic level in a meaningful way. But we lose the relative significance when we try to compare motion at macro level to the motion at subatomic level. This is a problem of scales.
We may be able to express this problem better in terms of disturbance levels. The macro level may be approximated as DL100, where the frequency of electromagnetic disturbance is so high, and variations so rapid, that it looks “solid”. The subatomic level may be approximated as DL50 where the frequency of the electromagnetic disturbance is less “dense” by a factor of 250. The motion of a wavelength at one level shall appear to be shrunk by a factor of 250 at another level. This comparison is hardly significant to the senses.
The factor of 250 is likely to be inaccurate being a rough estimation, but it provides an explanation in terms of the orders of magnitude involved. The motion of the source of light at DL100 will hardly contribute to the motion of light at DL50.
The speed of light shall appear to be constant in all coordinate systems from the perspective of DL100.
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Let’s imagine a drum inside another drum. They both are rotaing about the same axis. The outer drum is rotating at the speed of light of DL50. The inner drum is rotating at the ordinary speed of DL100. Let us also suppose that we are looking at a certain characteristic through a narrow slit.
If we are at the inner drum looking at that characteristic in the outer drum, our c.s.(coordinate system) shall be the inner drum, and we shall see that characteristic in the outer drum changing very rapidly.
But if we are at the outer drum looking at that characteristic in the inner drum, our c.s.shall be the outer drum, and we shall see that characteristic in the inner drum changing very slowly.
In fact, when the c.s. is at DL100, and the background is DL50, the background shall appear to be full of light rays bouncing around at incredible speeds, as is the case in our experience.
But if the c.s. is at DL50 and the background is at DL100, the background shall appear to be dark and solid with a feeling of being totally closed in.
Einstein considers all c.s. to be at DL100 only. From that c.s. the differences in the surrounding speed of light shall not be appreciable because of the order of magnitude involved, and the speed of light shall appear to be constant.
The limitation in Einstein’s Theory of Relativity is that Einstein does not consider the coordinate system at any level other than the material level of DL100.
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