14. Relativity
In this section two derivations are done, one that yields length contraction and one that yields time dilation. Thus the theory has provided, without any ad hoc postulates (additional to those of classical electro-magnetism) all the experimentally established relativistic effects. Therefore since classical electromagnetism already predicts these results, there is no reason to introduce any additional theory, either a special theory of relativity or an aether theory with Lorentz transformations.
Notice that in Eq.(12-16) when the absolute velocities are equal the force is unchanged. However, if one uses qq= qE=0 in Eq.(12-8) the result is
(1)
where v is the absolute velocity of the source of the field and the charge (being the same). Longitudinally the force is dependent on the velocity. If there is a structure which depends on force to assign positions, then the positions must be changed to account for this change in force. That is the position of the charge elements in a structure at an absolute velocity must change so that the force is the same as it would be at rest. Since the force is only changed longitudinally and since the force decreases, the structure must contract in the direction of motion. We will find in Section 23 that atoms are electrostatically quadrupolar, thus, since the field falls off as 1/r4, the contraction1 is given by:
(2)
where x is the actual length in relation to the length x0 at rest.
Consider the effect on natural frequencies from the increase in mass. For such systems we have
(3)
where m is the vibrating mass and k is the restoring constant. The restoring constant is dependent on the force, but the charges are at near equal absolute velocities so the force is the same (after the contraction in the longitudinal case). However, the mass increases at high velocity (Eq.(13- 4)). By substituting this equation into Eq.(3) the frequency dependent on high velocity is found to be
(4)
The time2 being governed by this natural system is then altered such that
(5)
where t is the actual time in relation to the time t0 at rest3.
1. This length contraction in relation to relative velocity (as in special relativity) has not been experimentally verified. However, as this effect here is based on absolute velocity, there are relevant experiments which will be discussed in Section 22.
2. This compares with observations, some classic examples being Rossi and Hall5 using cosmic rays, Ayres et al6 using pions, and Bailey et al7 using muons. This also compares well with observations of Doppler shift which will be discussed in Section 21.
3. Eq.(2) and Eq.(5) are in place of the Lorentz transformations of special relativity to describe the same body of experimental evidence. There are fundamental differences in the concepts, however. Here length and time are not altered. They are completely independent of velocity. The changes described here are physical. The length of a physical body is decreased in relation to the absolute velocity of the body. The aging of a body is decreased in relation to the absolute velocity of the body. These properties have not been devised to specifically satisfy the Michelson-Morley experiment, but rather have been arrived at naturally from what is essentially classical electromagnetic theory.
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