7.2 Appropriate and non-appropriate reference frames
I shall say that an appropriate reference frame is the one in which the electron being studied keeps P and w constant. It is, therefore, the reference frame adapted for the mathematical analysis of the electromagnetic field of the electron because this field is the function of w and r. Particularly if the appropriate reference frame is inertial, the electromagnetic field of the electron will simply be the functions of these two variables (equations 6.5). In the rest of this article we will only study fields produced by electrons placed in an appropriate and inertial reference frame.
7.2.1. The observer placed in a non-appropriate reference frame
The x and b fields —when observed through a non-appropriate reference frame— manifest an effect that is linked to a phenomenon described by Linard (1898) and Wiechert (1900) for the potentials of Maxwell’s theory. This phenomenon should be carefully analyzed because x and b are functions of two variables (j and w ). Both contributions are interesting but the one that owed w acquires epistemological importance because it generates fateful consequences for the classic physics [42]. The non-consideration of this portion evidenced the foundations upon which Einstein’s relativity theory was established.In the first place let us see how j is transformed. With the considerations made in item 6.4, expressed by equation 6.11, we can admit that when r is an invariant, h (and consequently j ) is transformed according to:
h = rc h' = rc' ,
in which c' = c + v, when v is the speed of the e.m.i. emitter electron and observed from the non-appropriate reference frame.Now let us see how w is transformed. Then, let us consider an observer placed in a Q point of an inertial reference frame and an electron placed in a P point and moving in relationship to this inertial system with a constant speed v. So I will say that the v unitary vector appears for the observer in Q as if it were another unitary vector, v’, which suffered an aberration preserving its unitary module. For the calculation of this aberration and observing the conventions adopted in figure 11 we should do the following:
| 1) to determine the P’ point admitting that the field spreads
in a radial way with a c speed when analyzed from the appropriate reference frame; 2) to join the points P, P’ and Q; 3) to trace a cone with the vertex in P and containing v in its surface, with the axis in the PQ direction; 4) to transfer the cone with v to P’; 5) to rotate the cone around P’ and according to a perpendicular axis to the plan of the figure (plane PP’Q) until the axis of the cone is located in the P’Q direction; 6) the unitary vector obtained by this rotation of v it is v’.
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As I observed in a previous article [40], the K scalar of hypothesis 1 (and, therefore, the absolute value of vector w ) seems to contain some secrets related to the inertial reference frame that only experimental physics can decipher. It would be extremely interesting to verify whether its absolute value, once defined, keeps or not an identical whatever reference inertial frame is considered. The K variability, as I believe, would be a strongly suggestive indication to corroborate Newton’s intuition in relationship to the existence of an absolute reference system. It can be expected, however, that K keeps constant for v < < c.
7.3. The (x, b) field of the electron in movement
When the transformations for h and v are known, we can despise the apostrophes and assume that the x and b fields are expressed by
x = -h
v |
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both in the appropriate reference system and in the non-appropriate reference system. It elapses then from 7.1. —regardless of the considered inertial frame of reference—the sumis a classic relativistic function of position:
