Abstract
The electron on a trajectory around a nucleus radiates energy since it is accelerated and, following the classical theories of physics, should fall on the nucleus. But since it does not fall, it exists a cause, not taken into account by these theories, that prevents it from this fall. Indeed, in our precedent publications we showed that the fields and the particles are changes in a specific elastic medium called "ether". In particular, that a particle is a globule called “single-particle wave” that vibrates in the ether and is denoted . This that moves at the velocity V of the particle, contains all the parameters relative to it, and modulates the amplitude of the superposition of a wave called “phase-wave”, denoted , (and not ) of phase velocity V_p . In the present paper, one considers that the electron moves on a circle of circumference C, under the attraction of a nucleus. is then present simultaneously several times, e.g., N times, at each point of this circle, that is, in , which is influenced by these N superpositions, due to the fact that interferes with itself at each round. It appears then the two possible cases: the resonant and the nonresonant.In the resonant case, C contains an integer number of wave lengths of that therefore superposes itself at each round in a constructive addition, and creates a relatively large , i.e., of a relatively large energy. The electron that radiates then only a limited percentage of its large energy, does not fall on the nucleus.In the nonresonant case, C contains a non-integer number of , then superposes itself at each round in a destructive addition, and creates a much smaller , i.e., of much smaller energy. The electron that radiates then almost the same energy as in the resonant case, loses in fact a much larger percentage of its energy than in the resonant case, cannot remain in this state.
Highlights
The electron on a trajectory around a nucleus radiates energy since it is accelerated and, following the classical theories of physics, should fall on the nucleus
Contains an integer number of wave lengths of that superposes itself at each round in a constructive addition, and creates a relatively large, i.e., of a relatively large energy
Contient un nombre entier de longueurs d’onde de qui donc se superposent elles même à chaque tour en une addition constructive, et créent une relativement grande, i.e., de relativement grande énergie
Summary
This nonresonant case is the one where strictly 0 < < 1. In this case, the explicit expression for the term. It appears, for example, that for = 0.5, Eq (17) becomes (− ) = 0.5[1 − (−1) ] ,. Which is much smaller than (1 + ) as it appears in the case where = 0, i.e., in (15)
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