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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Photon as a classical wave packet from classically stabilized electron orbits

Jan Olof Jonson

Published Aug 26, 2007• 3 citations
Publisher

Abstract

The fact that an orbiting electron does not collapse into the nucleus of its parent atom has thus far been considered a major obstacle to a classical interpretation of the stable states of orbiting electrons. Quantum mechanics avoids the very problem by discussing the probability of finding it, a method that confessedly has been very fruitful in the exploring the behaviour of elementary particles. Nonetheless, why should necessarily those two approaches be regarded as each others' enemies? In this paper it is shown that the classical mechanistic approach is still capable of explaining the eternal, circular movement of an electron around a nucleus. It is possible if reformulating the laws of action involved, returning to the simple electrostatic model, based upon Coulomb's law (1785, 1771). Further, in this paper it is also discussed, how electromagnetic radiation due to the de-excitation of excited electrons, orbiting around a positive nucleus, can be explained classically, as a sudden peak in the otherwise zero electric field, due to the inwards spiralling movement connected to the de-excitation. The concept of a distinct particle, the 'photon' is thereby rejected.

DOI
10.1117/12.747574

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The fact that an orbiting electron does not collapse into the nucleus of its parent atom has thus far been considered a major obstacle to a classical interpretation of the stable states of orbiting electrons. Quantum mechanics avoids the very problem by discussing the probability of finding it, a method that confessedly has been very fruitful in the exploring the behaviour of elementary particles. Nonetheless, why should necessarily those two approaches be regarded as each others' enemies? In this paper it is shown that the classical mechanistic approach is still capable of explaining the eternal, circular movement of an electron around a nucleus. It is possible if reformulating the laws of action involved, returning to the simple electrostatic model, based upon Coulomb's law (1785, 1771). Further, in this paper it is also discussed, how electromagnetic radiation due to the de-excitation of excited electrons, orbiting around a positive nucleus, can be explained classically, as a sudden peak in the otherwise zero electric field, due to the inwards spiralling movement connected to the de-excitation. The concept of a distinct particle, the 'photon' is thereby rejected.
Classical mechanics, which gives a fairly accurate description of large systems (e.g., solar system) as also of mechanical systems in our every day life, however, breaks down when applied to small (microscopic) systems such as molecules, atoms and nuclei. For example, (1) classical mechanics cannot even explain why the atoms are stable at all. A classical atom with electrons moving in circular or elliptic orbits around the nucleus would continuously radiate energy in the form of electromagnetic radiation because an accelerated charge does radiate energy. As a result the radius of the orbit would become smaller and smaller, resulting in instability of the atom. On the other hand, the atoms are found to be remarkably stable in practice. (2) Another fact of observation that classical mechanics fails to explain is wave particle duality in radiation as well as in material particles. It is well known that light exhibits the phenomena of interference, diffraction and polarization which can be easily understood on the basis of wave aspect of radiation. But light also exhibits the phenomena of photo-electric effect, Compton effect and Raman effect which can only be understood in terms of corpuscular or quantum aspect of radiation. The dual behavior of light, or radiation cannot be consistently understood on the basis of classical concepts alone or explained away by saying that light behaves as wave or particle depending on the kind of experiment we do with it (complementarity). Moreover, a beam of material particles, like electrons and neutrons, demonstrates wave-like properties (e.g., diffraction). A brief outline of phenomena that require quantum mechanics for their understanding follows.
The results of Bohr model can be used to explain the motion of macroscopic objects or big objects (like orbiting planets and sun, falling stone etc.). These macroscopic objects have essentially a particle nature and Newtonian laws of motion can be applied on them. But it fails when applied to explain the motion of microscopic objects or small objects (like electrons, atoms, molecules etc.). This is because: According to Bohr model, an orbit is a well-defined path and this path can completely be defined only if both the position and velocity of the electron are known exactly at the same time. But this is not possible according to the Heisenberg’s uncertainty principle. Thus, Bohr model contradicts the Heisenberg’s uncertainty principle . According to Bohr model, an electron is regarded as a charged particle moving in well-defined circular orbits concentric about the nucleus. The wave character of the electron is not considered. Thus, Bohr model ignores the de-Broglie dual nature of matter .
The results of Bohr model can be used to explain the motion of macroscopic objects or big objects (like orbiting planets and sun, falling stone etc.). These macroscopic objects have essentially a particle nature and Newtonian laws of motion can be applied on them. But it fails when applied to explain the motion of microscopic objects or small objects (like electrons, atoms, molecules etc.). This is because: According to Bohr model, an orbit is a well-defined path and this path can completely be defined only if both the position and velocity of the electron are known exactly at the same time. But this is not possible according to the Heisenberg’s uncertainty principle. Thus, Bohr model contradicts the Heisenberg’s uncertainty principle . According to Bohr model, an electron is regarded as a charged particle moving in well-defined circular orbits concentric about the nucleus. The wave character of the electron is not considered. Thus, Bohr model ignores the de-Broglie dual nature of matter .
This paper re-examines the mechanism of electron motion inside atoms and the causes of photon radiation and photon absorption, abandoning the inherent cognition of fixed electron orbits and quantum transitions in traditional atomic physics. It clarifies that electrons have no physical fixed orbits; orbits are only imaginary concepts constructed for convenience of description, not objective physical realities. With mass, electrons possess inertia and kinetic energy. Under the three-force equilibrium of Coulomb force, electromagnetic force and inertial effect, electrons naturally move in elliptical trajectories rather than regular circles. When an electron moves along an elliptical trajectory, it naturally passes through low-energy regions near the atomic nucleus and high-energy regions far from the nucleus. This change in position arises entirely from its own inertia, involving only the conversion between kinetic energy and potential energy. The electron neither gains nor loses total energy, so it emits no photons and undergoes no energy-level change. An electron loses total energy when emitting a photon outward, and transitions smoothly and continuously to a lower overall motion range under mechanical equilibrium and inertia. Meanwhile, an electron can also absorb external photons and gain energy; its total energy increases, and it similarly expands smoothly to a higher motion range. Photon energy is indivisible and can only be emitted or absorbed as a complete unit. This is the fundamental reason why atoms show discrete emission and absorption spectra. Electron motion is entirely smooth and continuous; instantaneous quantum transitions assumed in traditional physics do not exist. Based on classical mechanics and energy conservation, this paper unifies the laws of macroscopic celestial bodies and microscopic particles, and reconstructs an atomic motion model closer to the essential nature of physics.
In 1897, Thomson demonstrated that cathode rays (observed to be emitted from the cathodes of vacuum tubes) were in fact charged particles which he called electrons. Thomson proposed that the atom consisted of a positively charged sphere in which were embedded negatively charged electrons. Rutherford subsequently found in 1911 that the electrons orbited at some distance from a central positively charged nucleus. Rutherford proposed that electrostatic attraction between the nucleus and the electron was balanced by the centrifugal force arising from the orbital motion. However, if this were the case, then the electrons (being accelerated inwards towards the center of rotation) would continuously radiate all their energy as electromagnetic waves and very quickly fall into the nucleus. In 1913, Bohr postulated two important additions to Rutherford’s theory of atomic structure: 1. Electrons can orbit the nucleus in what are called stationary states in which no emission of radiation occurs and in which the angular momentum L is constrained to have values: 2. Electrons can make transitions from one state to another accompanied by the emission or absorption of a single photon of energy E = hf thus leading to absorption and emission spectra.
All of the mathematical formulations of quantum mechanics describe the interaction between radiation and atoms, but we show here that only Einstein has been able to establish a solid logical connection with classical theory. His methods are used to interpret the other mathematical models by requiring that observables be described in a physically-defined coordinate system and that there be strict adherence to the conservation of momentum. The properties of momentum exchange are included in a quantum oscillator, or clock, by replacing the non-relativistic Hamiltonian model with a relativistically correct Lagrangian model. Equal contributions are assigned to photon, electron, and nucleus; and field boundaries are defined that coincide with the electron shells. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The Lagrangian model accounts for the 720 degree rotation of a wave function as an initial 360 degree electromagnetic wave cycle (photon absorption) followed by a second wave cycle (photon emission), yielding two wave cycles to correspond with one complete electron cycle. The abstract space of quantum mechanics is replaced by a real classical space.