Kepler Quantization: The Inverse Analogy
Origin of Bohr Quantization
Bohr quantization is related to the process of creation of light. The description of creation of light according to human understanding involves a certain image of the relationship between light and matter, whereby the matter has a certain atomic structure, while the light’s structure is undecided. We will bring here this story, in a very short version, in order to make our argument more comprehensible. More to the point, we hope that it will become evident that the connection which we consider essential for the human knowledge is, indeed, that between light and matter.
The history of scientific relationship between matter and light really starts with Hertz. He succeeded in describing and realizing the action at distance in the form of electromagnetic signals, thus taking his place in history as the discoverer of electromagnetic action at distance. Hertz described it in the language of the Maxwell theory of electromagnetic fields. The Hertz dipole, as the material structure capable of creating and receiving electromagnetic fields is usually called, was the corner stone in all decisions upon the material structures connected with the creation of light, starting very early in the last century. What are these material structures?
First of all it was the electron. It was discovered by J. J. Thomson in 1897. Based on this discovery, and also on the fact that the matter seems to be in a natural electrically neutral state, i.e. it has no electric charge at a certain scale, while the electron is charged with negative electric charge, J. J. Thomson advanced the idea that, if the matter is formed of atoms, then these can be thought of as islands of negative charges in a confined continuum of positive charge. This is the so-called “plum pudding” model of the atom. This explanation of the structure of matter had, however, to be soon abandoned under the pressure of experimental facts which it couldn’t accommodate.
Towards the end of 19th century it became more and more obvious that the matter is unstable. Not from the known common viewpoint of Chemistry but, we might say, from the point of view of Alchemy: the elements themselves, therefore the atoms, are unstable, going over into other elements – the dream of alchemists! More to the point the heavy elements are decomposing in lighter elements, with emission of three kinds of radiation, called by Ernest Rutherford alpha, beta and gamma. The first two of these proved to be radiations of particles, inasmuch as they respond to electric and magnetic forces. The beta radiation was easily identified with the electrons of J. J. Thomson. The alpha radiation was electrically charged with positive charge, but was formed of particles much heavier than the electrons. These particles had the mass of a helium atom, the only difference being that they were electrically charged. The gamma radiation was electrically neutral and very penetrative within matter. Its nature couldn’t be decided quite so easily.
It was during such experimental studies, whose conclusions were drawn based upon the Thomson atomic model, when Rutherford and Geiger accidentally noticed that, if one interposes a mica platelet between the source of alpha radiation and the plate recording the particles, the recorded particle intensity is diminished. This means that not all of the alpha particles emitted by source succeeded passing through matter; some are stopped within matter. It has immediately been initiated a study for quantitative evaluation of this effect in different materials and, just for scientific completeness imposed by the mere professional ethics, Marsden was asked to experimentally certify the fact that there are not scattering events at different angles with respect to the direction between the source of radiation and the target. This would completely confirm the theory based on the Thomson model of atom. The surprise was overwhelming: the alpha particles were scattered in any direction, even backwards. Of course, the majority of them went forward, however not all of them!
From these experimental results Rutherford figured out that the image of “plum pudding” for the atom is not quite correct. Much more realistic is the idea of an atom mostly empty, with the positive charge concentrated in a nucleus and electrons at large distances from the nucleus. Now, because long time ago Charles Coulomb had already proved that the force between electric charges varies with the distance between charges exactly like the Newtonian gravitational force, i.e. it is inversely proportional with the square of that distance, it was then only natural to assume that the electrons move around positive nucleus just like the planets around Sun. Thus came out in the world the planetary or nuclear model of atom (Rutherford, 1914).
At this moment, the Theoretical Physics happily met the Astrophysics, a science in need of explanation of the process of producing light by the Sun and stars alike. The spectra of this light presented significant regularities, known as spectral series, with bright colored lines in definite positions in spectrum. The Experimental Physics had at its disposal means to associate spectra of this light with chemical elements abundantly existing on Earth, especially the hydrogen, which seemed to be dominant in the spectral of celestial bodies. Therefore it was only natural to allocate the creation of light to the hydrogen atom in different environments, existing with certainty in Sun and stars.
As long as the light was conceived as an electromagnetic radiation, the situation was pretty clear and easy to explain: the hydrogen atom as imagined by Rutherford can produce naturally electromagnetic radiation, because its electron has acceleration and therefore emits radiation as a dipole antenna. Indeed, a Rutherford atom can be assimilated to a plane harmonic oscillator, which then can be treated as a Hertz dipole. But then emission of radiation is continuous. This is the point where it was discovered that the Rutherford atom doesn’t work according to usual classical rules. Indeed, the emission of radiation means emission of energy, and this cannot take place but as long as energy exists. When it is exhausted, the emission ceases. It will be therefore natural that the atom as a structure vanishes through the continuous light emission, but there was no experimental fact to show that this is indeed the case in reality.
By comparing the regularities of the hydrogen spectrum with the mechanical possibilities of the classical planetary model, Niels Bohr found the answer in the energy of that model indeed: it works in such a way that only certain orbits of the electron around nucleus are possible, and these have fixed energy (Bohr, 1913). The light created by the atom corresponds to some instantaneous transitions of the electron between different orbits, and carries with it the difference of energy of the orbits between which the transition is made. In the construction of this image, Bohr used the idea, new in that epoch, that the light in such cases is not quite dense, and can be represented, according to Einstein, by an ideal gas of particles, each one of them carrying a quantum of energy: at the atomic level the light is emitted and absorbed as photon.
By this Bohr went actually back at the times when Newton explained how the planetary system works. In fact, both Newton and Bohr explained the very same structural model, but at different scales of contemplation of the Universe. The Newtonian equations of motion are indeed invariant to a scale transformation of space coordinates and time (Mariwalla, 1982). Newton’s idea was perfect, and so was Bohr’s. It’s just that at the atomic scale there should be a new explanation of the appearances. This explanation seems to imply that one electron, unlike a planet, can have many possible trajectories. In the case of a planet one cannot talk about many trajectories, it doesn’t make sense. We can obviously talk of many planets, each with its own trajectory, but this is an entirely different thing. Anyway, the conclusion was that the Rutherford atom is unstable only because we assume that it works classically, a fact at variance with reality. Although apparently dictated by the same type of forces, the Mechanics of Atom is different from Newtonian Mechanics; it is the future Quantum Mechanics developed by Heisenberg, Born, Jordan and Dirac a decade after Bohr.
In a Kepler model for the solar system a connection with light in the manner of Bohr is unconceivable: one cannot imagine a planet jumping from an orbit to another with emission of light. For, the current scientific opinion is that light is electromagnetic by its nature and therefore it is intimately connected with the dynamics of electric charges. Therefore the Bohr’s rules may have nothing in common with the solar system. But the new wave of “macroquantization” shows exactly what we should follow in a quantization process, and this is the most important message it carries. We daresay that it may tell us to change our mind about how the light is really created.
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