This paper presents Chapter IX (section 4) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.
The paragraphs of original material are accompanied by brief comments in color, based on the present understanding. Feedback on these comments is appreciated.
The heading below links to the original materials.
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Theory of the Atom
We return now to further experimental knowledge of quanta. The mysterious quantity h crops up inside the atom as well as outside it. Let us take the simplest of all atoms, namely, the hydrogen atom. This consists of a proton and an electron, that is to say a unit charge of positive electricity and a unit charge of negative electricity. The proton carries nearly all the mass of the atom and remains rock-like at the centre, whilst the nimble electron moves round in a circular or elliptic orbit under the inverse square-law of attraction between them. The system is thus very like a sun and a planet. But whereas in the solar system the planet’s orbit may be of any size and any eccentricity, the electron’s orbit is restricted to a definite series of sizes and shapes. There is nothing in the classical theory of electromagnetism to impose such a restriction; but the restriction exists, and the law imposing it has been discovered. It arises because the atom is arranging to make something in its interior equal to h. The intermediate orbits are excluded because they would involve fractions of h, and h cannot be divided.
The significance of the mysterious quantity ‘h’ (Planck’s constant) is that it is energy per cycle at the center of the atom. Here the frequency is near infinite, and the energy per cycle is the lowest. Actually, ‘h’ is the limiting value as frequency goes to infinity.
An atom is a whirlpool of field-substance, much like a galaxy. The rotating field-substance is increasing in substantiality as it approaches the center. At the center it condenses into a nucleus. The nucleus anchors the atom.
The rotating field-substance within the atom is diffused at the periphery but it increases in frequency and quantization as it approaches the center. Increasingly discrete field-particles appear closer to the nucleus. In case of the simplest hydrogen atom, the whirlpool-like field-substance is identified as an “electron”, and the condensed nucleus at the center is identified as a “proton”. The field-substance and field-particles have charge instead of mass. The property of mass belongs to the whole atom.
This field-substance has many quantization levels. Each quantization level has a unique energy per cycle. It acquires the lowest value ‘h’ at the center. The value ‘h’ appears to be constant and indivisible only because it is a limiting value for infinite frequency.
But there is one relaxation. When wave-energy is sent out from or taken into the atom, the amount and period must correspond exactly to h. But as regards its internal arrangements the atom has no objection to 2h, 3h, 4h, etc.; it only insists that fractions shall be excluded. That is why there are many alternative orbits for the electron corresponding to different integral multipliers of h. We call these multipliers quantum numbers, and speak of 1 -quantum orbits, 2-quantum orbits, etc. I will not enter here into the exact definition of what it is that has to be an exact multiple of h; but it is something which, viewed in the four-dimensional world, is at once seen to be action though this may not be so apparent when we view it in the ordinary way in three-dimensional sections. Also several features of the atom are regulated independently by this rule, and accordingly there are several quantum numbers—one for each feature; but to avoid technical complication I shall refer only to the quantum numbers belonging to one leading feature.
Within an atom the highest quantization level exist at the center where the frequency is the highest and energy per cycle is the lowest. As one moves towards the periphery of the atom, the quantization decreases and the energy per cycle increases.
At lower quantization levels, the space and time units are larger because of lesser substantiality. The energy per cycle at these levels is identified as the wave-energy sent from or taken into the atom. The values of energy per cycle appear to be unique and as strict multiples of ‘h’.
Bohr’s atom seems to identify different quantum-orbits filled with electrons. Instead there seems to be different quantization levels manifested as unique field-particles for that level. These field-particles are not completely discrete.
According to this picture of the atom, which is due to Niels Bohr, the only possible change of state is the transfer of an electron from one quantum orbit to another. Such a jump must occur whenever light is absorbed or emitted. Suppose then that an electron which has been travelling in one of the higher orbits jumps down into an orbit of less energy. The atom will then have a certain amount of surplus energy that must be got rid of. The lump of energy is fixed, and it remains to settle the period of vibration that it shall have when it changes into aether-waves. It seems incredible that the atom should get hold of the aether and shake it in any other period than one of those in which it is itself vibrating. Yet it is the experimental fact that, when the atom by radiating sets the aether in vibration, the periods of its electronic circulation are ignored and the period of the aether-waves is settled not by any picturable mechanism but by the seemingly artificial h-rule. It would seem that the atom carelessly throws overboard a lump of energy which, as it glides into the aether, moulds itself into a quantum of action by taking on the period required to make the product of energy and period equal to h. If this unmechanical process of emission seems contrary to our preconceptions, the exactly converse process of absorption is even more so. Here the atom has to look out for a lump of energy of the exact amount required to raise an electron to the higher orbit. It can only extract such a lump from aether-waves of particular period—not a period which has resonance with the structure of the atom, but the period which makes the energy into an exact quantum.
There are no electrons jumping from one quantum orbit to another. Instead there are field-particles being added or subtracted at different quantization levels due to interactions. Each field-particle constitutes a cycle, which is absorbed or emitted as light.
There is no aether. There is only field-substance quantized as field-particle, and which may de-quantize back to field-substance (light).
As the adjustment between the energy of the orbit jump and the period of the light carrying away that energy so as to give the constant quantity h is perhaps the most striking evidence of the dominance of the quantum, it will be worthwhile to explain how the energy of an orbit jump in an atom can be measured. It is possible to impart to a single electron a known amount of energy by making it travel along an electric field with a measured drop of potential. If this projectile hits an atom it may cause one of the electrons circulating in the atom to jump to an upper orbit, but, of course, only if its energy is sufficient to supply that required for the jump; if the electron has too little energy it can do nothing and must pass on with its energy intact. Let us fire a stream of electrons all endowed with the same known energy into the midst of a group of atoms. If the energy is below that corresponding to an orbit jump, the stream will pass through without interference other than ordinary scattering. Now gradually increase the energy of the electrons; quite suddenly we find that the electrons are leaving a great deal of their energy behind. That means that the critical energy has been reached and orbit jumps are being excited. Thus we have a means of measuring the critical energy which is just that of the jump—the difference of energy of the two states of the atom. This method of measurement has the advantage that it does not involve any knowledge of the constant h, so that there is no fear of a vicious circle when we use the measured energies to test the h rule.* Incidentally this experiment provides another argument against the collection-box theory. Small contributions of energy are not thankfully received, and electrons which offer anything less than the full contribution for a jump are not allowed to make any payment at all.
* Since the h rule is now well established the energies of different states of the atoms are usually calculated by its aid; to use these to test the rule would be a vicious circle.
There are no electrons in the atom jumping orbits. There are only the field-particles condensing and de-condensing at certain energies of quantization levels.
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