Chapter 4. Bound Electrons and Positrons in the Vacuum Space

4.1 Creation and annihilation of e^–e⁺ pairs

The positron was discovered in 1932 by Carl David Anderson (born 1905), who observed the track of this particle in the cloud chamber. From the deflection of the particle in electric and magnetic fields, Anderson determined the positive charge $+e$ of the positron, as equal and opposite to the $-e$ charge of the electron, and the mass $m_e$ of the positron as identical with the mass $m_e$ of the electron.

Anderson also discovered that when a $\gamma$-photon of at least 1.02 MeV is absorbed in the vacuum, an electron and a positron may appear. He also observed reverse processes, occuring when an electron and a positron approach each other. Then it could happen that these particles disappear, and, simultaneously, two $\gamma$-photons of combined energy 1.02 MeV are emitted.

Anderson's discovery was in agreement with some theoretical predictions made by P.A.M. Dirac (1902-1984) in 1928. Dirac developed a quantum theory of the electron, which tried to unify the quantum approach with relativity. He assumed that there is an 'electron sea' with quantized negative energy levels filled with electrons. Electrons on neqative energy levels are not detectable. The highest negative energy level is 511 keV below the zero energy of an electron, at which the electron becomes observable. Here 511 keV is the energy equivalent of the mass $m_e$ of the electron, $m_e c^2 = 511 \ \mathrm{keV}$. For consistency, Dirac had to assume, that negative energy levels, which are not occupied by electrons, or "holes" in the electron sea, should appear and behave as particles having the mass of the electron and a positive charge, equal and opposite to the charge of the electron. An electron which falls into such a hole, or "recombines" with it, becomes undetectable, as are the electrons of the "electron sea".

Dirac's 'hole' could be considered as a prediction of the positron. The appearance of the electron and positron in Anderson's experiment with the absorption of 1.02 MeV could be interpreted as the pulling of an electron out from the highest negative energy level in the 'electron sea'; 511 keV are then needed to "produce" the mass of the electron, and 511 keV for the mass of the appearing hole. Therefore, Anderson's discovery was initially considered as having been predicted by Dirac, thus proving the theory. However, Dirac's theory did not fit the developing theories and was abandoned in particle physics. It inspired, though, the electron-hole generation and recombination interpretations in solid state physics.

The appearance and disappearance of electrons and positrons with the absorption and emission of 1.02 MeV of $\gamma$-ray energy is considered as the "creation" and "annihilation" of the two particles. However, it is well known that 511 keV is far from sufficient to really create an electron or a positron. Such creation, as well as "annihilation", i.e., turning into nothing, or the destruction of a single electron or of a positron, was never observed. A more appropriate name for these processes is just the "appearance" and "disappearance" of the two particles, and, in reverse order, of the $\gamma$-photons.

4.2 The indestructibility of electron and positron masses

In high energy physics acceleration and collision experiments electrons and positrons are subject to gains and losses of many GeV energies. However, not once has the creation or destruction of a single electron or positron been observed. Therefore, we do not even have an idea if the real creation or real destruction of an electron or of a positron is at all possible.

The appearance and disappearance of electrons and positrons always occurs in pairs. This suggests, that each of these particles does exist before the alleged creation and after the alleged annihilation, but in a bound, therefore indetectible form.

Let us reach for a helpful analogy. When sodium ions $(\mathrm{Na^+})$ and chlorine ions $(\mathrm{Cl^-})$ meet to form $\mathrm{NaCl}$ molecules, or the rocksalt $(\mathrm{NaCl})$ crystal, the $+e$ and $-e$ charges of the ions disappear. However, we do not consider the charges to have been destroyed or annihilated. We know that they exist in the molecule or in the crystal, in spite of the fact that they cannot be detected. We also know, that the charges are undetectable because they are bound to each other. And, when the molecules dissociate, the charges reappear, intact. It is also our firm knowledge that the energy needed for the molecule to dissociate into the two free ions, which is the energy needed for the $+e$ and $-e$ charges to appear, is much smaller than their "creation" energy, and smaller than even the ionization energy of the $\mathrm{Na}$ and $\mathrm{Cl}$ atoms.

When an electron and a positron meet and form an electron-positron pair, or a positronium quasi-atom (in which the electron orbits around the positron), the $-e$ and $+e$ charges of the two particles disappear. Just as in the case of the formation of the $\mathrm{NaCl}$ molecule, we know that the charges were not destroyed or annihilated, that they are undetectable because they are bound to each other, and that when the pair or the positronium dissociates, the charges appear intact.

When the pair or the positronium does not dissociate but 'annihilates' into the vacuum space, their masses disappear, too. The disappearance of the masses should therefore be interpreted as analogous to the disappearance of the charges: not as their destruction, but due to their binding to other bound electrons and positrons in the vacuum space. The masses of the electron and the positron are not detectable as long us they are bound, because it is impossible to move them individually, neither by gravitational nor by inertial means. When an amount of energy is supplied to the two particles, equal to their binding energy with the other particles in the vacuum space, they may free themselves out of bonds. Then they appear intact with their masses and charges, able to respond individually to electrical, magnetic and gravitational forces. They appear, i.e., they become detectable because of this ability to respond.

4.3 Charge and mass conservation laws

We interpreted the disappearance of masses in a way similar to the commonly accepted interpretation of the disappearance of electrical charges, i.e., as due to their binding. This similarity in handling rehabilitates the mass-conservation law, raising it to the same level, at which the charge-conservation law stands now.

The law that electric charges cannot be created or destroyed was introduced in the middle of the XVII century without any elaborate argumentation. It was not challenged, and stands firm in modern science. Relativity, which reduced the mass-conservation law to a second-rate status, has raised charge conservation to become an absolute law.

Unlike the "poor childhood" of the charge conservation law, the law that masses cannot be created or destroyed was subject to elaborate investigations by the most prominent physicists and chemists, and was a most important pillar of science until 1905. It was then challenged by A. Einstein with the introduction of the formula for the 'equivalence' of mass and energy. As we saw, this formula leads to the wrong conclusion that 511 keV is the creation energy of an electron. With our conclusion that $m_e c^2 = 511 \ \mathrm{keV}$ is the binding energy of the electron to the bound positrons and electrons existing in the vacuum space, the mass-conservation law is restored to its full glory, while the Einstein mass-energy relation remains perfectly valid.

4.4 Efficiency of e^–e⁺ pair production

The efficiency of the electron-positron, or $e^-e^+$ pair production processes is largely enhanced in the presence of heavy nuclei, the more so the larger their masses. In the theory of the Compton scattering, such an enhancement is explained as the "pinning down" of the free electrons in the vicinity of the heavy nuclei. This prevents the runaway of the target electrons from the $\gamma$-photons. A similar explanation should also be given for the enhancement of the $e^-e^+$ pair creation. This means that the heavy nucleus pins down the surrounding $e^-e^+$ pairs, preventing them from evading the $\gamma$-photons. The photons can therefore be absorbed as entities (all or nothing) and the probability of their splitting into ineffective smaller quanta is reduced.

The increase in efficiency of the $e^-e^+$ pair-production in the presence of heavy nuclei provides an additional evidence for the existence of electrons and positrons hidden in the vacuum space. It is obvious that the nuclei do not pin down the vacuum. Hence, for the efficiency enhancement to occur, the $e^-e^+$ pairs must exist in the vacuum before their alleged creation, else there would not be a thing to pin down.

An additional experimental fact of importance is that the $e^-e^+$ pair production processes occur everywhere in any spot of space, and that the efficiency of the processes corresponds to the density of the $\gamma$-ray photon flux. Therefore, we should conclude that there is a high density of bound electrons and positrons everywhere in the vacuum space.

4.5 The freeing and entrapment of e^–e⁺ pairs

We have shown that the terms "creation" and "annihilation" of electron-positron pairs are wrong and misleading, because these particles cannot be created or destroyed even by energies exceeding the 1.02 MeV many thousands of times. We replaced these terms by "appearance" and "disappearance", which label the experimental observation without suggesting the physical process behind it. We may now name these processes as the freeing of the $e^-e^+$ pairs from their bonds with other $e^-e^+$ pairs existing in the space, and as the reverse entrapment into these bonds. We conclude that

electrons and positrons exist in the vacuum space in a hidden or bound form, undetectable by usual means, but with all their faculties intact, and "ready to go".

Also,

the 1.02 MeV is the binding energy of the electron-positron pairs to one another in the vacuum space; submission of this energy to any spot in space allows an electron-positron pair to free itself out of the bonds; then the two particles appear as a free electron and positron.

Vice versa,

when a free electron and a free positron meet, slowly enough and closely enough, there is a high probability of their falling or entering into their bonds in the vacuum space, thus becoming undetectable; then their binding energy is released into the vacuum space in the form of $\gamma$-photons.

4.6 Bound e^–e⁺ pairs as radiation carriers

Our conclusion that there is a massive presence of bound electrons and positrons everywhere in the vacuum space suggests that these particles participate in the propagation of electromagnetic radiation. This suggestion is strongly supported by the correlation between the appearance of the particles and the disappearance of radiation energy in pair production processes, or in the reverse disappearance of the particle pairs and the appearance of radiation. Therefore, we should consider the possibility that these bound electrons and positrons, or rather the system formed by the bound electrons and positrons in the vacuum space is the carrier of electromagnetic radiation.

The fact, that the carrier of electromagnetic radiation must consist of electron-like particles should have been assumed when experiments showed that in definite particle-to-particle events this radiation knocks out electrons not only from solids, as in the photoeletric effect, but also from the outer and inner orbits of atoms (ionization by ultraviolet, X-ray and $\gamma$-ray radiation). Then in Compton scattering the photon-particle of the radiation transfers to the target electron not only amounts of energy in the range, equivalent to the electron mass, but also momentum, as only an electron-like particle could do. Therefore, during the time of the interaction between the photon and the free or target electron in all these experiments, the photon is an electron-like particle, thus, an electron or a positron.

4.7 The lattice system of bound e^–e⁺ pairs

The aggregate state of the system formed by the bound electrons and positrons in the vacuum space cannot be gas-like, because then it would not exhibit quantum effects. Quantum effects are exhibited by liquids, however the ordering of particles of the liquid has a short range. Hence, the free path of guest particles, which can move in channels between the particles of the liquid is short, as the channels are short. The system expected has to provide for the observed profound quantum effects in the carrier of electromagnetic radiation, and for the observed long free-paths of free electrons and other dense particles in the vacuum space. Therefore, we should assume that the system formed by the bound electrons and positrons in the vacuum space is a lattice, reminding the crystal lattices of solids.

We propose that the lattice, formed by the bound electrons and positrons in the vacuum space be named "the electron-positron lattice", or, for short. "the epola" (accent on the o, please). The notation "$e^-e^+$ lattice" will also be used.

The only structural characteristic of the epola which we have right now is the binding energy per particle of the lattice, which is 511 keV. To obtain other structural characteristics we will use the formulas of solid state physics, derived for a crystal lattice, which is the closest analog of the epola. We shall see that the lattice of the rocksalt $(\mathrm{NaCl})$ crystal is the most suitable analog.