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Chapter VIII: Gravitational Ionization

Most of the observable universe consists of plasma, or partially ionized gas. The processes of ionization and their sources of energy are regarded as one of the important open questions in astrophysics. According to Newton’s theory, the gravitational force between a proton and an electron is weaker than the electromagnetic force between them by a factor of about . For this reason, the influence of gravitation on the atomic scale, specifically its ability to ionize an atom, is assumed to be non-existent. Furthermore, according to Newtonian dynamics, the gravitational acceleration of a particle is independent of its mass, a belief that led to Einstein’s principle of equivalence. Consequently, under Newton’s theory of gravitation and general relativity, free falling protons, electrons and neutrons are expected to accelerate at the exact same rate. Therefore, the ionization of atoms is extremely unlikely to be caused by the gravitational force.1 Rather, current theories attribute ionization to either a thermal process or to strong electromagnetic fields.

However, massive ionization by the gravitational force alone is predicted and explained by the UG theory, even at distances of , where the exponent . According to equation 2-1-2, at distances of , the UG gravitational force between a superheavy particle of mass and a nucleon of mass is greater than the equivalent Newtonian force by an order of , and is thus capable of exceeding the electromagnetic force between an electron and a proton, given a sufficiently large SHP mass. 23 In addition, the acceleration of a proton by a superheavy particle of mass from a distance is expected to vary from the acceleration of an electron from the same distance.

Consider the simpler case of a hydrogen atom encircling the center of a star or galaxy dominated by a single SHP type of mass M surrounded by ordinary matter. To simplify the analysis, the velocity of the atom relative to the superheavy particle is assumed to be non-relativistic. The energy of the atom is thus given by

Equation 8-1

where the atom is assumed to rotate in a circular orbit of radius around a group of SHPs of particle mass concentrated in a small sphere of a radius that is negligible relative to . The sphere of superheavy particles is assumed to be surrounded by a spherically symmetric distribution of ordinary matter of mass . The electron-proton bonding energy of a free atom must be negative, where at the ground state of the hydrogen atom, .4 Note that only the terms and in equation 8-1 are non-linear functions of the proton and electron masses, and are therefore the only terms capable of generating a differential force that can separate the electron from the proton to ionize the atom.

The orbiting atom gravitates toward the potential energy minima generated by its interaction with the galactic superheavy particles and ordinary matter. The magnitudes and locations of the zonal oscillation maxima and minima of both the proton and the electron due to the dominant SHPs of mass can be derived via equations 2-1-1 and 2-1-42 respectively. Since the proton and the electron are independent particles of vastly different masses, their interactions with the superheavy particles generate distinct sets of potential energy minima. As the zonal oscillation range of the SHP-proton pair is proportional to , and the zonal oscillation range of the SHP-electron pair is proportional to , the radius of the proton’s zonal oscillation range is about 1,836 times greater than that of the electron.

The characteristics of the interaction between the atom and the central superheavy particles can be viewed at three different distance ranges. At distances , the UG potential energy of the proton and the electron approach their Newtonian form, and the differential gravitational force (as well as the total gravitational force) applied on the proton and the electron is negligible relative to the electromagnetic force between them. Therefore, the hydrogen atom remains intact.

At distances , the UG force applied on the electron is still Newtonian, and therefore negligible. However, the protons (as well as neutrons) are within their zonal oscillation range with the SHPs and are attracted toward their nearest minimum .5 Consequently, free protons, atoms, molecules and ions are drawn toward the nearest minimum. As the UG force applied on the electron at this range of distances is negligible, the electron will remain bonded to the proton by the electromagnetic force.

Note that since , the potential energy of the proton is given by , and the minima occur where . At these minima the potential energy is approximately , which is equal to Newton’s gravitational potential energy. Consequently, the atoms will assume circular Newtonian orbits. However, in contrast to Newton’s theory, only a discreet (or quantized) set of orbits at close proximity to the minima are allowed.

At distances , the electrons, as well as the protons and neutrons, are situated within their SHP zonal oscillation range. As the electron mass is about 1,836 times lighter than the mass of the protons (or neutrons), all protons, atoms, ions and molecules are attracted toward the nearest minimum of the proton’s set of minima . As long as the differential UG force between the hydrogen’s proton and electron is smaller than the electromagnetic force which bonds them, the atom is likely to remain intact, and the electron is forced to follow the heavier proton and to gravitate toward the potential energy minima of the proton. The locations of these minima can be derived using equation 2-1-42. For the case where and , the energy minima of the proton and the electron occur at

Equation 8-2a

where and , or. Thus,

Equation 8-2b


where minima occur at any integer , and where of equation 8-2b fulfills and . Similarly, the electrons are drawn by the UG force toward their own minima at approximately

Equation 8-2c

where and , or, or

Equation 8-2d


where minima occur at any integer .

Since , there are proton potential energy minima at distances greater than the first minimum of the SHP-electron UG interaction, and there are 1,836 proton potential energy minima between any two successive minimum contours of the electron.

According to equation 2-1-2, the UG force steering the electron toward its closest potential energy minimum is approximately times smaller than the force acting on the proton. Therefore, the atom settles in the immediate vicinity of the proton’s potential energy minimum, and in the case of a weak local UG gravitational influence, the electron is prevented from approaching its own potential energy minimum by the electromagnetic force that bonds it to the proton. Since there are approximately 1,836 proton potential energy minima between any two successive electron potential energy minima, most of the electrons that are bonded to orbiting hydrogen atoms demonstrate orbital radii that deviate significantly from the radii of their UG minima. It will be shown that at some of these minima, the overall stability of the proton-electron system may increase due to the ionization of the hydrogen atom, while the barrier threshold of the ionization is either too small or non-existent, and therefore cannot prevent massive ionization. An atom is likely to be ionized at a given location if its overall energy is higher than the total sum of the energies of the ion and its displaced electron, where the electron’s amount of displacement is larger than, but of the same order of magnitude as the Bohr radius. For massive ionization to occur, the following equation must hold true at the radius where ionization takes place:6

Equation 8-3

where is of the order of the radius of the hydrogen atom. Note that the loss of the electron has virtually no significant effect on the location of the ion (in this case, a proton), as . Also note that since , . Therefore, massive ionization will take place when

Equation 8-4

With of the order of the Bohr radius, the term is negligible relative to . Using the trigonometric equation

, , and results in massive ionization occurring when

Equation 8-5

As , massive ionization can happen only if . Therefore, massive ionization of hydrogen atoms at their ground state, where , can occur only when .

The gravitational ionization of other atoms or molecules can be treated similarly. Atomic ionization energy ranges between (for cesium) and (for helium). Therefore, massive atomic ionization at requires the total mass of the dominant SHP in the present scenario to be at least .7 Note that via equation 8-5, the removal of the last electron from the ground state of an atom with protons will require approximately .

The above discussion reveals two key concepts. First, a substantial portion of the massive amount of plasma detected in the universe may be produced via gravitational ionization. Second, the electrons freed by ionization settle into entirely different orbits than the orbits of ions or atoms.8 In the following chapter, this phenomenon will be shown to explain the generation of the magnetic fields created by planets, stars and galaxies, and may be instrumental in understanding the observed phenomena of jets and pulsars.

1 An exception to this statement is when extremely strong tidal forces exist. For sufficiently strong tidal forces to occur over distances of the order of the diameter of an atom, the gradients of Newton’s gravitational force must be enormous. Such gradients are theoretically possible within black holes. However, in order to experience such enormous gravitational tidal forces in the general relativity scenario, the atom must cross the black hole event horizon. In such a case, the ejected electrons must remain trapped within the black hole and cannot be detected by an outside observer, as even light cannot escape. Therefore, this process cannot produce any observable ionization.

2 This value was calculated using ,and.

3 Following the non-relativistic force equation 2-1-2, , the oscillation amplitude of the cosine term is negligible relative to the amplitude of the term . Therefore, at the maxima the UG force becomes larger than the Newtonian force by a factor of .

4 The ionization energies of the other energy states of the hydrogen atom, are roughly equal to , where is an integer greater than zero.

5 For simplicity, the small difference between the mass of the proton and the neutron can be neglected.

6 Note that due to a quantum tunneling effect, ionization may also occur when the overall energy is increased due to ionization. However, in such a case the ionization rate would be low, and massive ionization would not occur.

7 Lower values may be sufficient to ionize some large molecules, which may lower ionization energy.

8 Note that in the first order of approximation, where the masses of the protons and neutrons are assumed to be equal and the mass of the bonded electrons is assumed to be negligible relative to the mass of protons, all ions, atoms and molecules share the same orbits. For a sufficiently large , these orbits may split into a series of nearby sub-orbits. For example, different isotopes of the same atom may demonstrate slightly different radii of orbit, or the orbital radius of an ion of a given element may differ slightly from the orbital radius of an atom of the same element.

©2022 Gil Raviv

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