Plasma and Universal Gravitation

Melvin A. Cook

Plasma and Universal Gravitation

G^½ is dimensionally charge/mass and is 2.58x10^-4 e.s.u. per gram. That it may actually be electrostatic charge per gram thus offers itself as an explanation of gravity. But this naive interpretation has been avoided because of the formidable problems incurred by the apparently complete nonpolarity of gravity and the absence of a satisfactory mechanism for the accumulation of the required amount of charge on one body, e.g., 1.54x10²⁴ e.s.u. for the earth and 5.16x10²⁹ e.s.u. for the sun. On the other hand there are several reasons to believe that gravity is actually of electrical and magnetic origin. Let us summarize several of these reasons:

1. Experimental evidence shows that the earth is being continually and uniformly bombarded by cosmic radiation at a rate evidently in excess of 10¹⁵ cosmic-ray particles per second. Moreover, the primaries of cosmic radiation are apparently almost entirely positive ions.⁽⁹⁾ As a matter of fact our magnetic field is such as to permit penetration by charges only of e/m =[overdot] 10¹⁴ e.s.u./gram or less. Therefore electrons would need to have relativistic masses of around 3x10³ m₀ to penetrate the earth's magnetic field. While this is well within the energy range of cosmic radiation, at least many times more positives than negatives should be and evidently are able to penetrate into the earth's atmosphere. But at a minimum of 10¹⁵ elementary positive charges per second or about 10⁶ e.s.u. per second for the whole earth the charge on the earth would increase at a rate of at least 10¹³ e.s.u. per year.

2. The magnetic moment of the earth has the value required by a circulating charge distribution corresponding to the charge G^½ M_e distributed approximately uniformly throughout the earth⁽¹⁾, i.e.,
   [mu]_e = e_e h_e/2M_ec (iii.35)

   where e_e is G^½ M_e , [mu]_e the earth's magnetic moment, h_e the mechanical moment of the earth and c the velocity of light. This relationship was first noticed by P. M. S. Blackett^(1a), and applies also to the sun and other stars.

3. In reference 1 the author presented a general unification concept which seems to show that the same fundamental laws apply in celestial as in atomic and molecular (and probably also nuclear) systems. Moreover it was there shown that gravity is intimately related to the radiation from the central body. The most important correlation bearing out this intimate relation to atomic systems is the observed coupling between orbital and spin states brought out in reference 1.

4. It is possible to take a large sample of the matter on the earth, namely that comprising the atmosphere, or 5.27x10²¹ grams, and show that it contains, within experimental error, the required electrical charge, namely about 1.36x10¹⁸ e.s.u. Thus, if we treat the atmosphere as a concentric-sphere condensor with the base of the atmosphere or the lithosphere as the inner sphere, the charge q on the atmosphere is found to be
   q = CV = r₁ r₂ / (r₁ -r₂) [INTEGRAL]^r2 _r1 (dV/dr)dr =[overdot] 4 x 4 x 10¹⁷ (dv/dr)[overbar] (iii.36)

   Experimentally (dV/dr)[overbar] amounts to about 0.6 to 3.17 volts/cm (positive vertically upward so that q is positive) near the earth's surface. The average value is required to be 3.1 volts/cm in order that G^½ M =q which is in excellent accord with the observed atmospheric potential gradient.

5. There is a tremendous accretion process going on in the solar system that amounts evidently to about 10¹³ grams of micrometeorites on the earth each year (Whipple).⁽⁸⁾ Assuming a ratio of more than one thousand to one for the gaseous material (H, He, CO₂ , H₂O, etc.) compared with solids in the accretion process as indicated by relative abundance data, there may be about 3x10⁸ grams/sec total accretion on the earth. This is, at least within an order of magnitude, the amount of accretion necessary to maintain a constant e/m (e.g., G^½) on the earth against the observed cosmic radiation accumulation of charge.

6. If the earth's mass increase due to accretion were 3x10⁸ grams/sec., one might expect the sun's accretion to amount to 3x10⁸ x 4[pi]r²_s-e / [pi]r²_e =[overdot] 10¹⁸ grams/see. assuming that the earth merely intercepts that portion of the (probably) spherically distributed total mass flux to the sun corresponding to the cross-sectional area of the earth. There is an approximate cheek on this total flux in the conditions existing in the chromosphere of the sun. This may be shown as follows:

   The electron density at the top of the sun's chromosphere is about 2x10¹¹ /cc which is therefore also approximately the positive charge density. If matter were undergoing effectively free fall into the sun, its velocity would be (GM/r_s)^½ = 4x10⁷ cm/sec. This velocity corresponds, through the relation ^½mv² =3/2.kT, to a temperature of about 2x10⁷ ̊K for a gas of average molecular weight unity. This agrees approximately with the temperature of the solar corona as evidenced by the appearance of charged atoms, e.g., iron, chromium, nickel, with charges of +13 to +16 in it. Hence the accretion on the sun may be as much as n₀m_Hv(4[pi]r²_s) = 2x10¹¹ x 1.7.10^-24 4.5 x 10⁷ 4[pi] x (7x10¹⁰)² =[overdot] 10¹⁸ g/sec. in agreement with the above earth-sampling result.

   It is of interest that this kinetic energy of accretion is ^½ mv² x 10¹⁸ x 2x10¹⁵ = 10³³ ergs/sec. which is about the known solar constant, namely 2x10¹³ ergs/sec. Apparently one thus has a likely explanation for the solar constant that need not include, or is at least approximately of the same relative importance as, the H --> He reaction via the carbon-nitrogen cycle that is supposed to be taking place in the core of the sun.

7. In stars, galactic nuclei (and a postulated supergalactic center) the average kinetic energy of any body should be approximately the negative of the gravitational energy GM²/a[bar] where a[bar] is the mean distance from any element of mass to the center of the system. Therefore

   T[bar] =[overdot] GM²/N.k.a[bar] (iii.37)

   From this assumption the following are approximate values of the quantities in equation iii.37 for three bodies of great interest to us (based on an average atomic weight of 0.5).

   Body	M(grams)	N	a[bar](cm)	T[bar](̊K)
   sun	2x1033	2x1057	4x1010	-2x107
   effective galactic nucleus	~3x1043	~1067	~1018	~1011
   effective supergalactic nucleus	~1056	~1080	~1023-1025	~1016-1018

Based on the above facts together with the quasi-lattice model of plasma outlined above, let us now present the following plasma model of gravitation:

Celestial bodies are positively charge particles existing as (positive) lattices meshed in tremendous multi-electron lattices (or cryscapades) in which the circulating electron lattices exist between and among the positive ions, i.e., in interplanetary, interstellar and intergalactic space, exactly as electrons in metals and plasma exist in the free space between the positive-ion lattice.

The charging of celestial bodies positively is easily understood and computed in terms (1) of the ion-cut-off characteristics of the powerful magnetic fields of celestial bodies and (2) of the binding energy of plasma for positive ions. First consider the selective absorption of an excess of positive ions by celestial bodies on the one hand and an excess of electrons by interplanetary, interstellar and intergalactic space on the other.

In order to understand why more positives than electrons are able to penetrate the magnetic field of bodies such as the sun and the earth one need simply realize that the cut-off energy is of the order of a billion electron volts even for the earth and, of course, greater for the sun and other luminous stars. To have such large energies, positive ions need to have relativistic masses actually not much greater than their rest masses, however, velocities always at least approaching closely the velocity of light. But it would be necessary for electrons to have relativistic masses more than 10³ times greater than their rest mass in order to penetrate the magnetic fields even of planets to say nothing of stars and galaxies. It is instructive to consider the radii of circular orbits of nuclei and electrons moving as satellites of the earth and sun in or near the eclyptic plane. From the equation

and realizing that the component of magnetic field H[perpendicular] perpendicular to the velocity vector falls off as the cube of the distance, one obtains

where the zero subscript designates the value at the surface of the body in question and [beta] = v/c. Equation iii.39 gives for protons and other completely-striped ions r/r_e =[overdot] 10[beta]^-½ for the earth, and r/r_s =[overdot] 10³ [beta]^-½ for the sun. But for electrons r/r_e =[overdot] 400 [beta]^-½ for the earth, and r/r_s =[overdot] 4x10⁴ [beta]^-½ for the sun. These are therefore the closest distances of approach for ions and electrons of external origin. Note that the earth's magnetic field at 60 earth radii (the moon-earth distance) about balances the sun's magnetic field at one AU (the earth-sun distance). This means that penetrating positive particles of 0.8 < [beta] < 1.0 originating outside the earth-moon system would orbit finally about the earth in an orbit inside the moon's orbit, but electrons in this range of energies would be so far out from the earth that they would be governed strictly by the sun's magnetic field. Likewise protons originating outside the solar system and finally orbiting around the sun at 0.8 < [beta] < 1.0 would orbit the sun inside the sun's asteroid system but electrons would orbit only outside the asteroid-ring system. These conditions seem to define the limits of the earth and the sun as nuclii placing the minor planets in a different category than the major planets. That is, the major planets in this respect would be little sisters to the sun whereas the minor plants would be daughters.

Now for electron -positron pair formation the photon energy is 10⁶ e.v. This corresponds to a temperature of about 10¹⁰ ̊K. Therefore the galactic nucleus should be able to emit large quantities of electrons-positron pairs, in fact even more than photons, because the spectral displacement law (the Wein law) would have the wave length of maximum intensity for emission from the galactic center at less than the Compton wave length for this electron-positron pair. By decay and rearrangement the main radiation from the center of our galaxy might therefore be expected to be simply protons and electrons or H-atoms of initial kinetic energy about 10^-6 ergs per particle. These would have slowed down, by gravitational attraction to the galactic center, to about 10⁷ cm/sec at 3x10²² cm (30,000 l.y.) from the center of radiation. This is approximately the observed velocity of hydrogen in our region of interstellar space. Therefore it seems reasonable to assume that the observed hydrogen in interstellar space is really predominantly that emitted as soft cosmic radiation from the galactic center. Moreover, from the high-energy tail of the Stephan-Boltzmann radiation from the galactic center one should except to find in our region of space hydrogen atoms or ions (soft cosmic rays) of velocity near the velocity of light, i.e., with energies perhaps 10³ to 10⁴ times greater than the average of the Stephan-Boltzmann spectral distribution radiated from the galactic center.

The existence of a supergalaxy now a quite definite reality, would lead one to look for a supergalactic nucleus of effective diameter comparable to the diameter of the supergalaxy's satellites, namely the galaxies, or 10²³ to 10²⁶ em. The supergalaxy would be the final one because in the system-within-thesystem concept any system is in general, i.e., within a factor of about 10, about 10⁵ times greater in diameter than its satellites. But at 10²⁸ cm the red shifts go to zero, hence all radiation either from the supergalactie nucleus or one of its satellites not intercepted by a primary, secondary, tertiary, etc., satellite would be returned, by space -curvature, to the gigantic nucleus. Now at the tremendous temperature of the supergalactic nucleus (~10¹⁷ ̊K) the peak of the radiation distribution would have an energy hv, of about 10¹³ e.v. with an upper limit radiation, corresponding again to the high-frequency tail of the Stephan-Boltzmann distribution, around 10¹⁷ e.v. This is approximately the observed upper-limit energy of cosmic radiation and this model for cosmic radiation is therefore consistent with observations and predicts that the source of the cosmic rays of highest energy is the supergalactic nucleus which is emitting simply in accord with the well-established Stephan-Boltzmann radiation law.

Next, applying the concept of the plasma let us compute the charge on a celestial body. A plasma has an energy well of depth given (for an overall uncharged plasma) by equation iii.33. This means that the plasma can absorb positive ions until the increase in energy due to repulsion, i.e., the energy CV²/2 of the charged condensor (q = CV), exactly balances the energy of the plasma providing one sprays the plasma condensor with positive charge. (Actually cosmic radiation is doing just this as far as the earth and presumably all other bodies are concerned). The earth as a plasma (it is a good conductor and therefore metallic, or a plasma, as far as the macroscopic earth is concerned) should therefore be able to absorb positive charge until the energy increase caused by this charge is

and the charge is

For a chemical (or solid) plasma of the nature of the earth | E_i | amounts to around 10^-11 ergs per positive ion. Also assuming an average atomic weight of 30, N_e =[overdot] 10⁵⁰. Furthermore, C_e = r_e = 6.4 x 10⁸ cm. Therefore, q_e = (2.6 x 10⁸ x 10⁵⁰ x 10^-11)^½ = 10²⁴ e.s.u. This agrees almost precisely with G^½ M_e and definitely, it would seem, identifies G^½ with charge per unit mass. Note also that for the earth

the condition NkT =[overdot] GM²/2a[overbar] give somewhat (possibly 3 times) too large a temperature evidently because the binding energy is largely chemical.

One may likewise compute the (positive) charge on the sun from equation iii.41, i.e., from the equation

However, one finds that | Ei |_s. must be about 500 e.v. for the sun. This is consistent with the composition of the sun and the fact that practically all of the orbital electrons of the atoms up to about Z = 13 to 15 should have been stripped at the thermal environment of the sun, and therefore are plasma electrons. For example, one needs less than 2 per cent of the sun to be atoms of atomic number 15 or greater to account for this plasma energy.

It is important to realize in this model that net universal attraction despite an excess of positive charge on a body is associated with the energy well of the plasma and ideal, metallic (or plasmatic) polarization, i.e., an effectively infinite dielectric constant. In fact the increased energyCV²/2 is exactly balanced by the decreased energy due to the interaction of the charge q with the negative charge of interplanetary electrons bonding the celestial particle in the celestial lattice. Indeed, owing to excellent conduction in the plasma each particle-on-a-particle is held to the system, despite the local positive excess by the familiar image force with a strength determined simply by the binding energy of elementary ions for the plasma, as determined by the energy well.

Universal Plasma Development

As noted above the supergalactic nucleus should emit at a maximum intensity in the energy range of about 10¹³ e.V. per photon. At this frequency, which is above the Compton wave length for neutrons, the photons should decay in their (relativistic) half -life cycle to matter itself, i.e., possibly first to neutrons (if the photon is not identically a neutron to start with), [alpha]-particles, etc. and the electrons all probably initially, as they leave the nucleus, in charge balance. An electron excess then become trapped in the space between the supergalactic nucleus and its satellites by the magnetic fields of the galaxies, leaving therefore an excess of negative charge in this space and an equal positive excess, owing to the greater penetration of the positives, in all of the galaxies combined. Under conditions where the positives and negatives can recombine to neutral atoms in the free space between the galaxies the neutrals can then accrete into the galaxies without being hindered by magnetic fields. Evidently neutral accretion must take place universally at a fixed ratio to the charge accretion in order to maintain the gravitational constant. The penetrating positive excess thus adds charge to the galaxies leaving an equal amount of excess negative charge in the space between the galaxies and supergalactic nucleus, providing the chemical binding energy of the galaxy to its positive supergalactic nucleus. This same process is repeated between a galactic nucleus and its satellites; by emission followed by decay to charged particles, a positive excess of which is able to penetrate the galactic satellites, the constellations, galactic clusters and the stars of the galaxy also become positively charged. Moreover, the excess negative charge remaining behind, owing to the inability of all but a relatively few of them compared with the positives to penetrate the satellites, add to the negative-excess intergalactic charge. The hard cosmic rays of the primary process each produce, of course, a large number of high energy, positive and negative secondaries. Thus these secondary charges again become separated to some extent (about one part in 10¹⁸) within the galaxies by the tremendous dynamo-action of the rotating magnetic fields of the stars and clusters of stars of the galaxy, and the greater penetrating power of the high-energy tail of the positives of this softer cosmic radiation. One should realize that this process repeats itself again between the stars and their planets by soft cosmic radiation from the star itself, and again between the planets and their satellites by cosmic-ray "star" formation inside the system. This latter process is the predominant one and occurs in all systems. That is, cosmic-ray "star" (or explosion) processes occurring inside any given system will be subject to the same dynamo-action of the rotating magnetic moment of the bodies of the system as between the supergalaxy and the galaxy described above, irrespective of the order or size of the system. This dynamo-action thus serves to produce a positive excess on all massive bodies and a negative excess throughout all space, extragalactic, intergalactic, interstellar and interplanatory.

Chemical Binding in Plasma

A remarkable feature of the plasma interpreted by the quasi-lattice model is that it provides a means, under high internal temperatures and high density, for realizing chemical-binding energies far in excess of that in the strongest chemical bonds in our terrestrial environment, e.g., as in CO, N₂ , diamond, platinum, etc. For instance, it was indicated that the chemical or plasma binding energy in the sun m, ay be about 500 e.v. per atom. This concept is simply that when the nuclei of a plasma are sufficiently close together, and the temperature high enough to remove by ionization many or all of the electrons of atoms that are ordinary core electrons comprising the positive -lattice ions at low temperatures, the chemical-binding energy then becomes comparable to [SUM]^z_i=0 I_i, where z is the total number of electrons per atom removed by ionization and moving in the quasi-lattice of the plasma, and I_i is the ionization potential of the ith electron.

This seemingly quite plausible property of plasma thus offers a simple explanation for the high-density dwarf stars. That is, if a body were comprised largely of high atomic weight nuclei, e.g., atoms of 16 electrons or more, and had an internal temperature of say 10⁸, about 16 electrons per positive ion would be plasma electrons, and the binding energy would then be tremendously greater than in a plasma with only one or two electrons per positive ion. At such a large binding energy the density would be comparably large.

This feature of the quasi-lattice model of the plasma also offers a plausible explanation of the tremendous binding energy of nuclei if one also postulates a new realm of elementary particles, e.g., of size as much smaller than a nucleus as the stars, constellations, and clusters of stars are smaller than a galaxy. A proton might then be regarded as a plasma comprising a tremendous number of more elementary particles (e.g., Frenkel's "N-particles")² with a positive excess of 4.77.10^-10 e.s.u. per galaxy, and a neutron as a plasma with no charge excess. Realizing that the proton with its large positive excess is a stable plasma, one also realizes that the combination of two such plasma one with the maximum possible positive excess and the other with no positive excess, e.g., the proton and the neutron, would combine to form a plasma of a still deeper energy well simply because it is more massive. The tremendous log of new, strange particles that are known to comprise atomic nuclei is strongly suggestive of extremely minute, nuclear galaxies with characteristic minute galactic clusters, globular clusters, constellations, tars and planets held together in extremely tight, high temperature plasma.

References