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Plasma and Universal Gravitation

Melvin A. Cook

Reproduced with permission of the author
From Appendix III, /The Science of High Explosives/
American Chemical Society Monograph Series No. 139.
Reinhold Publishing Corporation, New York, Chapman & Hall Ltd, London.
Copyright 1958 by Reinhold Publishing Corporation
Library of Congress Catalog Card Number 58-10260.

/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., 1.54x10^24 e.s.u. for the earth and 5.16x10^29 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 10^15 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] 10^14
e.s.u./gram or less. Therefore electrons would need to have
relativistic masses of around 3x10^3 m_0 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 10^15 elementary positive
charges per second or about 10^6 e.s.u. per second for the whole
earth the charge on the earth would increase at a rate of at least
10^13 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_e c (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 5.27x10^21 grams,
and show that it contains, within experimental error, the required
electrical charge, namely about 1.36x10^18 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 = r_1 r_2 / (r_1 -r_2 ) [INTEGRAL]^r2 _r1 (dV/dr)dr
=[overdot] 4 x 4 x 10^17 (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 10^13 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, CO_2 , H_2 O, etc.) compared with solids in the accretion
process as indicated by relative abundance data, there may be
about 3x10^8 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 3x10^8
grams/sec., one might expect the sun's accretion to amount to
3x10^8 x 4[pi]r^2 _s-e / [pi]r^2 _e =[overdot] 10^18 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
2x10^11 /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 = 4x10^7 cm/sec.
This velocity corresponds, through the relation ^½ mv^2 =3/2.kT,
to a temperature of about 2x10^7 ?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 n_0 m_H
v(4[pi]r^2 _s ) = 2x10^11 x 1.7.10^-24 4.5 x 10^7 4[pi] x (7x10^10
)^2 =[overdot] 10^18 g/sec. in agreement with the above
earth-sampling result.

It is of interest that this kinetic energy of accretion is ^½ mv^2
x 10^18 x 2x10^15 = 10^33 ergs/sec. which is about the known solar
constant, namely 2x10^13 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 GM^2 /a[bar] where a[bar] is
the mean distance from any element of mass to the center of the
system. Therefore

T[bar] =[overdot] GM^2 /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 2x10^33 2x10^57 4x10^10 -2x10^7
effective galactic nucleus ~3x10^43 ~10^67 ~10^18 ~10^11
effective supergalactic nucleus ~10^56 ~10^80 ~10^23 -10^25 ~10^16
-10^18

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 10^3 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

Mv^2 /r = e v H [perpendicular] / c (iii.38)

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

r/r_0 = (eH_0 r_0 /Mc^2 [beta])^½ (iii.39)

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] 10^3 [beta]^-½ for the sun. But for
electrons r/r_e =[overdot] 400 [beta]^-½ for the earth, and r/r_s
=[overdot] 4x10^4 [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 10^6 e.v.
This corresponds to a temperature of about 10^10 ?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 10^7 cm/sec at 3x10^22 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 10^3 to 10^4
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 10^23 to 10^26 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 10^5 times greater in diameter
than its satellites. But at 10^28 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
(~10^17 ?K) the peak of the radiation distribution would have an energy
/hv/, of about 10^13 e.v. with an upper limit radiation, corresponding
again to the high-frequency tail of the Stephan-Boltzmann distribution,
around 10^17 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 CV^2 /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

CV^2 /2 = q^2 /2C = N x | E_/i/ | (iii.40)

and the charge is

q = (2C x N x E/_i /[overbar] | )^½ (iii.41)

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] 10^50 . Furthermore, C_e = r_e = 6.4
x 10^8 cm. Therefore, q_e = (2.6 x 10^8 x 10^50 x 10^-11 )^½ = 10^24
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

| E_/i/ | =[overdot] GM^2 _e /2a[overbar] x N;

the condition NkT =[overdot] GM^2 /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

CV^2 /2 = GM^2 /2a[overbar] = q^2 /2C = q^2 /2d

or

q = G^½ M (iii.42)

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 energyCV^2 /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 10^13 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 10^18 ) 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, N_2 , 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 /i/th 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 10^8 , 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

1a. Blackett, P. M. C., Phil. Mag. 40, 125 (1949).

1. Cook, M. A., /Bulletin No., 74/ Vol. 36, No. 16, Utah Engineering
Experiment Station, Nov. 30, 1956. 2. Cook, M. A., "Properties of
Solids," /Bulletin No. 53/, Vol. 42, No. 2, Utah Engineering Experiment
Station, September, 1951.

3. Cook, M. A., /J. Chem. Phys/., 13, 262 (1945).

4. Cook, M. A., /J. Chem. Phys/., 14, 62 (1946).

5. Cook, M. A., /J. Phys. & Colloid Chem/., 51, 487 (1947).

6. Cook, M. A., /Utah Acad. Sci/., 25, 145 (1948).

7. Slater, J. C., /J. Chem. Phys/. 1, 687 (1933).

8. Whipple, F. L., /Proc. Nat. Acad. Sci/. 36, 687 (1950); 37, 19 (1956).

9. Wilson, J.G., "Cosmic-Ray Physics", North-Holland Publishing Co.,
Amsterdam (1952).

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