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February 23, 1992
PUSHATT.ASC
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This file shared with KeelyNet courtesy of Woody Moffitt.
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A Pressure/Energy Density Interpretation of
Attractive Behavior and Forces
Newtonian gravitation, and the body of theory which developed from
it, is dominantly expressed in the language and concepts of action
at-a-distance, a practice which, in some ways, is little better than
saying that ghosts are responsible for physical phenomena.
It may be easily shown, however, that "attractive" forces are
readily interpreted as a consequence of local cause dynamics, field
effects notwithstanding. Two examples will illustrate this principle
and describe the procedure whereby attraction appears in two-body
interactions.
The first is drawn from quantum mechanics and treats in brief a
theoretical model of two-body attraction via the Casimir Effect. The
second example derives attractive behavior from a classical
treatment of momentum currents and stress-tensor analysis, resulting
in a simple mechanical representation of gravitational action. Some
theorists believe that both effects are a reflection of the same
process, albeit with some modification in the case of gravity, to
account for its vastly weaker amplitude.
The Casimir Effect treats the problem of two conductive (dielectric)
plates brought into close proximity. In this case, quantum
fluctuations (zero-point energy) provide the actual motivating
source responsible for the observed "attraction", though the
specific mechanisms of this source will not be addressed here.
The model of this action is both simple and straightforward. It
begins with a consideration of vacuum fluctuations and their
distribution, which takes the form of an isotropic "sea" of
electromagnetic waves filling space.
Any two bodies imposed on this isotropic flux immediately alter its
distribution, creating a form of energy "shadow" between the plates.
More precisely, the presence of the plates alters the distribution
of modes in the vacuum, with fewer modes being maintained between
the plates than on their exterior surfaces.
The ensuing imbalance, with a greater amount of energy impinging on
the plates from outside than is contained between them, produces a
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"push" on the plates, which in older terminology would be construed
as an attraction. The strength of the Casimir Effect is proportional
to (hc/r^4), where "h" is Planck's constant, "c" is the speed of
light in vacuum, and "r" is a unit distance.
Thus, the interaction is proportional to the energy density or
pressure created by the difference in flux on opposite sides of the
plates. The "attraction" is perfectly analogous to what happens if
two discs, or balls, are placed in the two ends of an empty pipe.
Were the pipe to filled with fluid or high-pressure gas at both
ends, the discs or balls would be pushed together in proportion to
the pressure of fluid flow. At no time does a true attraction take
place.
A more explicitly dynamic model of both gravitational and
electromagnetic "attraction" is presented by Hermann and Schmid (1-
4), who treat field effects as a function of momentum currents,
where force results from a flow of (negative) momentum between two
or more bodies, and mechanical stress is a function of (negative)
momentum current density.
A useful result of this representation is the ability to visualize
streamlines of momentum flow in such a way as to make tensor effects
immediately intuitive, thereby adding greatly to understanding of
the principles involved.
The starting point for study of this process is a stress tensor,
written in Cartesian form,
î=(1/8ãG)( 3(dP/dj)^2*ë-2(dP/di)(dP/dk) )
where "G" is Newton's constant, "P" is the gravitational potential,
(i,j,k) are the Cartesian coordinates, or indices, and "ë" is the
Kronecker symbol. The "d" refers to partial differentiation, and
the three expresses a sum over the principal axes. This expression
is essentially the same as the negative of Maxwell's stress tensor
for electrostatic fields, with the electric potential replacing the
gravitational potential. The momentum current interpretation treats
a negative stress tensor as a momentum current density tensor.
When couched in Cartesian matrix form, the rows or columns of the
matrix, (i, j, k) or (x, y, z), represent the vector current
densities of the respective coordinates. These are the functions
which may be graphed to produce streamlines of the relevant currents
and forces responsible for gravitational dynamics. (Not shown.)
Two different flows are produced and revealed by the streamline
pictures. The first is a flow which returns to its body of origin.
This creates a static pressure on the body which is responsible for
gravitational collapse.
The second flow circulates between two bodies and relates more
dynamical information. In the x-momentum plane, one finds that a
body will lose momentum as the currents from a second body flow away
from it and back to the second body.
The currents originating from the second body return to it with a
surplus momentum taken from the first body, and actually increase
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its momentum. These currents do not take the shortest path between
the bodies, but instead take wide loops around them. Little or no
momentum is exchanged in the other two planes between the bodies.
When this picture is evaluated in terms of mechanical stress, one
finds that the bodies are not being pulled together by the
gravitational field, but are instead pushed together by the pressure
of their common field.
A curious conclusion of this analysis is that gravity is shown not
to act along the center line of the bodies; there is in fact a
region along the center line where the current density vanishes.
In the figure below, a yoke and spring assembly illustrates the
basic process of momentum flow and gravitational action. Springs 1
and 2 are under pressure, with x-momentum flowing from left to
right. Springs 3 and 4, with x-momentum flowing from right to left,
are under tension. Gravity acts similarly. Positive x-momentum in
the field translates to local pressure, whereas negative x-momentum
translates to local tension.
3
--O--O--O--O--O--O--O--O--O--O
I I
I 1 2 I
I I
I--O--O--A B--O--O--I
I I
I I
I I
--O--O--O--O--O--O--O--O--O--O
4
Both the models discussed here, the Casimir Effect, and the momentum
current analysis, present a dynamics of attraction which derive from
a local cause "push" mechanism, contrary to common terminology and
belief.
This "push" is a function of energy density or pressure, described
by Hermann and Schmid in terms of momentum density currents, and by
Casimir in terms of radiation pressure. Gravitation is still a bit
mysterious, as it lacks a clear source of energy and medium for
momentum exchange, in contrast to the Casimir Effect and well known
electromagnetic interactions.
Some theorists, notably Puthoff, suggest that the quantum
fluctuations responsible for the Casimir Effect are responsible for
gravity as well. (5) Close approximations of Newton's constant have
been derived, based on two forms of Casimir potentials and
fluctuation phenomena. (6) If, in fact, quantum fluctuations are the
energy source of gravity, Hermann and Schmid's representation would
not be negated, nor would Einstein's theory of spatial curvature.
Both employ the language and concepts of tensor dynamics to reveal a
deeper structure in nature, one that is largely independent of the
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detailed qualities of a source or system. Einstein's theory, for
example, recreates the dynamics of a ball on a rubber sheet. The
method is no less accurate for being applied to gravity, as the
dynamics involved are perfectly analogous to one another.
Similarly, Hermann and Schmid's representation is just as valid
within its domain of applicability. It has practical usefulness, for
it explicitly reveals the vanishing point of momentum flow where
another body (satellite) could be stably inserted. By contrast,
those models of gravity which address its source contain dynamical
information in more implicit form, removed from easy access.
The momentum current dynamics of Hermann and Schmid largely succeed
because of their simplification of source details, which are
submerged in the mathematical device of the potential. A hybrid form
of gravitational theory would, ideally, apply the information of
source details to the construction of more accurate potentials, and
thereby achieve more exacting control over those processes effected
by gravity.
A potential created by Casimir-type sources would necessarily
involve short-range corrections similar to those suggested by recent
reexamination of Eotvos' experiments. Such corrections might be
negligible at long range (i.e., for geostationary satellites), but
could have observable effects in low-altitude ballistics (i.e., the
classified "shortfall" distance of ICBM's).
Measurements of Newton's constant, in turn, evaluate the total force
on two bodies at close range, and usually fail to distinguish the
contribution from Casimir effects, which are far more powerful at
short distances. As Hermann and Schmid illustrate, the details of a
process one observes are often dependent on the technique and
qualitative construction one employs. The choice of technique and
interpretation applied to a given problem depend on the information
one requires, and that is always subjective in nature. One choice
need not negate the other, so long as one is aware of the strengths
and weaknesses of the method chosen.
Darrell Moffitt
References
1-4. F. Hermann, G.B. Schmid, Am. J. Phys., 52, 146, 1984; Eur. J.
Phys., 6, 16, 1985; Am. J. Phys., 53, 415, 1985; Eur. J. Phys., 8,
41, 1987
5. H.E. Puthoff, Phys. Rev. A, 39, 5, 2333, 1989
6. D. Moffitt, "cpedog", "casgrav", KeelyNet file, 1991
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