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
"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
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 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", 1991

Call THC BBS: +1 604 361 1464 HST   1:340/26   Over 6,200 Text Files!
"Reach for the edges of your mind"