265 lines
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265 lines
13 KiB
Plaintext
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(word processor parameters LM=8, RM=75, TM=2, BM=2)
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Taken from KeelyNet BBS (214) 324-3501
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Sponsored by Vangard Sciences
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PO BOX 1031
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Mesquite, TX 75150
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There are ABSOLUTELY NO RESTRICTIONS
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on duplicating, publishing or distributing the
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files on KeelyNet except where noted!
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February 23, 1992
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PUSHATT.ASC
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This file shared with KeelyNet courtesy of Woody Moffitt.
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--------------------------------------------------------------------
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A Pressure/Energy Density Interpretation of
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Attractive Behavior and Forces
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Newtonian gravitation, and the body of theory which developed from
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it, is dominantly expressed in the language and concepts of action
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at-a-distance, a practice which, in some ways, is little better than
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saying that ghosts are responsible for physical phenomena.
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It may be easily shown, however, that "attractive" forces are
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readily interpreted as a consequence of local cause dynamics, field
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effects notwithstanding. Two examples will illustrate this principle
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and describe the procedure whereby attraction appears in two-body
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interactions.
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The first is drawn from quantum mechanics and treats in brief a
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theoretical model of two-body attraction via the Casimir Effect. The
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second example derives attractive behavior from a classical
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treatment of momentum currents and stress-tensor analysis, resulting
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in a simple mechanical representation of gravitational action. Some
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theorists believe that both effects are a reflection of the same
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process, albeit with some modification in the case of gravity, to
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account for its vastly weaker amplitude.
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The Casimir Effect treats the problem of two conductive (dielectric)
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plates brought into close proximity. In this case, quantum
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fluctuations (zero-point energy) provide the actual motivating
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source responsible for the observed "attraction", though the
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specific mechanisms of this source will not be addressed here.
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The model of this action is both simple and straightforward. It
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begins with a consideration of vacuum fluctuations and their
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distribution, which takes the form of an isotropic "sea" of
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electromagnetic waves filling space.
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Any two bodies imposed on this isotropic flux immediately alter its
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distribution, creating a form of energy "shadow" between the plates.
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More precisely, the presence of the plates alters the distribution
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of modes in the vacuum, with fewer modes being maintained between
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the plates than on their exterior surfaces.
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The ensuing imbalance, with a greater amount of energy impinging on
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the plates from outside than is contained between them, produces a
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Page 1
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"push" on the plates, which in older terminology would be construed
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as an attraction. The strength of the Casimir Effect is proportional
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to (hc/r^4), where "h" is Planck's constant, "c" is the speed of
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light in vacuum, and "r" is a unit distance.
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Thus, the interaction is proportional to the energy density or
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pressure created by the difference in flux on opposite sides of the
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plates. The "attraction" is perfectly analogous to what happens if
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two discs, or balls, are placed in the two ends of an empty pipe.
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Were the pipe to filled with fluid or high-pressure gas at both
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ends, the discs or balls would be pushed together in proportion to
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the pressure of fluid flow. At no time does a true attraction take
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place.
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A more explicitly dynamic model of both gravitational and
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electromagnetic "attraction" is presented by Hermann and Schmid (1-
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4), who treat field effects as a function of momentum currents,
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where force results from a flow of (negative) momentum between two
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or more bodies, and mechanical stress is a function of (negative)
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momentum current density.
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A useful result of this representation is the ability to visualize
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streamlines of momentum flow in such a way as to make tensor effects
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immediately intuitive, thereby adding greatly to understanding of
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the principles involved.
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The starting point for study of this process is a stress tensor,
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written in Cartesian form,
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<20>=(1/8<>G)( 3(dP/dj)^2*<2A>-2(dP/di)(dP/dk) )
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where "G" is Newton's constant, "P" is the gravitational potential,
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(i,j,k) are the Cartesian coordinates, or indices, and "<22>" is the
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Kronecker symbol. The "d" refers to partial differentiation, and
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the three expresses a sum over the principal axes. This expression
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is essentially the same as the negative of Maxwell's stress tensor
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for electrostatic fields, with the electric potential replacing the
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gravitational potential. The momentum current interpretation treats
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a negative stress tensor as a momentum current density tensor.
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When couched in Cartesian matrix form, the rows or columns of the
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matrix, (i, j, k) or (x, y, z), represent the vector current
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densities of the respective coordinates. These are the functions
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which may be graphed to produce streamlines of the relevant currents
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and forces responsible for gravitational dynamics. (Not shown.)
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Two different flows are produced and revealed by the streamline
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pictures. The first is a flow which returns to its body of origin.
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This creates a static pressure on the body which is responsible for
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gravitational collapse.
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The second flow circulates between two bodies and relates more
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dynamical information. In the x-momentum plane, one finds that a
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body will lose momentum as the currents from a second body flow away
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from it and back to the second body.
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The currents originating from the second body return to it with a
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surplus momentum taken from the first body, and actually increase
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Page 2
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its momentum. These currents do not take the shortest path between
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the bodies, but instead take wide loops around them. Little or no
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momentum is exchanged in the other two planes between the bodies.
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When this picture is evaluated in terms of mechanical stress, one
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finds that the bodies are not being pulled together by the
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gravitational field, but are instead pushed together by the pressure
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of their common field.
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A curious conclusion of this analysis is that gravity is shown not
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to act along the center line of the bodies; there is in fact a
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region along the center line where the current density vanishes.
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In the figure below, a yoke and spring assembly illustrates the
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basic process of momentum flow and gravitational action. Springs 1
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and 2 are under pressure, with x-momentum flowing from left to
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right. Springs 3 and 4, with x-momentum flowing from right to left,
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are under tension. Gravity acts similarly. Positive x-momentum in
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the field translates to local pressure, whereas negative x-momentum
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translates to local tension.
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3
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--O--O--O--O--O--O--O--O--O--O
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I I
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I 1 2 I
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I I
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I--O--O--A B--O--O--I
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I I
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I I
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I I
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--O--O--O--O--O--O--O--O--O--O
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4
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Both the models discussed here, the Casimir Effect, and the momentum
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current analysis, present a dynamics of attraction which derive from
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a local cause "push" mechanism, contrary to common terminology and
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belief.
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This "push" is a function of energy density or pressure, described
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by Hermann and Schmid in terms of momentum density currents, and by
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Casimir in terms of radiation pressure. Gravitation is still a bit
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mysterious, as it lacks a clear source of energy and medium for
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momentum exchange, in contrast to the Casimir Effect and well known
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electromagnetic interactions.
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Some theorists, notably Puthoff, suggest that the quantum
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fluctuations responsible for the Casimir Effect are responsible for
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gravity as well. (5) Close approximations of Newton's constant have
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been derived, based on two forms of Casimir potentials and
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fluctuation phenomena. (6) If, in fact, quantum fluctuations are the
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energy source of gravity, Hermann and Schmid's representation would
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not be negated, nor would Einstein's theory of spatial curvature.
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Both employ the language and concepts of tensor dynamics to reveal a
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deeper structure in nature, one that is largely independent of the
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Page 3
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detailed qualities of a source or system. Einstein's theory, for
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example, recreates the dynamics of a ball on a rubber sheet. The
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method is no less accurate for being applied to gravity, as the
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dynamics involved are perfectly analogous to one another.
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Similarly, Hermann and Schmid's representation is just as valid
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within its domain of applicability. It has practical usefulness, for
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it explicitly reveals the vanishing point of momentum flow where
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another body (satellite) could be stably inserted. By contrast,
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those models of gravity which address its source contain dynamical
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information in more implicit form, removed from easy access.
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The momentum current dynamics of Hermann and Schmid largely succeed
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because of their simplification of source details, which are
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submerged in the mathematical device of the potential. A hybrid form
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of gravitational theory would, ideally, apply the information of
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source details to the construction of more accurate potentials, and
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thereby achieve more exacting control over those processes effected
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by gravity.
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A potential created by Casimir-type sources would necessarily
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involve short-range corrections similar to those suggested by recent
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reexamination of Eotvos' experiments. Such corrections might be
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negligible at long range (i.e., for geostationary satellites), but
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could have observable effects in low-altitude ballistics (i.e., the
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classified "shortfall" distance of ICBM's).
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Measurements of Newton's constant, in turn, evaluate the total force
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on two bodies at close range, and usually fail to distinguish the
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contribution from Casimir effects, which are far more powerful at
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short distances. As Hermann and Schmid illustrate, the details of a
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process one observes are often dependent on the technique and
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qualitative construction one employs. The choice of technique and
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interpretation applied to a given problem depend on the information
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one requires, and that is always subjective in nature. One choice
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need not negate the other, so long as one is aware of the strengths
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and weaknesses of the method chosen.
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Darrell Moffitt
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References
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1-4. F. Hermann, G.B. Schmid, Am. J. Phys., 52, 146, 1984; Eur. J.
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Phys., 6, 16, 1985; Am. J. Phys., 53, 415, 1985; Eur. J. Phys., 8,
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41, 1987
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5. H.E. Puthoff, Phys. Rev. A, 39, 5, 2333, 1989
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6. D. Moffitt, "cpedog", "casgrav", KeelyNet file, 1991
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--------------------------------------------------------------------
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If you have comments or other information relating to such topics
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as this paper covers, please upload to KeelyNet or send to the
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Vangard Sciences address as listed on the first page.
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Thank you for your consideration, interest and support.
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Jerry W. Decker.........Ron Barker...........Chuck Henderson
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Vangard Sciences/KeelyNet
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--------------------------------------------------------------------
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If we can be of service, you may contact
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Jerry at (214) 324-8741 or Ron at (214) 242-9346
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--------------------------------------------------------------------
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Page 4
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