(word processor parameters LM=8, RM=75, TM=2, BM=2) Taken from KeelyNet BBS (214) 324-3501 Sponsored by Vangard Sciences PO BOX 1031 Mesquite, TX 75150 There are ABSOLUTELY NO RESTRICTIONS on duplicating, publishing or distributing the files on KeelyNet except where noted! February 23, 1992 PUSHATT.ASC -------------------------------------------------------------------- This file shared with KeelyNet courtesy of Woody Moffitt. -------------------------------------------------------------------- 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 Page 1 "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 Page 2 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 Page 3 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 -------------------------------------------------------------------- If you have comments or other information relating to such topics as this paper covers, please upload to KeelyNet or send to the Vangard Sciences address as listed on the first page. Thank you for your consideration, interest and support. Jerry W. Decker.........Ron Barker...........Chuck Henderson Vangard Sciences/KeelyNet -------------------------------------------------------------------- If we can be of service, you may contact Jerry at (214) 324-8741 or Ron at (214) 242-9346 -------------------------------------------------------------------- Page 4