Bjerknes forces (See: Paragraph 3, below)     


McCarthy -- Scientific Materialism

Chapter II) Mechanical Models of Molecular Bonds and Attractions

The differences that arise between ideal gasses and real (molecular) gasses are due to the molecular attractions that occur between particles in the latter. The forces of various molecular bonds alter experimental results involving real gasses and fluid in ways that must be taken into account. Yet, to those unfamiliar with hydrodynamics or granular media experiments, it would seem improbable that such forces could be reproduced simply by particles in motion.

It is important to remember that in ideal gasses and fluids, low pressure systems will create vacuum "suction" or a seeming "attraction at a distance." High pressure systems, on the other hand, will create a repulsive force. Interestingly, it is well known to experts in fluid and granular mechanics that the complicated interaction of various flows, compression pulses, and pressure differentials will lead, through Newtonian contact forces, to various attractions, repulsions, stable bonds, and self-organized structures in hydrodynamic systems:

1) Bjerknes Forces
For more than a century, it has been known that particles that oscillate in media systems produce attractions and repulsions that are mediated through the medium. In the 1870's, the physicist C.A. Bjerknes (1) showed that "two spheres immersed in an incompressible fluid, and which pulsate (i.e., change in volume) regularly, exert on each other (by the mediation of the fluid) an attraction, determined by the inverse square law, if the pulsations are concordant; and exert on each other a repulsion, determined likewise by the inverse square law if the phases of the pulsations differ by half a period.... If the spheres instead of pulsating, oscillate to and fro in straight lines about their mean positions, the forces between them are proportional in magnitude and the same in direction, but opposite in sign, to those which act between two magnets oriented along the directions of oscillation.

"The results obtained by Bjerknes were extended by A. H. Leahy (2) in the case of two spheres pulsating in an elastic medium..... For this system, Bjerknes' results are reversed, the law being now that of attraction in the case of unlike phases , and of repulsion in the case of like phases; the intensity is as before proportional to the inverse square of the distance."

Quoted from: Whittaker, Sir Edmund. History of the Theories of Aether and Electricity, Thomas Nelson and Sons Ltd., London (1953) pp. 284-285

1. Repertorium d. Mathematik I (Leipzig, 1877) p. 268. Gottinger Nachrichten (1976), p.245; Comptes Rendus, lxxxiv (1877), p. 1375; cf. Nature, xxiv (1881), p. 360.

2. (Trans. Camb. Phil. Soc. xiv (1884) p.45)

Bjerknes forces have been studied in great detail in the late 1990's, particularly with regard to cavitation experiments. At the fluid mechanics website of Boston University, one finds:

"In addition, the coupled oscillations of small clusters of (two, three or more) bubbles under acoustic forcing are under investigation. Questions of energy transfer between breathing and shape modes, and Bjerknes forces (in the strongly nonlinear regime) acting upon bubbles are being addressed by means of both analytical and numerical studies."

It is also possible that Bjerknes forces are involved in bonds that occur between vortices (see below for vortex bonds), perhaps, resulting from oscillations in volume of the vortex that may result.

As the vortex begins to form, the external pressure of the medium causes the vortex to condense until the internal pressure and centrifugal force of the vortex becomes greater than the external pressure. At this point, the vortex stops condensing and begins to expand until the centrifugal forces and internal pressure becomes less than the external pressure. The external pressure of the medium then once again starts squeezing the vortex and the cycle begins anew. It is possible that for ideal gas vortices constancy of volume is never achieved. Instead the volume of the vortex continues to oscillate back and forth over a particular region of stability. This could result in the Bjerknes forces described above.

2) Rado Forces and Vortices as Elementary Particles

The equations for stable vortices in inviscid fluids (which are simply denser versions of ideal gasses) can be found in most any tome on hydrodynamics. In "Theoretical Hydrodynamics" by Milne-Thompson--Dover publications, (1996)--page 85 contains the equations regarding "Permanence of Vorticity" --so that given an inviscid fluid, conservative forces, pressure as a function of density, a "particle which has vorticity at any time continues to have vorticity."

The notion of a stable vortex as an elementary structure is not new. Thomson posited it in the late 19th century, and various aspects of the theory are presently being revisited by quantum loop and knot theorists.

At the publications website of Professor Stephen Lomonaco, full professor at University of Maryland, one has access to the following paper:

"The modern legacies of Thomson's atomic vortex theory in classical electrodynamics, in "The Interface of Knots and Physics," edited by L.H. Kauffman, AMS PSAPM, Vol. 51, Providence, RI (1996), pp. 145 - 166. (Invited paper) This paper is based on a one hour invited lecture given at the American Mathematical Society (AMS) Short Course on Knots and Physics at the Annual meeting of the AMS in January 1995 held in San Francisco, California. "

Slide 11 includes an interesting quote on why the modern vortex theory still persists today:
"Sir Michael Atiyah:

"Stability. The vortex atoms are stable, as are physical atoms.
"Variety--There is a great variety of knots as there are a great variety of atoms.
"Spectrum--Vortex atoms have energy states, and vibration modes.
"Transmutation--Knotted vortex atoms change their knot type if their energy is increased beyond a certain threshold, as do atoms physical atoms change their atomic structure."

In Rado's Aethrokinematics, Stephen Rado develops a detailed, imaginative, and mechanically intuitive explanation for many of the mysteries of electromagnetism and quantum mechanics, beginning with the formation of a stable "vortex-donut" from an ideal gas system. This vortex-donut comprises an elementary composite particle that directs ether flows perpendicularly (with respect to the motion of the vortex) through the eye of the vortex system, i.e., ether flows into the top and out the bottom or vice versa. Such a vortex particle is equivalent to a dipole, with one end of the vortex system serving as a hydrodynamic source and the other end a hydrodynamic sink. Such a system would behave as a particle in most respects, yet would still allow a myriad of kinematically plausible descriptions of repulsion, attraction, and stable bonds.

A picture of Rado's "fan-magnet" from his website, for example, helps show how these flows would circulate. Such forces that are due to the ether flows and currents through the sink-source system are defined here as Rado forces.

3) More Materialistic Examples of Attractions, Repulsions, and Stable Bonds

Regardless of the Materialistic theoretical descriptions for various electromagnetic type bonds, attractions, and repulsions, it is undeniable that examples of such phenomena are abundant in Material media systems--and particularly with vortices.

At the website of the Fluid Dynamics Laboratory of Eindhoven University of Technology, The Netherlands, one finds pictures of a naturally occurring tripolar vortex in the ocean--with one central vortex being orbited by two smaller ones. The structure lasted for days.

At nonneutral Plasma Group at the University of California, San Diego, one finds pictures of a two vortex merger and an evolution to a vortex crystal.

A nice depiction of the Havelock Instability appears at the vortex dynamics website of Berkeley. The Havelock Instability helps describe the interesting phenomenon where the stability of vortices depends on the presence and location of other vortices--particularly in ring like configurations.

Organization of crystal structures also occurs with hard spheres immersed in liquids (particularly in microgravity conditions) as well as with immiscible liquids. The NASA website includes interesting descriptions of these hard sphere experiments. Here's a quote from their page:

"When uniformly sized hard spheres suspended in a fluid reach a certain concentration (i.e., the fraction of the total sample volume actually filled by the spheres), the particle-fluid mixture changes from a disordered fluid state, in which the spheres are randomly moving, to an ordered crystalline state, where they are arranged periodically. The thermal energy of the spheres causes them to jostle each other until they form ordered arrays, or crystals, because this arrangement allows each sphere the most freedom of movement. "

At the website of physics professor Dr. Paul Umbanhower, Northwestern University, one finds an interesting description of immiscible fluid experiments:

"Emulsions are composed of two immiscible fluids: one fluid forms a continuous phase in which the other fluid is dispersed as drops. Emulsions can exhibit interesting rheological behavior including spontaneous ordering as shown below."

At Umbanhower's website is another more astounding example of self-organized, stable, bonded structures that form due to Newtonian contact forces. These structures, called oscillons, form when a medium of granules, like brass balls or sand, are made to vibrate up and down. [Brunardot's Note. See: Brunardot's Pulsoids.] When these patterns were first discovered, they were reported in the science section of The New York Times:

From The New York Times, 9/3/96

by Malcolm W. Browne

"A group of physicists at the University of Texas has reported an astonishing discovery: when a thin layer of tiny brass balls is spread over the flat bottom of a container and the container is jiggled up and down at a certain rhythm, the balls spontaneously organize themselves into patterns that seem to mimic behavior of atoms, molecules and crystals.

"Simply by tuning the rate and intensity of the jiggling, the Austin-based group headed by Dr. Harry L. Swinney induced the creation of tiny peaks and dimples in an otherwise flat layer of brass balls the size of sand grains. These peaks and dimples, which the group has named "oscillons," [Brunardot's Note. See: Brunardot's Pulsoids.]  react with each other almost the way electrical charges interact: similar oscillons, like similar electric charges, repel each other and move apart, while opposite oscillons attract each other and even seem to form stable bonds.

"Sometimes, as shown in a series of remarkable photographs published in the current issue of the journal Nature accompanying the Texas group's report, the peaks and dimples even join together to form objects suggestive of atoms. Some join to form molecule-like objects, including polymers, and others form checkerboard arrays suggestive of the atomic lattice structures of crystals....

"Dr. Sidney Nagel, who heads a group of physicists at the University of Chicago studying granular materials...worries about drawing too many inferences from analogous but very different systems, for example, the brass-ball patterns seen at the University of Texas, compared with the analogous behavior of real electric charges, atoms, molecules and crystals. Interactions at the molecular and atomic level obey the statistical laws of quantum mechanics, while brass balls in motion are governed by Newton's classical laws of motion.

"I think that what Harry Swinney has done is fascinating," Nagel said. "He has these beautiful, very intriguing patterns that have charge-like characteristics, attracting or repelling each other, and interacting in complex ways.

“But we understand much more about what happens at the quantum mechanical level than we do about the behavior of granular materials in motion. For the brass-ball analogy of quantum mechanical processes to be useful, we would have to find some link between the analogy and the reality. I don't think right now we have a good idea where the analogy starts or ends, and although there certainly seems to be an analogy there, we have to be careful of it. " [Brunardot's Note. See: for the link.] 

Journal References of effect:

Umbanhower, P.B., Melo, F. and Swinney H.L. “Localized excitations in a vertically vibrated granular layer,” Nature, Vol 382 No. 6594, August 29, 1996, p.793-796

New and Views- "Patterns in the Sand," P.B. Umbanhower, Nature 389, 541

Both Umbanhower's website above and this website at the American Institute of Physics contain pictures of oscillons in action.

Still, despite these interesting examples, the binding forces of atoms and molecules remain a black box for which many possible materialist explanations may be imagined. Experiments have led to data which have allowed various aspects of these forces to be described with equations and principles. But determining the precise mechanistic model of atoms and molecules that underlie the effect will need more experimental research and elucidation. [Brunardot's Note. See: Brunardot's Pulsoids.] 

The above examples should only help prove that such binding forces in no way refutes the notion of Materialism and that there exist a surprisingly large number of mechanisms and materialistic theories that would account for this behavior.

4) Inelasticity

Although the most fundamental particle of the ether is postulated to be perfectly elastic (or at least the most elastic object possible), the collisions with composite, compressible objects will tend to be inelastic. Some of the momentum of the collision will increase the momentum of the composite particles relative to the frame of the particle, i.e., part of the momentum is converted into "heat."

II) Thermodynamics

1) First Law: Conservation of Energy

As momentum is always conserved and all collisions of base particles are elastic, kinetic energy is always conserved. And, of course, according to Materialism all energy is kinetic.

2) 2nd Law: Entropy

The second law was derived by Boltzmann mechanically (with elastic spheres), in 1877. The following educational web-sites help detail this: At the Victorian Web , a website devoted, in part, to nineteenth century science, science-historian Diane Greco writes:
"Maxwell's treatment left one fundamental question unanswered: if entropy almost always increases, its growth is irreversible, yet the laws of mechanics are reversible. How can entropy be a mechanical quantity?

"Addressing this problem in 1877, Ludwig Boltzmann provided the fundamental statement of statistical mechanics: the second law of thermodynamics does not hold absolutely, but is rather a statement of relative probabilities. Specifically, Boltzmann showed that if molecules in a gas have many equally likely microstates, the vast number of molecules with states at equilibrium overwhelms the very few at any other condition. Boltzmann thus defined the entropy of a gas as proportional to the logarithm of the number of microstates that define its macroscopic condition. (This constant of proportion, k, is known as Boltzmann's Constant.) When a system is not at equilibrium, its entropy is almost always increasing; equilibrium states have a tremendously high entropy. "

The website of the Institute of physics of Yugoslavia, contains more information:
"In the 1870s Boltzmann published a series of papers in which he showed that the second law of thermodynamics, which concerns energy exchange, could be explained by applying the laws of mechanics and the theory of probability to the motions of the atoms. In so doing, he made clear that the second law is essentially statistical and that a system approaches a state of thermodynamic equilibrium (uniform energy distribution throughout) because equilibrium is overwhelmingly the most probable state of a material system. During these investigations Boltzmann worked out the general law for the distribution of energy among the various parts of a system at a specific temperature and derived the theorem of equipartition of energy (Maxwell-Boltzmann distribution law). This law states that the average amount of energy involved in each different direction of motion of an atom is the same. He derived an equation for the change of the distribution of energy among atoms due to atomic collisions and laid the foundations of statistical mechanics."

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