A review of the basics of special and general relativity. The basis of both special relativity and general relativity is superfluid equations -- Maxwell's equations for special relativity and generalized superfluid equations for general relativity. Demonstration that a superfluid aether results in both special and general relativity as special cases. Resolution of the Feynman arguments against an aether as a gravitational source. Discussion of the Thirring-Lenz experiment tending to confirm physical aether medium versus "mathematical" or "continuum" cause of gravity.

Introduction

"According to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable."

A. Einstein, Sidelights on Relativity, 1922, page 23.

This paper examines one possible physically causative agent for gravitation of matter bodies. This causative agent is a superfluid aether. This aether is not matter, but matter is affected by the aether. Superfluidity is the basis for Maxwell's equations, special relativity, and general relativity.

The concept of the aether arose from the study of the behavior of wave action and light. Even before the kinetic theory of gases provided microscopic concepts, the study of the sensible world allowed a fairly consistent view of wave action. Light was clearly identified in the wave category of phenomena. The debate as to what the ultimate underlying nature of light was (wave or particulate) spanned several centuries of theory and experiment. Not until the twentieth century was it ever contended that "waves" of light did not have an underlying physical medium.

The main objection to fluid aether theories came from light's propagation as transverse waves. Up to the time of the general abandonment of deterministic (classical) physics at the microscopic level (with the rise of quantum physics in the 1920's) no "reasonable" way to explain this behavior of light was generally accepted. "The" aether theory being tested by the famous Michaelson-Morely experiment was the "solid" aether theory that was in ascendence at the time. This theory assumed that the aether was physically separate from matter -- that is, they were not related.

The demise of the concept of the aether resulted from the tumultuous evolution of the physical concepts of the early twentieth century (quantum theory and general relativity). Quantum mechanicists developed the concepts of "probability density" and non-causality. General relativists picked up on the shorthand of space-time developed by Minkowski in 1908 for special relativity and expanded it to a mathematical "space-time continuum." Although most specifically denied a physical medium, Einstein clearly realized that both special and general relativity were based on fluid dynamical models {Handbook of Physics, Condon and Odishaw, Page 2-50, Section 29}.

The Derivation of Maxwell's Equations

One of the most successful theoretical works in physics is Maxwell's theory of electricity and magnetism. Maxwell's equations united and mathematically quantified the interaction of electrical and magnetic effects. In deriving these equations, Maxwell made certain assumptions about the nature of the medium that carried electricity, magnetism, and light. The primary assumption used by Maxwell was that the underlying medium could be described using the perfect fluid vortex theory developed by Hemholtz.

"The consideration of the action of magnetism on polarized light leads, as we have seen, to the conclusion that in a medium under the action of magnetic force is something belonging to the same mathematical class as an angular velocity, whose axis is in the direction of the magnetic force, forms a part of the phenomenon.

"This angular velocity cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis. This is the hypothesis of molecular vortices.

"The motion of these vortices, though, as we have shewn ..., does not sensibly affect the visible motions of large bodies, may be such as to affect that vibratory motion on which the propagation of light, according to the undulatory theory, depends. The displacements of the medium, during the propagation of light, will produce a disturbance of the vortices, and the vortices when so disturbed may react on the medium so as to affect the mode of propagation of the ray."...

"... We shall therefore assume that the variation of vortices caused by the displacement of the medium is subject to the same conditions which Hemholtz, in his great memoir on Vortex-motion, has shewn to regulate the variation of the vortices of a perfect fluid."

J. Maxwell, A Treatise on Electricity and Magnetism, 1873, sections 822 and 823.

There have been attempts in the past to "expand" Maxwell's equations in the name of symmetry. One of these was the concept of magnetic monopoles. It was determined that magnetic monopoles could be inserted into Maxwell's equations and the equations would remain self-consistent and usable. The hunt for magnetic monopoles in the 1970's ended without any confirmed monopoles. Another attempt was the expansion of Maxwell's equations to include positive and negative charges as "carriers" of the weak nuclear force. This is what is now known as the "electroweak" force. This expansion of Maxwell's equations is also self-consistent and usable. In this case particles of mass roughly in the range expected have been found.

What is missing from these expansions is any physical concept that would give rise to these expansions. It must be stressed that Maxwell derived his equations. He did not just write them down and then note that they happened to work. The derivation was the direct result of the physical postulates (superfluid aether and vortices) he made in his derivation. Magnetic monopoles and "weak" nuclear theory do not arise from Maxwell's equations. There is therefore no physical basis for expecting these equations to work.

The special theory of relativity was derived from Maxwell's Equations. The Special Theory was a leap of quantification based on an apparent anomaly. Maxwell's equations imply that the measured speed of light (in a vacuum) is constant for any observer -- regardless of how that observer was moving relative to the source of light.

In developing Special Relativity, Einstein postulated the universality of the speed of light and applied the mathematical consequences to see where they would lead. The primary result of the special theory of relativity was the equivalence of matter and energy (E=mc2). The Lorentz-Fitzgerald relations had been developed earlier from standard aether wave theories (which is why they are called Lorentz-Fitzgerald equations instead of Einstein equations). Special Relativity is therefore based on the superfluid derivations of Maxwell and Hemholtz.

Minkowski Space-Time

The concept of "space-time" was first developed by Minkowski in 1908 for use with the Special Theory of Relativity. In this first incarnation, Minkowski pointed out that the mathematical equations may be written in a shorthand form by regarding time and the three physical coordinates as four coordinates in a four-dimensional space, called "space-time."

In an inertial, cartesian reference frame a pulse of light emitted at time t=t0 and location x = x0, y = y0, and z = z0 will be noted at a point x, y, z, t given by the equation {eq 4.2 An Introduction to Tensor Calculus, Relativity and Cosmology, D Lawden, 1975, Wiley and Sons}:

This equation describes an expanding spherical shell for the light pulse. A shorthand version of this equation was developed by Minkowski by the use of the mathematical device of setting:

x = x1, y = x2, z = x3, and ict = x4; where i = SqrRoot (-1)

The standard Minkowski space-time is given as {eq. 4.5, An Introduction to Tensor Calculus, Relativity and Cosmology, D Lawden, 1975, Wiley and Sons}:

General Relativity

Einstein's "field" equations may be written in the tensor form:

In this form, Gaß is the "Einstein Tensor", Lambda is the "cosmological constant" (usually set to zero), g is the "metric" tensor, k is a constant set to 8p, and Taß is the "stress-energy tensor." This form is actually shorthand notation for ten coupled differential equations {Equation 8.7, A first course in general relativity, Schutz, Cambridge University Press, 1990}. The value of 8p is obtained by demanding that Einstein's equations predict the correct behavior of planets in the solar system -- the Newtonian Limit {ibid, p199}.

The claim is currently made that the mathematics of General Relativity requires the curvature of space. The question "How?" is answered with "It just does." The question of why the object travels the shortest path in curved space is also not addressed. General Relativity can give no answer because these are the basic postulates of the theory.

The differences in the concepts between General Relativity and Newtonian gravity are:

Newtonian: Mass (somehow) causes a gravitational force which causes true acceleration.

Einsteinian: Mass (somehow) causes a warping of space which results in apparent acceleration.

But the description of causation as a curvature of space is not sufficient to encompass what else General Relativity includes. If spacial curvature were all there were to General Relativity, there would be no difference in calculations between General Relativity and Newtonian gravity. General Relativity also imposes superfluid equations onto gravitational relationships. The imposition of superfluid equations has a very significant effect: the speed of propagation of gravity is thereby made finite. The finite transmission speed (and related superfluid properties) is the significant difference between Newtonian gravity and General Relativity.

General Relativity is a relativistic theory of gravity. The first postulate of General Relativity is that the source of the gravitational field is the stress-energy tensor of a perfect fluid, T {sections 4.6 & 4.7, A first course in general relativity, Schutz}. This "stress-energy tensor" contains four non-zero components. These four components are the density of the perfect fluid and the pressure of the perfect fluid in each of the three physical axes. A perfect fluid in general relativity is defined as a fluid that has no viscosity and no heat conduction. It is a generalization of the "ideal gas" of ordinary thermodynamics.

Newtonian gravity is regarded as the result of a force. General Relativity distinguishes gravity from all other forces because "all bodies given the same initial velocity follow the same trajectory in a gravitational field, regardless of their internal composition" {ibid, p121}. Specifically, attempting to define a primal reference frame is considered "vacuous, since no free particle could possibly be a physical 'marker' for it" {ibid, p122}. This second postulate became the Equivalence Principle: Uniform gravitational fields are equivalent to frames that accelerate uniformly relative to inertial frames.

Although it is often stated that General Relativity shows that mass curves space, what GR actually states is that a curved spacetime represents the effects of gravity. The distinction is critical. All GR really requires is that free particles (and photons) act as if space were curved in some manner. All this means is that their trajectories curve in the presence of a massive object {ibid, p125}.

The same argument could be made for Coriolis forces. If we examine the coriolis forces that affect trajectories of moving objects over the surface of a rotating planet, we could reach the same results by postulating that Latitude "curves" space. The results of our calculations would be identical to those based on the physical cause. But we would not gain any knowledge of the cause, because we would not be looking for one.

In the direct application of its basic postulate, General Relativity suffers from the same basic weakness as the Newtonian quantification of gravity. No basis is given in General Relativity for how mass "curves" space, why masses follow the "shortest" path through curved space, or why the principle of equivalence exists. This is "action at a distance" reformulated. Einstein himself noted this weakness in that matter had to be added in to the equations "by hand" {The Reluctant Father of Black Holes, Scientific American, June 1996, p83}.

Thirring Lenz Experiment

General Relativity has some weaknesses in explaining accelerations seen in the vicinity of massive, rapidly spinning objects. In this situation, the Einsteinian/Newtonian quantification predicts no effects on first principles. But the Einsteinian formula solutions "require" a non-zero tangential velocity to be imparted by a spinning mass.

First principles of a space-time continuum cannot explain accelerations in the vicinity of rapidly rotating massive objects because the "warp" of space-time does not change with the rotation of the object. It has been explained that "inertial dragging" takes place. The explanation of inertial dragging (reference frame dragging) is a description without identification of a cause that can be traced to the base theory {pp 6 & 18-20, Rotating Fields in General Relativity, J. Islam, 1985}. According to this reference "(t)he precise connection in all its details has not yet been worked out."

But such a "drag" implies that there is a friction in the motion of mass with respect to the space-time continuum itself. Friction due to motion with respect to the continuum requires that the continuum be a fixed, primal reference frame -- which must be denied due to the basic assumption of relativity, that there can be no primal reference frame. General relativistic formulations show the requirement of tangential motion when the assumption is made that the continuum is a superfluid.

Resolution of Some Arguments Against

Aether Cause of Gravity

LeSage first discussed the possible "shadowing" of "ultra-mundane particles" as a cause of gravity in 1784. This approach has been abandoned several times by different people. According to Feynman, LeSage-type theories fail as follows:

"This particular idea has the following trouble: the earth, in moving around the sun, would impinge on more particles which are coming from its forward side than from its hind side ... . Therefore there would be more impulse given the earth from the front, and the earth would feel a resistance to motion and would be slowing up in its orbit. One can calculate how long it would take for the earth to stop as a result of this resistance, and it would not take long enough for the earth to still be in its orbit, so this mechanism does not work. No machinery has ever been invented that 'explains' gravity without also predicting some other phenomenon that does not exist."

R. Feynman, Lectures on Physics, 1963, volume 1, chapter 7, pp 9-10

Performing a calculation of the type above leads to a "drag" on the order of 10-13 m/sec2 for the earth in orbit {Dr. Steve Carlip, private communication to Paul Stowe}. A continuous acceleration on this order would stop the earth in around a million years.

But there is an unstated assumption in Feynman's argument that the "aether particles" are not circulating with the Earth's orbital motion. This is an excellent first assumption, but is it true? The presumption of particles circulating at the same orbital speed of the Earth appears at first to be only an excuse for "saving the theory."

However, we saw above that the mathematics of General Relativity and the observed Thirring-Lenz effect requires that there be some rotational motion in the vicinity of a rotating body. According to the primary assumptions of General Relativity, the Thirring-Lenz effect has no "basis." A superfluid aether would cause accelerations as a result of imparting a vortex spin on the aether field which would then accelerate the target body.

The sun is rotating rapidly in the direction of planetary (earth) orbits. According to General Relativity, the only solution that is not possible in such a situation is irrotational motion in the aether corpuscles. The key assumption in the argument that the earth "would impinge on more particles which are coming from its forward side than from its hind side" is based on non-circulating particles. According to General Relativity, this assumption is found to be invalid! Also, if the aether fluid is indeed a superfluid, once a rotation of the fluid is started it will continue without loss of energy.

The Feynman argument against the LeSage-type hypothesis was completely plausible, for there is no obvious reason to expect that the aether would be rotating along with the earth. But field rotation is both observed and a mathematical requirement of the superfluid vorticity in General Relativity. So, for the moment at least, our theory remains consistent with General Relativity.

This is not the only possible explanation for the earth not spiralling into the sun. The Feynman argument rests on the additional assumption that gravity (and the aether drag) is the only force acting on the earth's orbital motion. But -- in order to contract from a protostar -- the sun must have somehow lost most of it's angular momentum to the planets. If this mechanism were the result of the rotating solar magnetic field, the solar field will interact with the magnetosphere of the earth (and the plasma within it). This interaction will lead to a transfer of angular momentum from the sun to the earth. In short -- all possible sources of orbital impulse must be examined before we throw out a superfluid aether.

The basis for Feynman's argument was the same as one made for the irrotational earth (geocentric cosmos), and dealt with by Galileo in his Dialog on Two World Systems in 1632. The argument went as follows:

According to (Claudius Ptolemy and Tycho Brahe), if the earth were moving (rotating) an object thrown vertically upward would not descend along the same line ..., the point on the earth under the object would have shifted while the object was in the air. Furthermore, if the earth were moving (rotating) from west to east, the direction required to explain the appearance of the heavens, then ... (p)eople on the earth would perpetually feel an east wind, just as a rider feels a wind in his face as he travels along. ...

Galileo had refuted the arguments ... in his Dialogue Concerning the Two Chief World Systems. Objects ... belong to the moving system of the earth, and as parts they participate in the motion of the whole in addition to their own observable motions."

Radner and Radner, Science and Unreason, Wadworth Publishing Company, 1982, p34

As the air moves with a rotating earth, so the aether moves with the orbiting earth. They are part of the same "world system." It is only because the aether is so much less noticeable than the air (to us) that we accept Feynman's argument without close examination. By General Relativity and the Thirring-Lenz effect, the aether MUST move around the rotating sun and the orbiting earth. A Feynman-type argument can only be used if it is demonstrated beyond any doubt that the two components are not part of the same "world system." Whenever one component is affected by the other they must be part of the same, coupled, world system -- and the interdependence cannot be dismissed without serious thought. In this case the wind affects the surface of the earth or the aether is presumed to affect the earth's orbit.

Even if the Thirring-Lenz effect has no bearing, there is also the gravitational "sling" argument. If gravity is the result of a superfluid aether, then the speed of propagation of gravity must be finite. If the speed of gravity is finite, then orbiting masses will accelerate out of orbit. This is supposedly due to the "lead" of the gravitational force, due to the past position of the second object. This is one "push" that could overcome or balance the "drag" of the aether. Proponents of GR state that it is only the "delicate balance" of GR that keeps the orbits from accelerating or decelerating.

Summary

Maxwell's equations were explicitly developed as fluid dynamical models, and require an underlying physical medium. Special relativity was derived from Maxwell's equations. General relativity is based on perfect fluid equations.

Thus, any theory based on one of these three theories implicitly retains all fluid dynamical properties. Any denial of an underlying physical medium by such a theorist is therefore hollow -- and merely shows ignorance on the part of the practitioner concerning the history and derivation of the equations that are being used.

"Fundamental challenges to disciplines tend to come from outside. It is customary for students to be introduced to their fields of study gradually, as slowly unfolding mysteries, so that by the time they can see their subject as a whole, they have been so thoroughly imbued with conventional preconceptions and patterns of thought that they are extremely unlikely to be able to question its basic premises."

Martin Bernal Black Athena: The Afroasiatic Roots of Classical Civilization, Vol. I, 1987