Does the Universe Have a Speed Limit

Does the Universe Have a Speed Limit?=

(A new way to look at relativity, space-time, and aether)

Tom = Van Flandern

Meta Research / <tomvf@metaresearch.org>

"The problem with relativity isn't that it's hard to understand, it's that it is hard to believe." – author unkn= own, conveyed by Larry Burford

(This paper= is dedicated to the memory of Richard Hazelett, 1923-2002 [[1]]; and J.P. Vigier, 1920-2004. [= [2]])

Abstract. What gives physics, as contrasted with mathematics, its intellectual appeal is its ability to explain nature with simple models. Some of that appeal has been lost through an increasing reli= ance on mathematical and geometric interpretations of relativity. However, such interpretations are not mandatory, and indeed may violate the logical constraints imposed by physical principles. Pursuing only physically viable interpretations of the same equations leads us back to the kinds of simple models that attracted students to physics in the first place.

Introduction=

            Newton’s uni= versal law of gravitation was a triumph for both physics and mathematics. Although= the law did not reveal the mechanism of gravity, it allowed practical predictio= n of the motions of bodies in gravitational fields that, for most applications, = was accurate to a few parts in 100 million. Gravitation became the most precise science. Its predictions were so dependable that, when eclipses of the moon= s of Jupiter by Jupiter’s shadow in the 17^th century were found= to occur early or late by as much as eight minutes, deficiencies in the law of= gravity were not high on the suspect list of possible causes. Roemer eventually pro= ved that the cause was the finite speed of light, and obtained the first good estimate of light’s velocity – about 8 minutes to traverse the radius of the Earth’s orbit. The eclipses would appear early when the Earth was on the same side of the Sun as Jupiter, and late when Earth was on the far side, because the travel time for light from Jupiter to Earth, which averages over 40 minutes, would get shorter or longer as Earth’s dist= ance from Jupiter decreased or increased, respectively. See Figure 1.

            Newton’s law remained the paradigm for gravitational dynamics until it was superceded by Einstein’s general theory of relativity (GR). That theory was able to explain a small effect that Ne= wton’s theory did not: a slow advance of the perihelion (point closest to the Sun)= of Mercury’s orbit. In addition, it predicted certain new effects on electromagnetic phenomena: the bending of light as it moved past the Sun by twice the amount that the Sun’s gravity would have on a particle movi= ng at that speed; a redshift of light (or a slowing of clocks that use electromagnetic phenomena as a basis for keeping time) in a gravitational p= otential field; and an extra propagation delay for light or radar beams passing the = Sun (or any significant mass). One by one, these predictions were verified to within 3% accuracy or better with modern, high-precision observations (very-long-baseline interferometry, lunar and satellite laser ranging, planetary radar ranging, spacecraft orbiting planets, etc.). So GR has now become the accepted model for predicting gravitational phenomena and the motions of bodies in space.

            The first introduction of major points made in this paper is marked by letters = in the left margin. See Table I for a description of these points.

The existence of two physical inte= rpretations of GR

      = ;      GR’s outstanding success at mathematically predicting phenomena influenced by gravity naturally led to a desire to have a deeper understanding of the phy= sics of gravity. Two different interpretations arose to explain the physics behi= nd Einstein’s equations. These have come to be called the “field interpretation” (gravity is a classical force) and the “geometr= ic interpretation” (gravity is just "curved space-time"). Eddington’s 1920 book refers to the possibility of explaining at least some GR phenomena with an optical medium instead of curved space-time [= [3]], indicating an awareness of two interpretations of the theory even that early. But many later physicists se= emed to adopt one or the other interpretation and use it without further qualification. This was possible because the mathematics of GR was the same either way. Indeed, many scientists came to believe that that the physical interpretation was not of great importance as long as the mathematics of th= e theory continued to predict phenomena correctly.

            In more recent times (i.e., over the last generation), the geometric interpretation of GR has become so dominant that the field interpretation is often no longer taught to today’s physics students and future relativists. But it should be taught because it is an important element in achieving a deeper physical understanding of the theory. Many of the great physicists of the last century, including Einstein himself, were partial to= the field interpretation. More recently, Nobel laureate physicist Feynman descr= ibed the two interpretations with these words:

“It is one of the peculiar aspects of the theory of gravitation, that it has bo= th a field interpretation and a geometrical interpretation. … the fact is = that a spin-two field has this geometrical interpretation: this is not something readily explainable – it is just marvelous. The geometrical interpretation is not really necessary or essential to physics. It might be that the whole coincidence might be understood as representing some kind of invariance. It might be that the relationships between these two points of = view about gravity might be transparent after we discuss a third point of view .= .. to get a feeling for some directions which we might take in attempting to understand how gravity can be both geometry and a field.” [= = [4]]

      = ;      In a meaningful sense, this paper discusses just such a possible “third point of view” as Feynman envisioned. Perhaps we have a better understanding now than Feynman did then about why it was almost inevitable = that two different interpretations of the theory would arise. To state the point succinctly, the expression “gravitational field” is used with t= wo entirely different meanings that are rarely distinguished by those using the phrase. The modern relativist normally means “gravitational potential field”, and the modern dynamicist or celestial mechanician almost alw= ays means “gravitational force field”, or equivalently, “gravitatio= nal acceleration field”. As someone specializing in celestial mechanics, I came to be keenly aware of the problem when I tried to have discussions wit= h mathematical relativists and found we were virtually unable to communicate because we we= re speaking of different concepts while using the same words.

            Indeed, those trained in these respective disciplines seem at times to have not even the math of GR in common. The 4-dimensional field equations and their solut= ions most mathematical relativists use when discussing implications of the theor= y (such as black holes) deal with the gravitational potential field. By contrast, t= he equations of motion (expressions for ordinary accelerations in flat, Euclid= ean space) that most dynamicists use to predict motions and compare with observations deal primarily with gravity as a force or, equivalently, as an= acceleration. (Force is just mass times acceleration.) The former math uses 4-D tensors, = the latter uses 3-D vectors.

The relativists point out that their solutions to the field equations are often exact, and in any case are closer to the Einstein equations. The dynamicist= s point out that their equations of motion, although approximate, can always be mad= e at least as accurate as the observations and experiments; are essential to the comparison of theory and observation; and are what ultimately give the enti= re theory legitimacy (i.e., take it from the realm of pure math to applied mat= h). Unfortunately for communication, each side describes the object of its equations as ̶= 0;the gravitational field”. In= this paper, we will qualify the expression “gravitational field” by inserting the word “potential” or “force”, as appropriate. And where the meaning of “field interpretation” (defined above) might be ambiguous, we will associate it with forces and ordinary (i.e., 3-space) accelerations, while associating the geometric interpretation with the geometry of the potential field.<= /p>

The geometric interpretation of GR=

      = ;      In classical physics, space and time are simply dimensions, mental concepts us= eful for the measurement of extent and change, respectively. As pure concepts, t= hey are of course not susceptible to manipulation by material, tangible bodies = or by their states of motion. In Euclidean geometry, space is flat, axes are straight and orthogonal, and time is unique and uniform. So to determine the distance between any= two points in space at some fixed time, we simply use the Pythagorean theorem: = . Here, the new quantities with the Greek capital delta prefix are the three spatial components of the interval between the two poi= nts. Hence, we describe positions and motions using just these coordinates as in “3-space”. In geometric GR, this Euclidean distance is generali= zed to a “space-time” path length : , where is the spee= d of light. Such a space-time path is called a "geodesic" path to distinguish it from a distance in space. Because there are now four coordinates, we refer to descriptions in this form as in “4-spaceR= 21;.

            The core idea behind geometric GR is that “gravity is just geometry”= ;, in explicit contrast to the idea that gravity is a force. Indeed, it is often = said that “gravity as a force does not exist” when discussing geomet= ric GR. More generally, geometric GR posits that bodies follow the geometry of space-time on geodesic paths because the geodesic path is the nearest equivalent of a straight line available in space-time (which here is the equivalent of “4-space”, a purely mathematical combination of 3= -dimensional-space and imaginary time [*]) whe= n space-time is curved by the presence of mass. The mantra of geometric GR is, “Ma= ss tells space how to curve, and space tells matter how to move”. Howeve= r, even in that mantra we have the seeds for later confusion and disagreement.= That seemingly innocuous word-switch here from “space-time” to “space” leads to problems with the physical interpretation of G= R, as we will shortly see.

            Because geometric GR is primarily about the gravitational potential field, it implicitly assumes that the normal relation “acceleration is the grad= ient of potential” means that potential causes acceleration. However, we m= ust not forget this is just an assumption, and one that has considerable influe= nce on which physical models for gravitation are considered viable. The causali= ty might well be the other way around, with gravitational force causing the potential field to have a gradient (a slope through space).

            Geometric GR has no propagating gravitational force because acceleration is imagined = to be a consequence of curved space-time geometry. So a static gravitational (= potential) field is like a frozen waterfall, having no moving parts (Figu= re 2). As such, the field carries no momentum, and deposits no energy into the bodies it affects.

            The importance of the potential field is that gravitational potential causes gravitational redshifts and clock slowing, propagation delay, and bending f= or electromagnetic waves, and is a factor in determining the “perihelion advance” effect on orbits as predicted by GR. Otherwise, potential is= not a factor in determining the motions of material bodies through 3-space. Newton’s gravitational force law, the main contributor to ordinary gravitational acceleration, would work just as well if there were no such thing as gravitational potential. Although we often mathematically derive accelerati= ons from changes in potentials, nothing compels us to do it that way. And we wi= ll shortly see advantages to reversing the direction of causality, with gravitational force causing the changes in potential.

The field interpretation of GR

  &nbs= p;         If half-a-dozen relativists were asked to define the field interpretation, we might hear as many answers. Indeed, the meaning of the concept has evolved = as discussions of the theory have evolved over time. Here we will adopt the vi= ew that, in field GR, gravity is a classical acceleration-producing force that propagates from the source mass to a target body. The gravitational field around a source mass is a field of force or acceleration vectors. The force field and the potential field are separate entities. Although the direction= of causality is often not of concern, physical models work best when the force/acceleration field acts on and shapes the potential field, rather than vice versa. (This is analogous to acceleration changing velocity, not vice versa.) In some of these physical models, the potential field has all the properties of an optical medium. It also has some properties in common with= the “light-carrying medium”, “luminiferous ether”, or “elysium”, which are variants on the same basic concept.[†][= = [5],= = [6]] None of these concepts is required to produce ordinary gravitational acceleration.

            Meanwhile, the gravitational-force-carrying field itself, even when “static̶= 1; as for a non-moving source mass, is always a dynamic field in the same sens= e as a flowing waterfall (Figure 3). It may look unchanging from a distance. But whe= n examined closely, we see that every drop of water is continually being replaced by another from behind. As such, the acceleration field of GR does carry momen= tum from the source mass to the target body, and does deposit energy in any bod= y it affects. This follows from the definition of force in classical physics: the time rate of change of (3-space) momentum; and from the necessity (from the= principles of physics) that all forces involve contact pushes. [= [7]] Inasmuch as momentum is proportional to velocity, the momentum-carrying entities must have some velocity, like the water droplets in the flowing waterfall.

  &nbs= p;         Experimentally, we know that force and acceleration have no direct effect on gravitational redshift or clock rates or electromagnetic wave propagation delay or light-bending – effects first introduced into gravitation by GR and related to gravitational potential. This absence of force effects remains t= rue even at accelerations as high as 10¹⁹g, where g is the acceleration of gravity at Earth’s surface. [[8]] However, gravitational acceleration is the primary determinant of the motio= n of bodies in a gravitational force field. The special GR effects over and above ordinary gravitational force must then arise only in the gravitational potential field, which apparently has all the properties of an optical medi= um.

Gravitational potential vs. gravitational acceleration

            The two interpretations of GR use two different concepts for “gravitation= al field”. Let’s now examine the relationship between these two concepts. Are they two different manifestations of the same thing, or are t= hey two independent things that appear to be related because they interact? We = will examine this from the perspectives of physics and mathematics.

            Physically, it is important to note that the strength of the local gravitational potent= ial itself (as contrasted with its gradient) is almost completely irrelevant to the mo= tion of a target body. That motion is determined to great precision by the local gravitational acceleration (which is the force per unit mass) alone, regard= less of the strength or weakness of the local potential. By contrast, if we are seeking the effect of gravity on the rate of ticking of a clock, only relat= ive speed and gravitational potential matter, but not acceleration or force.

            For example, Figure 4 shows a clock inside a uniform spherical shell. S= uch a clock feels no gravitational force because, as is well known in dynamics, gravitational forces from all parts of the shell cancel. However, the gravitational potential does not cancel, although it is uniform throughout = the shell interior. So the rate of the clock is slowed by the amount of the potential, which depends on the mass of the shell and could be substantial.= A similar example is presented by an infinite wall of uniform density. Away f= rom the wall, the force is everywhere constant and unrelated to the absolute st= rength of the potential, which likewise tends toward some constant value near the wall.

            Figu= re 5 shows a pair of identical clocks suspended from a tower. The one on the right is released and begins a free fall. Before the acceleration has a chance to change that clock’s velocity and therefo= re its rate of ticking, there is no effect on the rate purely as a consequence= of being in a state of free fall. The two clocks tick at the same rate until t= he falling one picks up speed.

<= ![endif]>  &nbs= p;         Now let’s examine the math of potentials and accelerations. Letbe the gravitational constant, andbe the mass of a source producing a field around itself. = If we measure that field at some point at distancein directionfrom the source mass (where is the vector from the source mass to the field point), t= hen the Newtonian gravitational potentialat that point is. The Newtonian approximation is sufficient for the qualitative distinction being made here. Of course, potential is a scalar a= nd has no associated direction. At the same point, the Newtonian gravitational acceleration is , where is the acceleration vector of a target body or massless f= orce field point, directed toward the source mass. (Each dot represents a deriva= tive with respect to time. Bold symbols with arrows are 3-space vectors, and bold symbols with carets are unit vectors.)

            {Note that celestial mechanics actually deals with accelerations (which are observable) rather than forces (which are usually only inferable). To conve= rt the acceleration into an inferred force, we would have to put a target body with massat the force field point, and use = Newton’s second law, . However, that is an unneeded complication because the motion of a body in a gravitational force field is independent of its own m= ass.}[‡] [⁷]

            The mathematical relationship between these two concepts is that gravitational acceleration is the negative of the gradient of gravitational potential: , where , and are the components of in the orthogonal directions respectivel= y. These three components are unit vectors centered on the source mass. Physic= ally, the gradient is essentially the slope of the potential field at the point of interest, and its negative naturally points toward the source mass.[§]

            At this point, we come to a problem that is usually ignored in both the geomet= ric and field interpretations of GR, but which is critical for any meaningful physics that might be associated with the concepts of potential and acceleration. If the point of interest is fixed relative to the source mass, then the instantaneous and retarded directions of the source mass from the point of interest are the same, and the above relation works without ambigu= ity. However, if the given point of interest represents a target body with a transverse motion relative to the source mass (as for the Earth orbiting the Sun), then the instantaneous and retarded directions of the source mass from the target body are two different directions in space. That leaves us with = an open question: Should the gradient relating acceleration and potential use instantaneous or retarded coordinates? I.e., should the negative of the gra= dient, and therefore the acceleration, point toward the instantaneous or retarded source mass location?

            The answer, as we will see, depends on which interpretation of GR is being invo= ked. To see why, we next examine the effect of propagation delay, which will show why the answer to our question makes a big difference.

The effect of propagation delay

            Propagation delay can cause a time lag in the application of the force to a target. The main signature of propagation delay when the target is moving relative to t= he source is to change the effective direction of application of the force to = the target. In astronomy, this change in the angular direction of a propagating entity due to a relative motion of the target is called “aberration”. See Figure 6. If the entity (e.g., our force) has a propagation speed of and the transverse component of the target’s relati= ve speed is, then the aberration angle is . For cases of interest here, >>, so the aberration in radians is simply. The source sees that as the angle through which the tar= get moves during the projectile transit time, or as the angle by which the projectile must lead the target when launched in order to arrive at the same place as the target at the same time. The target sees it as the angle moved= by the source during the same time interval; i.e., the difference between the retarded and instantaneous directions of the source.

  &nbs= p;         All motion is relative, so no experiment can tell the difference between a fixed-source, moving-target situation and a moving-source, fixed-target situation. I.e., both perspectives are equally valid. Moreover, the aberrat= ion angle represents a real, physical difference of path direction for the projectile depending on the reference frame, not just an illusion; and as a consequence, any force applied to the target by the projectile acts from the direction of projectile travel seen by the target, not that seen by the sou= rce. That is obvious for sub-light-speed projectiles; for example, encounters am= ong balls moving on a pool table or arrows shot at a moving target or water waves act= ing on a moving boat. It is equally true for projectiles moving at lightspeed, = such as the force of solar radiation pressure acting on dust particles or balloon satellites. Logically, it should be true for projectiles of any speed.=

            To see exactly why a force applied to a moving target must act at an angle to = the radial direction from a fixed source, visualize the target in Figu= re 6 as having a finite width and open windows on both sides. Then the projectile will enter from a forward window on the source-w= ard side, and leave by a more rearward window on the opposite side, because of = the forward motion of the target during the time it takes the projectile to cro= ss the width of the target. If the projectile enters via a rearward window, it= may hit the back wall of the target, showing that a component of its force must= act to oppose the forward motion of the target. (See an animation of this figur= e and moving geometry at http://metaresearch.org/media%20and%20links/animations/aberration04.s= wf.)

            So the principal manifestation of propagation delay is aberration, which must always exist for any type of projectile (whether particle or wave or wavicl= e or other) moving linearly between a source and a target with relative motion. = And the aberration of projectiles acts to oppose the relative motion of the tar= get, thereby assuring that the angular momentum balance between source and target cannot, in principle, be preserved. (I.e., some of the linear momentum delivered to the target by the projectile changes its angular momentum also= .) The target angular momentum can be preserved in practice only by having project= ile speeds so high compared with the relative motion of source and target that aberration is negligible.

            Therefore, the answer to the question posed in the preceding section about the directi= on of the negative of the gradient must be answered in favor of the retarded direction of the source. However, in both gravitation and electrodynamics, = this answer will change orbital angular momentum, causing all orbits to be spira= ls (inward for repulsive forces and outward for attractive forces). In light of this inconvenient fact, three propositions exist to justify the use of instantaneous coordinates for the gradient:

(1)&= nbsp; Deny the existence of momentum carriers (project= iles) between a source mass and a target body, thereby denying that gravity is a force. Then postulate that “gravity is just geometry”, the appr= oach taken in geometric GR.

(2)&= nbsp; Postulate the existence of a velocity-dependent = force arising from the force field, as needed to conserve angular momentum. This force must exactly cancel the main effect of propagation delay, aberration.= This approach avoids the necessity of having momentum carriers propagating faster than light in forward time, in violation of SR.

(3)&= nbsp; Postulate momentum carriers (projectiles produci= ng forces) that propagate so fast relative to velocities of target bodies that aberrat= ion is negligible. This requires propagation at speeds much faster than light in forward time.[**] Whi= le not allowed by SR, this solution is allowed by the mathematically equivalent and observationally viable Lorentzian Relativity (LR).

Problems with geometric GR

            The word “space-time” has led to considerable misunderstanding of GR because it begs the student to think of 4-space as simply 3-dimensional spa= ce plus time. However, in reality, the space-time metric (e.g., the formula for the square of the distance between two points) consists of the square of the product of the speed of light times the elapsed time interval between the t= wo points minus the sum of the squ= ares of the x, y, and z components of the spatial distance. That minus sign make= s each of the spatial coordinates unlike the scaled time coordinate, and the metric unlike what it would be if time were simply a fourth space-like dimension.<= o:p>

            Consider a practical example of this difference. Earth’s orbit around the Sun = is an ellipse with the Sun at one focus, to good approximation. Consider any t= wo points along that orbit, A & B, occupied by the Earth at different time= s. See 7. If gravity were “just geometry” and = time were like a fourth spatial dimension, then the shortest distance between A = and B would be that described by a taut rope stretched between those two points. The actual path followed by the Earth is a considerably longer distance requiring more time to traverse than if the Earth simply moved on a straight line through space.

  &nbs= p;         This example shows us two things. First, any hypothetical “curvature of space” is not a significant factor in determining the Earth’s trajectory because taut ropes (which must follow any curvature of space) do= not curve. And second, whatever “space-time” means, it is not simply space plus time. Yet in GR, the metric is an extremum along the path a body actually follows through a gravitational force field (e.g., along the orbit= in the figure). What, therefore, does the metric mean, if its square is not si= mply the squares of spatial and temporal distances combined?

            Consider the simple case of flat space-time (no gravitational field). Let the 4-space coordinates be, and the space-time path length be. Then the metric is:

To see the true natur= e of a space-time path, we divide everything by and note th= at, where is spatial = velocity. Then the metric becomes. The coefficient on the right side may be recognized as = closely related to the relativistic time dilation factor, whereis always greater than or equal to unity. So the metric becomes simply.

      = ;      In this simple form, we can see that both sides of the metric equation describe time intervals. is of course an interval in “coordinate time”, unaffected by gravitational fields or by motion. is an interval of “proper time”. We will deno= te this interval by. According to relativity, proper time describes the actu= al readings on any clock whose rate may be slowed by motion relative to the adopted coordinate frame and/or by a gravitational potential. So is the same as. This makes the distance traveled by a photon during a proper time interval. The important point her= e is that in particul= ar and space-time in general have a primarily time-like character rather than a space-like one or a combination of the two. So when we speak in relativity = of “space-time curvature”, we are speaking primarily of a clock-slowing effect, and not something that can be thought of as a curvatu= re of space. This is true even when a gravitational potential field is present. The primary effect of such a gravitational potential field is a further difference between coordinate time and proper time arising from gravitation= al potential; specifically, , where is always l= ess than or equal to unity. Note that the two relativistic factors and differ from unity by quantities of the same order. This is because and are of the same order, and indeed are equal for circular orbits.[††]

            These considerations have important implications for the geometric interpretation= of GR. The most basic is that the idea that “gravity is just geometry= 221; in geometric GR may now be seen as having dubious merit because “curv= ed space-time” is primarily a description of clock behavior; because tim= e (being one-dimensional, unidirectional and intangible) by itself has no geometry; = and because gravitational acceleration is not caused by any curvature of space. Note th= at this point does not question any aspect of GR as a valid mathematical theor= y, but only questions the physical meaningfulness of one particular interpreta= tion of that theory.

            Because the teaching of GR has evolved toward the geometric interpretation exclusiv= ely, some of today’s relativists have come to think of the 4-space model as reality. They are surprised to learn that relevant astronomical observation= s always involve 3-dimensional spatial accelerations measured against the proper tim= e of the observer. It is therefore only through the vehicle of mathematical expressions for this 3-space acceleration, called “equations of motion”, that GR is validated through successful comparisons between theory and observations. Solutions to the Einstein field equations are of no practical value in that regard, and must be converted to equations of motio= n before comparisons can be made.

That is done by using solutions (such as the well-known “Schwarzschild solution” to the field equations to form a Hamiltonian or a Lagrangia= n, then taking partial derivatives to derive equations of motion. This is a process quite similar to forming the gradient of a potential, and involves = the same decision, whether made implicitly or explicitly: Should the partial derivatives use instantaneous or retarded coordinates? While this issue is = usually not raised explicitly, instantaneous coordinates are always assumed in gravitation (and electrodynamics) because the alternative leads to equation= s of motion that quickly depart from reality. Once again, one of the same three choices previously mentioned must be invoked, at least implicitly, to justi= fy this choice.

Geometric GR is not physically via= ble

      = ;      Geometric GR is often taught by referring to the “rubber sheet analogy”, found in many textbooks, wherein the gravitational potential field is liken= ed to a rubber sheet with a huge dent located at a source mass M. See Figu= re 8. A target body sits on the sloping side wall of t= his dent at some point P. In the static situation, there is no ambiguity. The rubber sheet is like the gravitational potential field of M, and the slope = of the side wall is like the gradient of the potential. In the static case, the gradient at P (the analog of gravitational force) is unique and unambiguous, and its negative points at M.

  &nbs= p;         Consider the case where M remains fixed on the rubber sheet, and P has a transverse motion. Then the direction of the negative of the gradient would still alwa= ys point toward the instantaneous position of M because it is independent of the transverse motion of P; i.e., it has no aberration. This is what the geomet= ric interpretation of GR proposes.

  &nbs= p;         In this example, nothing propagates from M to P. So aberration is not applicab= le, and apparent agreement with experiment is secured. Note that this agreement does not result from a propagation speed of , but from no propagation at all. However mathematically elegant this solution might be, a gradient, a slope, or a curvature cannot induce a body at rest in a potential field (e.g., at point P) to begin movi= ng toward the source mass unless a force acts on that body. This is because, without a force to initiate motion, the body has no reason to choose any one direction over any other direction. Moreover, momentum would not be conserved if the = potential field had no moving parts, yet a body at rest in it began moving in some direction without a force acting. (By "force", we assume the classical meaning: "the rate of transfer of momentum".)

Such a hypothetical m= otion would be initiated without a cause, violating the causality principle; and would create momentum from nothing, violating the “no creation ex nihilo” principle. [= [9]] While such violations are all= owed in math and are considered in philosophy, they are forbidden in deep-reality physics because an effect without a proximate, antecedent cause or creation= ex nihilo is a form of magic or mi= racle, with no hope of ever being understood or explained in physical terms. It is therefore the logical equivalent of “God made it that way.”

            In the rubber sheet analogy, if the small target body is at rest on the side o= f a dent caused by a source mass, it will remain at rest forever until some for= ce acts. The rubber sheet analogy works in our imaginations only because we instinctively imagine gravity under the rubber sheet, with its pull providi= ng a meaning to the concept of “downhill”. But without pre-existing gravity, the small body has no cause to accelerate, either on the rubber sh= eet or in the geometrical interpretation of GR. So the idea behind geometric GR= , as easy as it is to implement mathematically, violates two principles of physi= cs and is therefore physically impossible.

  &nbs= p;         But there is another allowed interpretation of Figure 8 and of geometric GR. Consider M to have some transverse motion relative to the rubber sheet and relative to point P whil= e keeping point P fixed on the rubber sheet. As M moves, the dent it causes moves too. Let's assume the rubber sheet takes some finite time to adjust its shape to= the new location of M. If the adjustment wave propagates out at speed , and if point P is a distance r away from M, then the propagation delay is a time interval . If M moves at speed , P will always feel a gradient (the “downward̶= 1; slope of the dent) that lags behind the true, instantaneous position of M by the approximate angle in radians.=

  &nbs= p;         In this interpretation, the negative of the gradient cannot point toward the n= ew position of M until the adjustment wave has time to propagate from M to P. = The conventional way around this difficulty is to hypothesize a “velocity field” in the rubber sheet paralleling the motion of M and maintaining the needed gradients. One difficulty with that hypothesis is that the veloc= ity field has independent existence. (If it was caused by M, it too would have propagation delay.) So what would make it ever pass out of existence? Even = if M sets off a new velocity field based on some new motion, that shouldn’t affect the old velocity field because the old field is no longer controlled= by M. If one hypothesizes a characteristic decay time for the old velocity fie= ld, it would go away too soon at large distances from the source and too late at small distances, so it could not imitate the behavior predicted by GR and supported by experiments. In other words, any such "velocity field&quo= t; is a deus ex machina, lacking a= ny physical justification.

      = ;      As we explained earlier, static potential fields are either continually regenerated by a source mass, or are rigid in the sense of having no moving parts. However, for gravitation we require not only a velocity field but al= so an “acceleration field” to remain in conformity with observatio= ns. This weighs heavily against the rigid potential field interpretation, which we h= ave already shown to be non-viable. But the velocity field fares no better beca= use even the Sun accelerates as it moves around the solar system barycenter, yet planets respond almost instantly to such accelerations. Binary pulsars are = an even more dramatic demonstration of the effect, and most clearly demonstrate the need for an acceleration field too. Lastly, velocity fields would clear= ly be unable to continually update as needed in the case of two black holes in mutual, elongated elliptical orbits, because no communication of mass or location information across the event horizon is permitted. [= [10]] We therefore conclude that the “velocity field” interpretation is not viable on physical groun= ds either.

            Although it is obvious to anyone familiar with the GR equations of motion of an n-bo= dy system, we take special note that these equations contain no terms that are first order in (v/c), and therefore have no aberration. [[11]] Some relativists do not disput= e that aberration is an essential requirement of physics, but claim that aberration has been cancelled by a “velocity-dependent term” (same as a velocity field). [[12]] However, the derivation of the equations of motion shows that neither aberration nor a canceling term was ever considered. [= [13],= [14]] The needed partial derivatives simply used instantaneous coordinates with no propagation delay, thereby implicitly adopting an infinite propagation speed for gravitational force.

            Finally, we note the existence of one experiment designed to test the weak equivalen= ce principle, which is the idea that “gravity is just geometry” an= d is therefore always independent of the mass of the target body. In a neutron interferometer experiment, a target-body mass-dependence was observed, ther= eby falsifying the geometric or “curved space-time” interpretation = of GR experimentally. [[15]] The experiment is not better known today mainly because its result flies in= the face of conventional wisdom, and no one has attempted to replicate it.=

        &= nbsp;   In summary, we have a conflict of conclusions about the validity of geometric = GR taught almost exclusively today as a mathematical theory describing potenti= al fields, and the constraints imposed by the principles of physics and logic = that exclude the geometric interpretation of GR in favor of the field interpreta= tion. The two interpretations began to diverge in a serious way with the popular = book Gravitation [¹⁰], which emphasized the geometric interpretation= to the exclusion of the field interpretation. This view has perhaps reached its culmination with several books by Wald, who denies the viability of the fie= ld interpretation altogether with these words: “The basic framework of t= he theory of general relativity arises from considering ... that we cannot in principle -- even by complicated procedures -- construct inertial observers= in the sense of special relativity and measure the gravitational force. This is accomplished by the following bold hypothesis: The space-time metric is not flat, as was assumed in special relativity. The world lines of freely falli= ng bodies in a gravitational field are simply the geodesics of the (curved) space-time metric. In this way, the ‘background observers’ (geodesics of the space-time metric) automatically coincide with what was previously viewed as motion in a gravitational force field. As a result we = have no meaningful way of describing gravity as a force field; rather, we are fo= rced to view gravity as an aspect of space-time structure. Although absolute gravitational force has no meaning, the relative gravitational force (i.e., tidal force) between two nearby points still has meaning and can be measure= d by observing the relative acceleration of two freely falling bodies. ...”= ; [= [16]]

        &= nbsp;   But as we have seen above, this geometric view is either in conflict with the principles of physics or requires hypothesizing the existence of an unphysi= cal, undetectable “velocity-dependent force” whose sole reason for existing is to explain the absence of the required aberration from the theo= ry. And in either case, this interpretation is contradicted by the neutron interferometer experiment. This is no cause for concern because the field interpretation is still viable, notwithstanding Wald’s opinion. Moreo= ver, when we follow where these considerations logically take us, we will see th= at some ideas about relativity thought to conflict with ideas about quantum mechanics may now be seen as reconciled.

Gravitational force propagates fas= ter than light

      = ;      Physics requires that both gravitational and electrodynamic forces, like anything propagating, must experience both propagation delay and its principle manifestation, aberration. Yet experiments are unambiguous and undisputed in indicating that neither force displays aberration at a detectable level. We described three possible ways to resolve this apparent contradiction, and h= ave now eliminated two of them. The physical model that remains on the table is= the field interpretation of GR and momentum carriers that propagate much, much faster than light. This reduces aberration below presently detectible levels by making very large. This model has implied momentum carriers, and therefore has a cause for inducing motion in the target body, and requires = no creation of motion from non-motion (momentum from nothing). It avoids the logically inconceivable “instantaneous action at a distance” by retaining finite force propagation speeds, however large they might be. It makes gravitational force fields dynamic carriers of energy able to deposit heat in affected masses. And it implies that these force fields create gravitational potential changes, for example, by altering the density of an underlying “light-carrying medium”, hereafter referred to as “elysium”. This interpretation therefore has no need of a “velocity-dependent force” in the force field separate from gravitation or electrodynamics. And it has recently been developed into a complete model for the nature and origin of gravity, including its relativi= stic effects. [= [17]]

            However, SR forbids propagation at faster-than-light speeds in forward time. So what remains to be discussed is how this interpretation can survive SR’s c= onstraint. We will begin with a review of the experimental evidence that compels us to this conclusion of faster-then-light force propagation speeds, followed by = a brief discussion of the role of gravitational waves.

            First, we take notice of a simple, basic fact: gravitational force and light from = the Sun are not parallel in the Earth’s frame of reference. The Sun’= ;s light and gravity may be presumed to originate at the same place at the same time, and to propagate along the same radial path to the same target body, say, t= he Earth. Yet when they arrive, they appear to come from directions that diffe= r by 20 arc seconds on the sky – the angle of aberration for light. This reflects the fact that light takes about 500 seconds for this journey, duri= ng which time the Sun has moved through an angle of 20 arc seconds from Earth’s perspective; whereas the Sun’s gravity always acts towa= rd the Sun’s true, instantaneous direction, a direction in which the Sun will not be seen by the observer until 500 seconds in the future. When sunl= ight applies a force to a target body (the force of solar radiation pressure), t= he direction of that force is likewise offset by 20 arc seconds from the direc= tion of gravitational force. This difference indicates that the speed of gravitational force in the Earth’s frame is so fast that no offset fr= om the Sun’s instantaneous direction can yet be detected; whereas light propagates so comparatively slowly that the main effect of its propagation delay, aberration, is readily seen both directly (for eclipses) and indirec= tly (through radiation forces).

            If gravitational force had a propagation speed as slow as light, it too would = have an aberration of 20 arc seconds and would appear to parallel light from the Sun. Moreover, the force of gravity would be applied in an offset direction also because of Earth’s orbital speed. This offset would cause orbits= to spiral outward. For Earth’s orbit, the average distance from the Sun would double in 660 revolutions. For Mercury, about 100 revolutions would suffice. For binary pulsar PSR1913+16, the orbital radii would double in ab= out a month. The absence of such an acceleration in binary pulsar PSR1534+12 se= ts the most stringent lower limit available for the speed of gravity: 2x1010 c. [⁹]

            Experiments that show the absence of an expected effect are revealing and important. Bu= t in view of our discussion of potential fields with no moving parts, it is reassuring that we also have an experiment with a non-null result. Total so= lar eclipses reveal that the gravitational maximum of the Sun’s force on = the Moon follows the maximum visual eclipse by about 40 seconds of time on aver= age. This coincides with the time it takes the Moon to traverse along its orbit through the angular distance between the apparent Sun and the true, instantaneous Sun. Interestingly, the visual eclipse corresponding to the propagation-delayed image of the Sun occurs first, followed by the gravitational maximum of the Sun’s force on the Moon. [^=
9] If the Moon had a retrograde orbit, the vi= sual eclipse would occur after the gravitational maximum.

            All six experiments (described in the preceding reference), whose results bear = on the speed of gravity question, yield a lower limit to that speed well in ex= cess of the speed of light.

The physical meaning of potential<= o:p>

            Until now, it has usually been assumed that force fields and potential fields, whether gravitational or electrodynamic, were both different manifestations= of the same phenomenon. This is especially true for electrodynamics, where the linkage between electric and magnetic forces on the one hand, and light wav= es or other parts of the electromagnetic spectrum on the other, is well-established. In the case of gravitation, the counterpart of light wave= s is supposed to be “gravitational waves”. Although these hypothetic= al entities would be ultra-weak and have yet to be detected from any source in= our solar system, indirect evidence for their existence in distant astrophysical systems has been seen in the binary pulsar PSR1913+16.

            It is clear how a potential and a corresponding force are related mathematical= ly – as function and its spatial derivative. But what is their relations= hip physically? We have seen above that the remaining physically viable interpretation of forces is that they are the effect of a continuous stream= of tiny momentum impulses transmitted between a source mass and a target body = at speeds far greater than lightspeed. However, the spatial integral of such forces would have no particular significance – unless space was filled with a medium that can also be affected by the momentum carriers. In the ca= se of gravity, the density, or at least the pressure, in such a medium would increase in the vicinity of source masses because the downward force of gra= vity would pack more medium into that vicinity, or at least increase the downward pressure if the medium were incompressible. Under equilibrium conditions, t= he density or pressure would increase linearly with decreasing distance from t= he source mass.

        &= nbsp;   Consider an atmosphere. If no forces acted on it, density everywhere would tend to equalize within its container. But if a force such as gravity acts on it, a density gradient will develop. We could measure atmospheric density and the speed of sound as a function of height, yet learn nothing about the propert= ies of the gravitational force that created and maintained these properties of = air, except its strength.

Air density is the analog of gravitational potential {the medium responsible for “space-time” (i.e., proper time) in the geometric interpretation of GR}, and sound waves are the analo= g of gravitational waves. The wave speed is a function of the properties of the space-time medium, such as its permeability and permittivity. For gravitati= onal waves, this speed happens to be the speed of light, c. This wave speed tell= s us almost nothing about the speed of gravitational force. For example, in our analogy, if sound waves and air density changes were set off by an asteroid impact, these properties of air would likewise be quite insensitive to the speed of the asteroid.

Let’s assume that a gravitational pote= ntial exists due to the presence of a single, isolated, massive star fixed in spa= ce. The retarded and instantaneous scalar potential values (but not their gradients) then coincide for observers in all frames. We will examine the v= iew from a massless particle (target body) moving on a circular orbit so that t= he potential remains rigorously constant for that target body at all times. Wi= th that setup, there is still an issue to be understood. The constant potentia= l has a time-variable gradient because the direction of the gradient is always changing. So when we take the gradient, we must specify whether it will be = the instantaneous or the retarded gradient, even though the potential itself is rigorously constant for all time. In general, it does not matter whether th= e scalar potential itself is retarded or not. The whole issue of the speed of gravitational force revolves around the gradient, which has properties not derivable from the potential alone.[‡‡]

            Elysium is, by definition, the light-carrying medium. If we now identify the hypothetical gravitational potential medium with elysium, we see at once th= at several remarkable properties emerge. First, note that elysium, like scalar potenti= al, has an arbitrary background level (zero point). We are concerned mainly with the effects of changes in that background level, but not normally with the absolute level itself. Then if light propagates past a source mass, the increased density of elysium there will refract the path of the light, bend= ing it away from the normal to the source mass. Moreover, propagation speed of = the light waves will be slowed, as will be the rate of ticking of any clock bas= ed on electromagnetic phenomena because of the increased medium density and consequent slowed propagation speed. Indeed, it was already known to Edding= ton in 1920 that such an optical medium would give exactly the same predictions= (to first order in the potential) as geometric GR for the tests of GR that desc= ribe the behavior of light in a gravitational potential field. [= [18],^=
2,¹⁷] And it has since been shown that the same optical medium can yield the same results for the fourth test of GR, the advance of the pericenter of orbits in general or of the perihelion of Merc= ury in particular.[§§] [= [19],= [20]]

            The upshot of these considerations is that the potential field may be visualize= d as the elysium, with its density increasing as any source mass is approached. = We then have a clear visualization of why a gravitational potential field and a force field are physically different entities, yet related to each other as= a function and its derivative. We also see why “space-time curvature= 221; (now visualized as optical refraction) is so important to potential fields,= yet has no discernible effect on the basic Newtonian component of gravitational force. The clock-slowing effects of speed and potential can either cancel or combine depending on the resultant effective density of the elysium.[***]<= /a> The radial velocity between a source and an observer does not affect the wave s= peed or path, but only its wavelength and perceived energy. By contrast, aberrat= ion does affect the direction of the path of a light wave, and depends on the t= ransverse velocity between source’s local potential field and the observer. = 220;Local” is important. For example, aberration is the same for both components of a double star, even though each star has a different velocity relative to Ear= th. But each component of the double star is immersed in a larger, combined potenti= al field. So the wave speed depends on the local density all along its path, a= nd aberration depends on propagation delay along the same path.

Gravitational waves propagate at t= he speed of light

Lastly, we readily see why the subject of the “speed of gravity” has le= d to so much confusion and debate. That speed is necessarily equal to the speed = of light for disturbances of gravitational potential fields, and is necessarily much faster than light for gravitational force fields.[†††] Today, there is little reason to doubt the existence of gravitational waves. But inasmuch as these entities are the result of disturbances of a gravitational potential field, they have nothing to do with changes in grav= itational forces or force fields. Only the belief that potential and force fields are= two manifestations of a single phenomenon implies such a relationship. But as we have seen, such a belief is ill-founded. We now have reason to suspect that gravitational waves are simply very-long-wavelength electromagnetic waves, = and that the hypothetical spin-2 entity in quantum physics now called a “graviton” actually describes the basic constituent of the potential field, and as such would more appropriately be named the “elyson”. When two bodies with a relative speed orbit one anoth= er, the smaller will experience more drag from the elysium medium than the larger, which would manifest itself to us as gravitational waves (disturbing the potential field of the other mass) and losing angular momentum as a consequ= ence, as observed in binary pulsar PSR1913+16. Likewise, the elysium field would produce a torque on a rotating body, analogous to the “frame-dragging” effect predicted by GR. This is because anythi= ng not on an equipotential surface will tend to have a horizontal torque as its path around the center tries to precess because atomic processes are being forced to occur at different rates for different parts of the body. [‡‡‡]

      = ;      Some textbooks suggest that gravitational waves are simply changes in gravitatio= nal forces. However, that interpretation cannot be correct because gravitational waves originating in the solar system have not yet been detected. Consider these examples:

(1)&= nbsp; When we walk into a room, a gravimeter can track changes in the gravitational acceleration we produce. These are easily detected.

(2)&= nbsp; In a static potential field, an orbiting body is continually changing its acceleration. We can easily measure these force/ac= celeration changes.

(3)&= nbsp; The GR equations of motion are expressions for accelerations of bodies as a function of location, velocity, and potential.= As such, they describe changes in acceleration through second order in potenti= al or fourth order in velocity. Yet there is no gravitational wave component i= n these equations.

Moreover, gravitation= al waves passing through a body merely cause its atoms to oscillate slightly, but produce no net force on the body. It is therefore safe to conclude that gra= vitational waves have nothing to do with ordinary gravitational acceleration or with changes therein.

            We have seen that geometric GR is based primarily on properties attributable to potential fields that are then assumed to apply also to force fields. One of those is that fields are “fossilized”; i.e., have no moving par= ts unless disturbed, like the frozen waterfall of Figure 2. By contrast, the force field interpretation of GR with momentum-carrying entities has fields that continually regenerate, and= as such are a potential source of energy and can do work, much like the flowing waterfall of Figure 3. In further support of the latter interpretation,= we note how much easier it is to understand the properties of gravitational fo= rces with the force field interpretation. [¹⁷]

            For example, while it might be convenient to describe the Sun’s gravitati= onal force field as “static” to explain why planets accelerate toward the true, instantaneous Sun rather than the light-time-retarded Sun, realit= y is that the Sun is in a constant state of acceleration relative to the solar system barycenter, with amplitude great enough that the barycenter is often located outside the physical body of the Sun. This is more acutely pertinen= t in the case of binary pulsars, where the acceleration of each component is tow= ard the true, instantaneous position of the other to better accuracy that even = the linearly-extrapolated-retarded position can provide. And the fossilized for= ce fields explanation is never more strained than when it tries to explain how binary black holes in mutual elliptical orbits can continually update the curvatur= e of space-time when the mass and location information needed to do so is hidden behind a pair of event horizons.

@@@ [gravitational wave diagram and physical explanation to be added here]

Is faster-than-light propagation a= llowed by the laws of physics?

            The proof that faster-than-light propagation is not allowed is simple. Special relativity forbids it because time slows and app= roaches a cessation of flow for any material entity approaching the speed of light.= So no matter how much energy is brought to bear, the entity cannot be propelled all the way to, much less beyond, the point where time ceases. The entity’s inertia simply increases towards infinite as the speed barri= er is approached. Hypothetical mathematical entities with imaginary masses (wh= atever that means) might exist, according to the equations. These “tachyons&= #8221; would always travel faster than light, but must always propagate backward in time and could never be slowed enough to cross the light-speed barrier eith= er. Relativists are confident that SR is a valid theory because it has passed eleven independent experiments testing most of its features and predictions. And t= he very successful theory of general relativity is based on SR, and has likewi= se passed several major experimental tests.

            As solid as this reasoning appears to be, it has a logical flaw, because anoth= er theory exists about which the same supporting claims can be made, but which= has no universal speed limit. This is the so-called “Lorentzian relativity” (LR). Let’s briefly review what this theory is, how= it differs from SR, and what the experiments have to say about it.<= /span>

            Lorentzian relativity is a modern updating of the Lorentz Ether Theory, first publishe= d in 1904 a year before Einstein published SR. [[21]] It is based on the relativity principle, first formulated at least a generation earlier; and on the famous transformations named after Lorentz, thereby hav= ing the same mathematical form as SR. In essence, LR is relativity for the aeth= er. Einstein’s innovation in SR was to abolish the need for aether, or mo= re specifically, the need for a preferred frame, by making all inertial frames equivalent, with each having the same speed of light. In SR, the Lorentz transformations apply to time, space, and mass; whereas in LR, they apply to clocks, meter sticks, and momentum. That is why there is no universal speed limit in LR – nothing ever happens to time itself, just to clocks attempting to keep time.

            Because time is never affected, LR recognizes a “universal time” applic= able to all frames, and a universal instant of “now”. In SR, all inertial frames are equivalent, so the Lorentz transformations apply recipr= ocally (i.e., both ways between two frames); whereas in LR, the local gravitational potential field constitutes a preferred frame, and the Lorentz transformati= ons work just one way from the preferred frame, but not reciprocally.

            Eleven independent experiments confirm the basic behavior of nature predicted by S= R, but also predicted by LR. [[22]] Just as with the two interpretations of GR, the physical interpretations of= the two variants for the relativity of motion differ, but not the mathematical = form or the observable phenomena in most instances. Although claims have been ma= de over the years that various experiments on this list falsified either SR or= LR, subsequent discussion indicated that was not the case. It is now widely believed that no experiment dealing with lightspeed or slower phenomena can distinguish the two theories.

            To cite just two examples, particles in accelerator experiments do seem to approach the speed of light indefinitely closely without ever exceeding it,= no matter how much energy is supplied, which appears to favor the SR interpretation. However, LR notes that one cannot expect to push particles faster than the speed of light using forces which themselves propagate only= at lightspeed. This would be like trying to use propellers alone on a plane, w= ith no gravity assist, to exceed the speed of sound. And in the Global Position= ing System (GPS), all atomic clocks aboard satellites with a variety of orbital planes, and all atomic clocks all over the rotating Earth, are all synchron= ized with one another, and remain synchronized, despite being in many different inertial frames. This appears to be a practical realization of Lorentz̵= 7;s universal time. But SR points out that the clocks had to be adjusted in rat= e to achieve this synchronization, and that the measured speed of light is then = not constant in frames other than the local gravitational potential field. If t= he two postulates of SR are adhered to, then the clocks behave in all frames j= ust as predicted by SR, albeit at the cost of adding considerable complexity to= the system. That is avoided by synchronizing each clock to a momentarily co-loc= ated imaginary clock at rest in the local gravitational potential field, and wor= king only in that Earth-centered inertial frame.

            Conspicuously missing from the list of experimental results is any experiment testing reciprocity of the Lorentz transformations. Specifically, GR is built on SR using only one-way Lorentz transformations relative to the local gravitatio= nal potential field (center-of-mass reference frame), and is therefore just as consistent with LR as SR. The famous Twins Paradox, an attempt to show that= SR had an inconsistency, has no counterpart in LR because LR’s transformations work only one way. [[23]] It now seems that only an experiment demonstrating a real phenomena propagating faster than light in forward time could decide between SR and LR. That issu= e now appears to have been decided in favor of LR by experiments implying that gravitational and electrodynamic forces propagate faster than light in forw= ard time. [²] In any case, the mere existence of LR as a viable alternative to SR means that nature need not have a speed limit.

Gravitational force has no inertia=

@@@ [include material from “inertia article and add discussion= of equivalence principle]

Conclusion
            General and special relativity are elegant mathematical theories with non-unique physical interpretations. When physical principles are brought to bear, the interpretation ambiguities can be resolved in favor of the force field interpretation of GR and the Lorentzian variant of the relativity of motion, LR. Both of these interpretations allow faster-than-light propagation of material entities in forward time. The tightest experimental constraints indicate that the propagation speed of gravitational force must be no less = than 2x10¹⁰.

            This change of perspective does not yet require any change in the math of either= the relativity of gravitational fields or the relativity of motion. Yet it potentially provides the missing key to unification of the fundamental forc= es of nature, and eliminates the locality requirement for quantum phenomena su= ch as those involved in the EPR paradox. It also permits developments in the f= ield of quantum gravity that were previously blocked. [¹⁷]

A<= o:p>

GR has two physi= cal interpretations – field and geometric.

B

“Gravitati= onal field” has two meanings – force field and potential field.

C

“Space-tim= e” is not a combination of 3-dimensional space plus time. (See also G.)

D

Potential affects clock rates, acceleration and free fall do not.

E

Physics requires= that gradients of potentials must be retarded gradients.

F

Retardation impl= ies orbit spiraling that can be avoided in three known ways.

G

Orbital motion i= s not caused by any curvature of space.

H

The physical interpretation of “space-time” is usually just proper time.

I

Gravity accelera= tion is not caused by geometry.

J

The geometric interpretation of GR is not physically viable.

K

“Velocity fields” are not a viable explanation for the lack of observable aberration.

L

Gravita= tional force propagates faster than light in forward time.

M

Gravita= tional potential has the character of density of a light-carrying medium.

N

Gravita= tional waves have nothing to do with ordinary gravitational acceleration.

O

Lorentz= ian relativity allows faster-than-light propagation in forward time.

P

Gravita= tional force has no inertia.

Table I. Major points made in this pape= r, and locations in the text where they are first raised.

            If these conclusions are, in the main, valid, then our chief concern would be = the progress this represents toward the scenario forecast by Douglas Adams: "There = is a theory which states that if ever anybody discovers exactly what the univers= e is for and why it is here, it will instantly disappear and be replaced by something even more bizarrely inexplicable. There is another theory which states that this has already happened.” [[24]]

Acknowledgments<= /b>

  =           The author thanks the Meta Research Board and members for financial support, wi= th a special thanks to Tim Seward a= nd the late Richard Hazelett. Many of these ideas were inspired and supported by t= he late J.P. Vigier.

[last revised 2005/12/30]

A<= o:p>	GR has two physi= cal interpretations – field and geometric.
B	“Gravitati= onal field” has two meanings – force field and potential field.
C	“Space-tim= e” is not a combination of 3-dimensional space plus time. (See also G.)
D	Potential affects clock rates, acceleration and free fall do not.
E	Physics requires= that gradients of potentials must be retarded gradients.
F	Retardation impl= ies orbit spiraling that can be avoided in three known ways.
G	Orbital motion i= s not caused by any curvature of space.
H	The physical interpretation of “space-time” is usually just proper time.
I	Gravity accelera= tion is not caused by geometry.
J	The geometric interpretation of GR is not physically viable.
K	“Velocity fields” are not a viable explanation for the lack of observable aberration.
L	Gravita= tional force propagates faster than light in forward time.
M	Gravita= tional potential has the character of density of a light-carrying medium.
N	Gravita= tional waves have nothing to do with ordinary gravitational acceleration.
O	Lorentz= ian relativity allows faster-than-light propagation in forward time.
P	Gravita= tional force has no inertia.