Acceleration of the inherent motion in space. How can gravitation be explained in a spatiomaterial world? To be adequate, it must explain not only the acceleration due to gravity that Newton recognized, but also all the new phenomena predicted by the general theory of relativity. That is a challenge, because it must do so without appealing to spacetime. How can gravitation be explained with nothing but two opposite substances that exist only at the present moment?

As in the reduction of special relativity, there is no need to reject the mathematical equations or the interpretations by which they are tested empirically. All that needs to change is what we take them to refer to. Since we shall be starting from the assumption that space is absolute, this is to take an approach opposite to Einstein, just as we did in explaining special relativity.

Einstein called his explanation of gravitation a general “theory of relativity” because he assumed that gravitational phenomena, like all other phenomena, must obey the same laws in every reference frame, and his strategy was to explain gravitation by describing a way of transforming coordinates assigned by observers on different reference frames into one another that leaves the laws of physics unchanged. He assumed that the velocity of light has the same value in every reference frame, and a tensor calculus was required to formulate the mathematical transformation.

As ontologists, however, we start by assuming that space and matter are substances existing in time, and since that means that light may have different (one-way) velocities, different reference frames are not ontologically equivalent. Thus, it is not appropriate to call it a theory of relativity. On the contrary, it will explain the general equivalence of reference frames, or the premise of Einstein’s argument, as an appearance constituted by space and matter as ontological causes, much as it did in explaining the premises of Einstein’s argument in STR.

The key to the spatiomaterialist theory of gravitation is its explanation of the apparent truth of STR.

In its ontological explanation of the truth of the special theory, spatiomaterialism rejects Einstein’s assumption that the velocity of light is the same relative to every inertial frame and assumes, instead, that it is due to an inherent motion in space. It also assumes (or shows) that the motion of material objects through space causes four Lorentz distortions in them. The Lorentz distortions enable it to explain why inertial frames are empirically equivalent locally, and by taking into account how clocks are mis-synchronized on moving reference frames by adhering to Einstein’s definition of simultaneity at a distance (that is, ignoring the difference between the one-way velocities of light in each direction), they also explain why inertial frames appear to be equivalent globally, that is, why the (net) Lorentz distortion always seem to be occurring in the other member of any pair of inertial frames.

These assumptions and conclusions are all taken for granted in explaining the truth of the general theory of relativity, and only one additional ontological assumption is required to explain gravitation. That is the assumption that the accumulation of matter at certain locations in space has an effect on space, mediated by the inherent motion in space, that, in effect, accelerates the inherent motion in the nearby space toward it.

There are various consequences of this assumption. They are described in the following sections, including their role in explaining the new phenomena predicted by Einstein. One consequence has to do with the velocity of light. Another has to do with effect on material objects that are forced to remain at rest relative to space itself in a gravitational field. The third is a result of how the effect of matter accumulation on space is mediated by the inherent motion itself. Finally, I will show how it explains the special phenomena that occur in very strong gravitational fields, such as black holes. At the end, I will return to the issue about the nature of the argument and show how this ontological explanation of gravitation explains “general relativity” in the sense of the observational equivalence of different models of GTR, which Einstein used to derive his conclusions.

In constructing its theory of gravitation, spatiomaterialism takes its lead, as Einstein did, from the assumption that reference frames free-falling in gravitational fields are equivalent (locally) to reference frames in inertial motion. Einstein called this the “principle of equivalence.” But given its explanation of the truth of STR, this principle has a somewhat different meaning, for spatiomaterialism holds that different inertial frames, despite being observationally equivalent, are ontologically different.

When inertial frames have different velocities relative to one another, at least one must be moving relative to space, and since that means having a velocity relative to the inherent motion in space, we had to assume that material objects suffer Lorentz distortions as a result of their motion relative to the inherent motion in space, in order explain why they appear equivalent (locally and globally). Now, in order to explain all the old and new gravitational phenomena, we must assume yet another interaction between space and matter — an interaction that makes it appear that free falling frames are observationally equivalent, locally, to inertial frames outside gravitational fields.

Whereas Einstein took gravitation to involve an interaction between matter and spacetime, spatiomaterialism takes gravitation to involve an interaction between matter and space. Spatiomaterialism assumes that, instead of curving spacetime, accumulations of matter (mass and energy) change the velocity of the inherent motion in space.

I am speaking as if the inherent motion were something actually moving though space while space endures, as a substance, through time, but I have admitted that, if you prefer, it can be taken as just a spatio-temporal aspect of substantival space having to do with how fast what occurs in one location in space can affect what happens elsewhere. If space is to mediate the relations and interactions among bits of matter, some such limit on the velocity of their effects on one another is necessary, because otherwise spatiomaterialism would have to give up its assumption that space is a substance made up of many particular substances (one for each location in space and all connected as described by Euclidean geometry). There is no doubt that space involves an “inherent motion” in the sense of having a spatio-temporal aspect about how parts of space are related.

The only issue is whether there is anything actually moving through space other than bits of matter. That can be doubted, because, thus far, at least, the only candidates for what moves across space are bits of matter. Setting material objects aside (because the move slower than the inherent motion), we have, thus far, come across nothing that actually moves across space at that maximum velocity except light (and the forces exerted by material objects with an electric charge), which are forms of matter. The gravitational force is not an exception, for even though it also propagates at the velocity of the inherent motion, it is also a form of matter even on this theory (as I suggested in Forms of matter). But it does no harm to think of this aspect of the nature of space as an inherent motion, for we have already recognized that space is a substance enduring through time and seen that it must have a spatio-temporal aspect to the relations of its parts. Moreover, in explaining how quantum mechanics can be true in a spatiomaterial world, we will find that something other than matter also moves across space with the inherent motion.

Thus, I will continue to speak of space as if there were an inherent motion through every location, moving at the same velocity both ways in every direction in three dimensional space. It is something we can imagine, because as rational beings, we are able to think about space, time and motion, and thus, it will enable me to describe the effect of matter accumulation on space in a qualitative way, in terms of its effect on the inherent motion and, thereby, on all the electromagnetic interactions that are mediated by it.

Those with a more reactionary bent may, however, want to call the inherent motion in space by its traditional name. It is actually an ontological explanation of the ether. The luminiferous ether was supposed to be a material substance of some kind at rest in absolute space that mediated electric and magnetic forces like a very elastic material substance. To be sure, we have no need to postulate any form of matter to play the role of the ether, because we take space to be a substance, and its inherent motion can mediate electromagnetic interactions. But on the other hand, it would be appropriate to speak of the inherent motion in space as the ether, and that means that the new assumption being made here could be described just as well as an acceleration of the ether. (I would use this term, except that it is likely to inflame the antagonism of Einsteinians, who sometimes like to portray their denial of absolute space as merely discrediting a foolish metaphysical belief in unobservable entities.)

The assumption that spatiomaterialism makes in order to explain gravitation, therefore, is that the accumulation of matter exerts a force on other nearby bits of matter by way of its effect on the inherent motion in space that changes the velocity of the inherent motion in space as if the inherent motion itself were being accelerated toward the center of gravity at the rate described by Newton’s law.

The inherent motion flows both ways in every direction, and the gravitational change in the velocity of the inherent motion is different in opposite directions. The inbound velocity of the inherent motion is greater than it would be outside the gravitational field, and the outbound velocity is correspondingly less than it would be outside. Thus, it is as if the inherent motion itself had an inbound velocity.

Since the inherent motion is a velocity both ways in every direction at every location in space, there is always some pathway for material objects relative to it in which the two one-way velocities of inherent motion are equal in both directions. Let us call that motion relative to space “rest relative to the inherent motion” (or for reactionaries, “rest relative to the ether”). The effect of the force of gravity is, therefore, equivalent to accelerating rest relative to the inherent motion in space, so that it has velocity relative to space in a gravitational field.

(It might, therefore, be better to describe the effect of the force of gravity as accelerating the ether, because it is rest relative to the ether that is undetectable. But that could be misleading. It might suggest that ethereal matter is accumulating at the center of gravity, whereas the inherent motion is just the way in which bits of matter coincide with space, and thus, the acceleration of the inherent motion is just a change in how bits of matter coincide with space. But it is useful to keep in mind that there is an inertial frame at rest relative to the inherent motion, and it is, in effect, what is accelerated by the accumulation of matter.)

The inbound velocity of the inherent motion at any point depends on how much it has increased as a result of accelerating all the way in from infinitely far away as a result of its acceleration.

The amount of acceleration varies directly as the product of the amount of matter (mass and energy) making up the objects accelerating one another and inversely as the square of the distance between them in space (though the force is exerted by way of the inherent motion).

At any point in a gravitational field, therefore, the increase in the inbound velocity of the inherent motion is equal to the escape velocity at that point. That is, relative to space, the inherent motion is moving toward the concentrated matter at the velocity of light plus a velocity that is equal to the outbound velocity a material object would have to have at that point relative to space to escape gravity and eventually come to absolute rest outside its influence. The decrease in the outward-bound velocity of the inherent motion in space is likewise the escape velocity, making the outward bound velocity of the inherent motion the velocity of light minus a velocity equal to the velocity a material objects would have to have to move outward and just escape the gravitational filed.

Since the gravitational variation in the velocity of the inherent motion at different points in space is equivalent to the acceleration of the inherent motion, any matter that coincides with space by way of the inherent motion also accelerates at the same rate. That includes, as we shall see, all forms of matter.

Photons are accelerated because they coincide with space in such a way that they are carried along by the inherent motion in space.

Material objects also coincide with space by way of its inherent motion. This is implicit in the spatiomaterialist explanation of the truth of STR. What makes it impossible to detect its velocity relative to the inherent motion experimentally are Lorentz distortions that material objects suffer because of their motion relative to the inherent motion. Indeed, some of those distortions depend on the difference in the one-way velocities of light in opposite directions in the direction of its motion relative to the inherent motion. Thus, when the inherent motion itself is accelerating inward, any material object that coincides with space by way of the inherent motion is also accelerated in the same way. And since electric charges move with the material objects and exert their forces by way of the inherent motion, their electric fields are accelerated along with them.

Since acceleration of matter by way of the acceleration of the inherent motion is a form of potential energy, the gravitational field is itself a form of matter. It is the form of matter I called “gravitational matter” at the beginning of the ontological explanation of the truth of the laws of physics (see Forms of matter), and the quantity of matter involved in constituting the potential energy of gravitational field is counted as part of the total matter (mass and energy) accumulated at the center of accumulation. Thus, as the kinetic energy of material objects increases because of their acceleration, the potential energy not only declines, but becomes less than zero (or maximum potential energy), and the total quantity of mass and energy is, thereby, conserved.

If the center of matter accumulation itself is in motion relative to space, then it already has a velocity relative to the inherent motion in space and all the effects of its gravitational field are affected accordingly.

Gravitation involves, according to this ontological explanation of the truth of the general theory, a second interaction between space and matter. The first was the reaction of space to material objects that acquire a high constant velocity relative to the inherent motion: it imposes the Lorentz distortions on such material objects. The second is more complex, because matter first causes a change in space, and then space, in turn, causes a change in matter. That is, accumulations of matter accelerate the inherent motion in space toward themselves, and the acceleration of the inherent motion not only accelerates the bits of matter it contains, but also changes the velocity of light at any point in space (because the inherent motion accumulates inward velocity over the entire gravitational field). It is as if space had a compound effect on the matter it contains, because either effect can occur separately, and both can happen at once.

The first effect occurs separately when material objects have a constant velocity relative to the inherent motion outside of a gravitational field.

The second effect occurs separately when material objects are at rest relative to the inherent motion being accelerated into a center of mass that is at rest in absolute space.

Both effects occur either when material objects have a constant finite velocity relative to an inherent motion that is being accelerated into a center of gravity that is at rest, or when the accumulation of matter itself has a constant velocity relative to the inherent motion in space outside gravitation. 

Let us consider the consequences of this additional assumption about the nature of space and matter. 

This ontological assumption explains why Newton’s law is approximately true in all those areas where it is recognized to be a good approximation, because it differs from Newton’s theory only in its assumption that gravitation acts by way of the inherent motion, that is, that it accelerates the surrounding inherent motion in space and that it does so as a force that is itself propagated by that inherent motion. 

It also explains Einstein’s equivalence principle ontologically. It entails that local experiments on free falling frames come out the same as on inertial frames outside gravity, for in both cases they have a constant velocity relative to the ether.

But the spatiomaterialist theory also explains intuitively certain new phenomena used to confirm Einstein’s GTR, including the three new kinds of phenomena that have been used to confirm the general theory as well as the predictions about black holes.

Variation in the velocity of light. The most immediate effect of the acceleration of the inherent motion is on the velocity of light. The photon coincides with space by having some direction in the inherent motion wherever it is located and being carried along by the inherent motion in space. Thus, the motion of the photon relative to space manifests the inherent motion in space any motion that the inherent motion itself has relative to space because of the gravitational field.

Since the inherent motion is different at different locations in space as a function of the force of gravity, a photon traveling inward toward the center of matter will accelerate as it moves, acquiring a velocity relative to space that is higher than the velocity of light outside of the influence of gravitation. Correspondingly, a photon moving outward will leave the center of mass with a velocity relative to space that is less than it would have outside of gravitation, and it will accelerate all the time it is moving outwards until it reaches the velocity of light outside gravitation just as it escapes the gravitational field.

The quantity of the increase (decrease) in the velocity of light at any point in space relative to what it would be if there were no gravitational force depends on the escape velocity, that is, how much velocity a bit of matter would acquire as a result of being acted on by the gravitational force as it moves across the gravitational field.

Consider for simplicity’s sake a center of matter (mass and energy) that is at rest in absolute space. The theory is that when matter accumulates in space, it acts on the surrounding space in a way that is equivalent to accelerating the inherent motion in space toward it, giving the inherent motion itself a velocity relative to absolute space. The rate of acceleration is determined by the force of gravity (which declines as the square of the distance from the center of gravity), and that means that the photon starts accelerating infinitely far away from the gravitating body and accumulates speed as it continues to accelerate inward (with its rate of acceleration becoming greater as the gravitational force increases), so that at points nearer the center of gravity, the photon has an instantaneous, inward velocity that is equal to the velocity of light outside gravitation plus the escape velocity at that point in the gravitational field.

If the gravitating body is not at rest in absolute space, but is itself moving relative the inherent motion in space, that will also alter the velocity of light the same way at every point throughout its gravitational field.

When enough matter accumulates to accelerate the inherent motion itself to a velocity in space that is faster than the velocity of light outside any gravitational field, it is called a “black hole.”^[1] The so-called Schwartzschild radius of a black hole at rest in space is the surface in space at which the inward velocity of the virtual inherent motion equals the velocity that light would have in that direction at that location, if the inherent motion were at absolute rest. Inward-bound light crossing that surface would have a velocity relative to space twice what light would have outside of gravitation, and thus, it is impossible for light being carried in the opposite direction by the inherent motion to cross that surface. Outward bound photons at the Schwartzschild radius of a black hole would be at rest relative to space.

Gravitational bending of light rays. The effect of the acceleration of the inherent motion on the velocity of light explains the most famous new prediction of the general theory, namely, the bending of light rays in a gravitational field.

Given that light, as a form of energy, has a mass and exerts a gravitational force, Newton’s law can be used to predict that light will be bent from its straight path by the force of gravity, much like a material object. But the general theory of relativity predicts that the light ray will be bent at about twice the rate predicted by Newton’s theory. And in a famous expedition in 1918, Eddington found that Einstein was correct by measuring the direction of a ray of light from a distant star as it passed behind the sun during an eclipse and the distant star could be seen.

The greater effect of gravitation predicted by Einstein is what would be expected on the spatiomaterialist explanation of gravitation, because two factors are involved in determining the pathway of the photon.

First, as the light ray passes the gravitating body, it is pulled sideways into the center of gravity by the inward acceleration of the inherent motion in the transverse direction, which diverts it from a straight path, much as expected on Newtonian grounds.

Second, as the photon is approaching the center of gravity, the inward acceleration of the inherent motion gives light an inward velocity higher than it would have outside the gravitational field. But since the inherent motion on the other side of the center of gravity has been accelerated in the opposite direction, the photon slows down as it passes the gravitating body to a velocity that is lower than it would be outside gravitation, and then it gradually speeds it up again to the normal velocity of light relative to space as it moves out of the gravitational field on the other side. The result of these changes in the velocity of light is that the photon spends a disproportionately longer period of its entire trip near the center of gravity where the sideways acceleration of the inherent motion toward the center is greatest than it does farther away when the sideways acceleration of the inherent motion is minimal. That explains the higher value of bending predicted by Einstein.^[2]

Time delay in radar signals. The effect of the acceleration of the inherent motion on the pathways of photons can also explain the time delay in radar signals reflected back to earth from planets on the far side of the sun when the paths of those signals lie near the sun.

There is a spatial symmetry about the velocity changes that occur both times the radar signal approaches and recedes from the sun. The signal gains velocity as it approaches the sun, because the inherent motion is accelerating under gravity in that direction. But it quickly comes to have a lower velocity than light outside of gravitation as it passes by the sun, because of the inbound acceleration of the inherent motion on the other side of the sun. And then the signal regains velocity as it recedes, because the inward velocity of the inherent motion on the other side is lower the father away from the sun.

It might seem that there should be no net effect on the total time it takes for the light signal to pass by the sun, because the higher velocity of its approach to the sun will be canceled out by the lower velocity of its retreat from the sun on the opposite side. After all, the approaching signal travels just as far at each higher velocity as the receding signal travels at comparably lower velocities.

There is, however, a net slowing down of the period required for the entire trip, because the equal distance on each side of the sun entails that the light signal spends more time traveling at slower velocities than it does traveling at faster velocities. Hence, it cannot make up all the time it loses going slower in the time it spends going faster. This happens both ways on its round-way trip to the distant planet, causing an overall delay in the radar signal’s return that does not occur when its path is not near the sun.^[3]

Time dilation caused by acceleration relative to the inherent motion. Another famous prediction of Einstein’s general theory of relativity is the so-called “gravitational red shift,” or a time dilation in gravitational fields. That is, all physical processes on material objects are slowed down at a rate that depends on the potential energy of the gravitational field (which would vary directly with the altitude, if the force of gravity were constant). It predicts that such a time dilation will be observed both in objects at rest in a gravitational field and in objects in free fall in a gravitational field.  

Gravitational time was observed by Pound and Rebca (1960) demonstrating a difference in the rate of oscillation of iron nuclei at the top and bottom of a tower at Harvard.

It was also observed in signals sent by a hydrogen maser shot up above the earth and allowed to fall back by Vessot (1980).

Gravitational time dilation can be explained by the spatiomaterialist theory of gravitation, but it implies that physical processes are actually slowed down only when material objects are at rest in a gravitational field. Objects in free fall in a gravitational field are not affected. But there is an appearance of a time dilation in objects in free fall that is caused by the change in the velocity of the light by which the speed of falling clocks is observed. Let us, therefore, consider each case separately.

Real gravitational time dilation. The principle of equivalence implies that material objects at rest in a gravitational field will suffer a time dilation, and the ontological explanation of the equivalence principle according to the spatiomaterialist theory of gravitation implies that the rate of time dilation is proportional to the energy that would be required to accelerate the object to keep in at rest given its velocity relative to the inherent motion.

This distortion is like the Lorentz time dilation, except that it depends on resisting the gravitational acceleration of the inherent motion rather than having a constant velocity relative to it. According to the spatiomaterialist theory, a clock at rest in a gravitational field, for example, will be slowed down compared to a clock in free fall. If a free falling clock happened to have an initial upward velocity in a gravitational field like a ball thrown into the sky and it was synchronized with a clock at rest on its way up, then, when it passed the same rest clock again on its way down, the rest clock will have fallen behind by an amount that depends on the period between the measurements and the energy required each unit of time to resist the acceleration of the inherent motion and keep it from falling in gravity, given the velocity of the accelerated inherent motion at that point.

The “gravitational red shift” in objects at rest is usually explained as a consequence of Einstein’s equivalence principle. Consider two clocks at rest at different altitudes in a gravitational field and what happens to a regular signal (such as photons of a certain frequency) sent between them, say from the upper rest clock to the lower. (See Diagram of Gravitational red shift.) The equivalence principle implies that, when this interaction is observed from a free falling frame, it must obey the same laws that hold for inertial frames outside gravitational fields.

Consider, therefore, a free falling frame as long as the distance between the two rest clocks, and suppose that it had been shot upwards so that its inertial motion brings the top of the free falling frame momentarily to rest in space alongside the upper rest clock just as it sends a photon of a certain frequency toward the bottom rest clock. If the photon were intercepted by the bottom free falling clock, it would have the same frequency observed when it left, because that is what would be observed if the inertial frame were outside the gravitational field. But that is not how the photon would appear to the bottom rest clock, as can be predicted by observers on the free falling frame. All the time that the photon is traveling downward, the free falling frame is also accelerating downward, and thus, when the observer at the bottom of the free falling frame sees the photon being received by the bottom rest clock, that clock will be moving upward toward the photon. Such motion would cause a Doppler effect, and so the free falling observer predicts that the photon will be measured by the bottom rest clock as having a higher frequency than the photon sent by the upper rest clock. Indeed, this is what the rest observer does find, according to GTR and actual experiment.

In this case, it is a gravitational blue shift, but if the signal had been sent upward, it would be a red shift. (By the time the photon arrived at the top rest clock, the free falling frame whose bottom clock was momentarily at rest beside the bottom rest clock when the signal was sent would have accelerated down­ward, and so the top free falling observers would see the top rest clock as receding upward when the signal arrives, entailing the prediction of a Doppler red shift, that is, a lower frequency of light received by observer located by the top rest clock.)

What is the cause of the red/blue shift observed by the receiving rest clock?

GTR explains the frequency change by the spacetime curvature between the two clocks, but it does not say whether it results from a change in the frequency of light signals during the flight or a difference in the intrinsic rates of rest clocks at different altitudes. Will (1986, p. 49-50) says that “it doesn’t matter” whether the “light signal changes frequency during the flight” or the “intrinsic rate . .  of the clocks change”, because there is “no operational way to distinguish between the two descriptions”.

Spatiomaterialism, however, cannot be indifferent, for it assumes that space and matter are substances that exist only at the present moment, and that means that the red/blue shift cannot involve any actual change in the frequency of signals as they travel across space through time. The frequency, or period between signals, cannot change, regardless how the velocity of light may change along the path, as long as each signal follows the same path in real time. The only possible spatiomaterialist explanation is that the frequency shift is an appearance due to an actual slowing down of the rest clock (and all processes involving material objects at rest).

Spatiomaterialism explains why the clocks at rest are slowed down by their relationship to the inherent motion. The inherent motion is accelerating at the location of the clock, which is evident in the free falling frame, and thus, the rest clock must be accelerated relative to it in order to keep it at rest. In order to understand the relationship between these two reference frames, let us consider the equivalent situation outside of gravitation according to the spatiomaterialist theory.

The relationship between these two reference frames in the gravitational field is not equivalent to one reference frame being accelerated relative to some inertial reference frame outside gravitation unless both frames are also in motion relative to the inherent motion in space, because at any point in a gravitational field, the inherent motion has acquired a certain velocity relative to absolute space. Thus, let us consider two reference frames outside of gravity that have the same velocity relative to the inherent motion as those in the gravitational frame, and let us suppose that one of them is accelerated relative to the other. In such a case, the Doppler effect would cause the same red (or blue) shift, depending on which way one frame was accelerated relative to the other during the brief interval of measurement.

Outside a gravitational field, the Doppler effect would not be interpreted as a time dilation, because it would be explained by the change in the velocity of one of the frame relative to the inherent motion due to its acceleration during the interval of measurement. The situation in the gravitational field is different because the acceleration of one frame relative to the other does not change the velocity of either one of them relative to the inherent motion.^[4] Instead, it is the inherent motion itself that is being accelerated. Thus, the red (or blue) shift cannot be explained as a result of the change in velocity relative to the inherent motion due to the acceleration of the frame at rest in gravitation, as it is outside gravitation. It can only be the result of a slowing down of physical processes on the reference frame at rest in gravitation. Thus, it is a real time dilation.

Rest clocks at different altitudes in a gravitational field suffer different rates of time dilation, even though they may be resisting the same rate of acceleration in the inherent motion (as in a uniform gravitational field). This can be explained on the spatiomaterialist theory, because they have different velocities relative to the inherent motion. Outside a gravitational field, according to Newtonian physics, different amounts of energy are required for the same acceleration in objects when the objects have different velocities. The force per unit time is the same, but since at higher velocities, the force must be exerted over a greater distance, and thus, the energy consumed in exerting the force over that period of time is greater. That is, the rate of gravitational time dilation is proportional, not the force required to accelerate the rest clock, but to the amount of energy required. (At lower altitudes, the force has to act over a greater distance relative to rest in the inherent motion in order to keep the clock at rest.) This explains why the rate of time dilation is proportional to the potential energy for its location in the gravitational field (or the kinetic energy an object falling from outside the gravitational field would have at that point).

Apparent gravitational red shift. An actual gravitational time dilation occurs only when the clock is being accelerated against the acceleration of the inherent motion. A clock in free fall in a gravitational field will actually tick away at the same rate as a clock outside of the gravitational field. But a clock free falling in a gravitational field will appear to suffer a gravitational time dilation, because the motion of the clock across the gravitational potential means that any signals it sends out at regular intervals will be received later than they are expected, making it seem like the clock is slowed down.

Consider a clock in free fall sending signals out of a gravitational field. To observers outside the gravitational field, those signals will make it appear that the clock is suffering a time dilation, though it is not, because in addition to the normal Doppler shift expected from the velocity it acquires from free fall, signals sent back from lower altitudes will also travel the additional distance at lower velocities of light because the outbound velocity of light is lower (because the inbound velocity of the inherent motion is greater the closer it is to the center of gravity). Each signal will be delayed a bit longer than expected.

Or consider a clock shot upwards in a gravitational field that sends regular signals to earth (Vessot’s experiment). The signals received from the clock on earth will be affected by several factors apart from gravitation, including its location at the moment the signal is sent and its instantaneous velocity. These factors can be calculated and compared with the signals actually received. The actual signals will seem to be arriving sooner that expected the higher the clock goes, making it seem that the clock must be speeding up as it rises out of the gravitational field. But that is not proof that objects in free fall suffer a time dilation. Instead, it merely indicates that the light signal is traveling faster toward earth than the velocity of light outside of gravitation, and the higher the clock rises, the more different this factor makes  (though the effect decreases as the altitude increases, because the signal travels the additional distance at a velocity that is closer to what it is outside gravitation).

The spatiomaterialist explanation of gravitational time dilation in general relativity resembles its explanation of the global equivalence of inertial frames in special relativity, because in both cases it recognizes both real and apparent distortions.

In special relativity, the Lorentz distortions are real in inertial frames that are moving relative to the inherent motion. But to observers on such a moving inertial frame, the inertial frame at rest relative to the inherent motion appears to be suffering Lorentz distortions. (The appearance is caused, as we have seen, by the mis-synchronization of clocks on the moving inertial frame and how that combines with its real Lorentz distortions.)

In general relativity, the gravitational time dilation is real material objects that are at rest in a gravitational frame, because that is how accelerate reference frames are related to the inherent motion. But free falling clocks appear to be suffering a time dilation, because as the clock falls, the signals travel pathways from the clock to the stationary observer at various velocities that are either faster or slower than the velocity of light outside of gravitation, depending on where the is located when the signal is sent.

Propagation of the gravitational force through the inherent motion.  The final famous prediction of Einstein’s general theory of relativity is precession of the perihelion of Mercury’s orbit around the sun  As Mercury orbits the sun, the main axis of its elliptical orbit rotates slowly around the sun (in the same direction as Mercury itself). It is a very small rotation (about 43 seconds of an arc per century, setting aside the other perturbations that Newtonian physics can also explain. This phenomenon also has an explanation in terms of the acceleration of the inherent motion in space according to the spatiomaterialist explanation of gravitation.

The gravitational force is exerted by a center where matter has accumulated by way of the inherent motion, that is, at the outbound velocity of light in the inherent motion it affects. The force is like a pulse of attraction propagating outward from the gravitating body, accelerating the inherent motion toward itself wherever the pulse reaches. The force is steady, because one pulse follows another continuously. But the gravitational force exerted anywhere in the field imposed by these pulses is exerted locally, by the inherent motion though which matter of any kind coincides with space at that point.

Gravitational waves. It helps to have a concrete model of how the gravitational force is exerted, and so let us think of it as being exerted by a flow of outbound pulses through the inherent motion affecting the velocity of inherent motion itself that it passes through. That will enable us to see why there are gravitational waves, as predicted by Einstein’s general theory of relativity.

When a gravitating body is at rest in space, its force field is basically spherical. The center of matter exerts a gravitational force on the surrounding space by way of the inherent motion (at the velocity of outbound light in it), and the acceleration it imposes on the inherent motion itself falls off at the square of the distance. Though the acceleration felt at any point in the gravitational field depends on a force that started propagating from the central body earlier, the acceleration at that point does not change over time, because each pulse of gravitational force is followed by another pulse the next moment.

At any point in the field, the arrival of a gravitational pulse accelerates the inherent motion inward (increasing its inbound velocity as it pulls it inward), but the pulse then moves on to the next location in space and does the same thing to the inherent motion located there. At each moment at any point in space, the inherent motion itself that arrives from farther out (because of the last pulse) is subject to the next pulse of gravitation, and so the inherent motion itself is accelerated inward, giving it a higher inbound velocity as it moves closer to the gravitating body. The gravitational field is, therefore, like a flow of gravitational pulses outward in the inherent motion everywhere pulling the inherent motion itself toward the gravitating body. Thus, it is a steady gravitational force field, which would affect objects in the way Newton’s law predicts.

However, when a gravitating body is moving back and forth across space (for example, when a pair of dense astronomical bodies are in orbit around one another), the pulses of forces propagating outward from the gravitating body come from different locations from one moment to the next, and thus, there is a wavelike change in the acceleration of the inherent motion at a distance. Thus, any material objects located there will feel a gravitational force that is changing directions from moment to moment.

Since the gravitational wave can accelerate material objects, it carries potential energy across space, and thus, it is a form of matter (which we are calling “gravitational matter”). If the gravitational field were imposed by a gravitating body at rest in space, the gravitational matter constituting it would be counted as part of the total quantity of matter (mass and energy) accumulated at its center (because the gravitational force is accelerating the inherent motion toward itself). But the gravitational matter making up waves is not counted in the rest masses of the gravitating bodies generating it (because the gravitational force is not accelerating the inherent motion toward itself. Thus, gravitating bodies lose energy as they exert gravitational waves. (The astronomical bodies orbiting one another will slow down and eventually fall into one another.)

Precession of the perihelion of Mercury. This explanation of how the force of gravitation is exerted can explain the precession of the perihelion of Mercury (or any planet around a star). The inherent motion itself is accelerated by gravitation, and thus the force of gravitation that is felt by any bit of matter depends on the acceleration of inherent motion in the part of space where it is located at the time.

Since the sun is so much more massive than Mercury, we can treat it as if it were at rest in space. Thus, although it is sending out pulses of gravitation through the inherent motion that accelerate the inherent motion it reaches towards itself, the gravitational field is basically spherical, with the strength of the gravitational force falling off at the square of the distance. This is the gravitational field through which Mercury moves.

Mercury is moving roughly perpendicular to the sun’s radial force field, and if that were all that determined the gravitational force that Mercury feels, Mercury would follow the pathway predicted by Newton’s law of gravitation (because its being the result of a pulse of gravitation propagating from the sun does not make any difference to the force that Mercury feels).

Mercury is also, however, another gravitating body. It is sending out pulses of gravitational attraction radically in the inherent motion, accelerating the inherent motion itself towards itself. Insofar as its pulses are oriented in the same direction as those propagating radially from the sun, this will make no difference, because Mercury’s force will be acting on an inherent motion that is everywhere being accelerated toward the sun. However, Mercury will also be accelerating the inherent motion toward itself in directions perpendicular to the sun’s radial forces. And since the sun’s radial pulses of gravitational forces travel by way of the inherent motion, they follow the path of light rays, and since Mercury will be bending light rays that pass by it (just as the sun does; see Gravitational bending of light rays), Mercury will be bending the sun’s pulses of gravitational forces toward itself as they pass by.

The acceleration of the inherent motion toward Mercury changes the location of the sun’s gravitational forces, but not the direction in which those forces accelerate bits of matter. As radial forces, they are normally pointing at the sun. But consider what happens to the inherent motion ahead of Mercury as it moves perpendicular to those radial forces. As it accelerates the inherent motion toward itself, it shifts the location of the inherent motion itself (the bending of the light rays), and thus, the gravitational force that would be exerted in those parts of space are no longer directed at the sun, but are slightly offset. They point to a location relative to Mercury that the sun would otherwise have only later in its orbit. Thus, when Mercury coincides with the part of space in which the displaced inherent motion is located, the force of gravitation will not be in the direction of the sun, but slightly offset.

To be sure, there is a symmetry about the acceleration of the inherent motion in front of Mercury and behind in its direction of motion. After all, light rays are bent towards it as they pass either in front or behind Mercury. But there is an asymmetry caused by Mercury’s motion. It is moving toward the inherent motion accelerated towards it in front, and it is moving away from the inherent motion accelerated towards it from behind. Thus, Mercury is affected by the displaced gravitational forces ahead of it, because it is moving into the parts of space where they are located. And it is moving away from the parts of space where the displaced gravitational forces behind it are located.

The net effect of the asymmetry caused by Mercury’s motion into the inherent motion it has accelerated towards itself in front of it as it moves is that its change of location relative to space amounts to a greater change of location relative to the inherent motion. The gravitational pulses, like light rays, are pulled closer together in front of it, so that its velocity relative to space makes a greater change in the direction of the gravitational force it feels than would otherwise be the case.

Since through its orbit, the direction of the sun’s force is always displaced in the same direction (as if Mercury were farther along in its orbit than it actually is), the sun’s gravitational force is always making Mercury change direction faster than it would otherwise, and thus, the orbit as a whole precesses around the sun in the same direction as Mercury itself.

The alteration in the direction of the effective gravitational force of the sun on Mercury is the major factor accounting for the precession, but there are two additional factors making it different from Newtonian expectations, which are relatively minor.

First, the propagation of Mercury’s pulses of gravitational attraction outward in the inherent motion is not quite at the velocity of light, because its acceleration of the inherent motion has given it an inbound velocity. In front of Mercury as it is moving though the inherent motion perpendicular to the sun’s radial acceleration, Mercury’s outbound pulses of gravitation have a velocity that is less than the velocity of light outside of gravitation by the escape velocity at each point in its outbound propagation.

Second, since Mercury itself is a material object, its motion relative to the inherent motion subjects it to Lorentz distortions, including a relativistic mass increase. Thus, it takes a greater gravitational force to change its direction.

Phenomena in Strong Gravitational Fields. The acceleration of the inherent motion in space is what replaces the curvature of spacetime in the spatiomaterialist explanation of gravitation. But we have considered mainly phenomena involving weak gravitational fields and velocities much slower than light, and its assumption about the nature of the gravitational force also explains other new GTR phenomena involving strong gravitational fields and high velocity.

In strong gravitational fields, for example, the velocity of the inherent motion itself (the ether) relative to space can approach the velocity of light mediated by the inherent motion, and thus, spatiomaterialism implies that a time dilation will occur even in free falling clocks, if they have a sufficient high velocity relative to the inherent motion in space.

Consider, for example, a free falling clock that is shot upwards out of a gravitational field so that it rises and falls back. At the top of its trajectory, the cock will be momentarily at rest relative to space, and even though it is not being accelerated against the gravitational attraction, it may be suffering a Lorentz time dilation. In this case, it would be caused by its constant velocity relative to rest in the inherent motion, which is rushing inward because of its acceleration by the gravitating body.

This Lorentz time dilation is different from the gravitational time dilation discussed above, which is caused by being accelerated in a gravitational field. But both factors may be contributing to the red shift that observers outside the gravitational field observe in light signals sent outward by such objects.^[5] But since the Lorentz time dilation is a second order effect (a function of v²/c²), while the gravitational time dilation is a first order effect (a function of v/c), it doesn’t become significant until the emitter’s velocity relative to the inherent motion approaches that of light itself in the inherent motion. In strong fields, however, the Lorentz time dilation may be a more significant cause of red shift than the gravitational time dilation.

Indeed, material objects in strong gravitational fields with very high velocities relative to the inherent motion will suffer all the Lorentz distortions: length contraction, mass increase, and flattening of electric force fields, as well as time dilation.

I have already mentioned that the acceleration of the inherent motion can give the inherent motion itself (the ether) a velocity relative to space that is as great as the velocity of light outside gravitation (that is, in the ether). This is what happens at the Schwartzschild radius of a black hole. No light can escape a black hole, because everywhere on that spherical surface surrounding the black hole the outbound velocity of light mediated by the inherent motion is canceled out by the inbound velocity of the inherent motion itself. Any such photons would be at rest in space, even though they are moving at the velocity of light in the inherent motion.

Nor could anything else escape the black hole, since doing so would require moving through the inherent motion faster than the velocity of light. That is why it is called an “event horizon”.

Free falling material objects cannot even be momentarily at rest at the Schwartzschild radius, for the Lorentz distortions caused by their velocity relative to the inherent motion at that point would require their lengths to be zero, their physical processes to have stopped, and their masses to be infinite.

Inside the event horizon, light traveling any direction in the inherent motion would have an increasing velocity relative to absolute space toward the center of the black hole. And any bits of matter being accelerated by that acceleration of the inherent motion would move and interact with one another as they do outside gravitational fields (except for tidal forces, which bring their radial pathways closer together), as implied by Einstein’s equivalence principle. But when the bits of matter reach the center of the black hole, they must come to a stop. Physics does not say what happens then. Material objects cannot withstand the forces on them at the center, and presumably, they would collapse spatially, making the gravitational forces infinite. Thus, the center of a black hole is aptly called a “singularity” in absolute space.

Since neither light nor gravitational pulses can propagate outbound from beyond the Schwartzschild radius, the only indication of the amount of matter that has fallen into the black hole is the size of the Schwartzschild radius.

Spatiomaterialism can also explain what is happening around rotating black holes. Rotating black holes are formed by matter spiraling in, and there is an asymmetry about the gravitational field they set up which draws bits of matter falling toward the back hole in the direction of its rotation.

The reason is that the force of gravitation exerted by matter falling into a black hole propagates outward at the velocity of light in the inherent motion, and since at the Schwartzschild radius, the inherent motion itself is moving inward at the velocity light would have in the inherent motion if it were outside gravitational influences, only the forces propagated outward just before passing across the radius have an effect on the inherent motion outside. And since the matter is spiraling past the Schwartzschild radius, it has a greater effect behind than in front of its direction of motion. Thus, other bits of matter in that region of space feel an attraction that is not directly into the black hole, but which pulls it around the black hole in the direction of the matter that preceded it.