Newton’s laws of motion. Newton’s laws of motion are remarkably simple.

First law of motion: “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it.”

Second law of motion: “The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”

Third law of motion: “To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Law of gravitation: material objects always attract one another in proportion to the product of their masses and inversely as the square of the distance separating them.

Newton’s laws describe how material objects move and interact, and since we postulate matter in the form of material objects with rest mass, we need only see how the regularities described by Newton’s laws of motion would be explained on the assumption that kinetic energy and potential energy are forms of matter as well. That requires making further assumptions about the specific essential natures of these forms of matter and about space, but as we shall see, it affords genuine, even illuminating, ontological explanations of some aspects of classical physics.

According to our working hypothesis, the motion of a material object with rest mass is due to the kinetic matter attached to it. The kinetic matter must coincide with the same part of space as the material object itself, but in a way that that moves the material object across space as time passes. Each speed and direction of motion for any given material objects would involve a (quantitatively) different variety of kinetic matter (which could be explained ontologically by aspects of how kinetic matter coincides with space, such as its direction and quantity).

Newton’s first law of motion. Newton’s first law is an immediate consequence of this ontological assumption about kinetic matter. Since the kinetic matter that makes the material object move is itself a substance that endures through time with the same essential nature, the object in motion will continue moving at the same speed and in the same direction (unless it interacts with another bit of matter).

What does not change according to the first law of motion is called “velocity,” because it includes two aspects of the object’s motion, its speed and its direction. That is why we assume that, for any given material object, each different speed and each different direction requires a different variety of kinetic matter. The velocity is not the kinetic matter, but just a property of the material object with the kinetic matter, that is, an aspect of the substances constituting the object with rest mass together with its kinetic matter and how both are contained by space. (The three dimensional structure of space makes it possible to represent any velocity mathematically as a certain speed in each of any three mutually perpendicular directions. Quantities that depend on direction in this way are called “vectors.”)

Newton’s first law must be true, if the motion of objects is due to kinetic matter, because all the ways that an object might be thought to change its speed or direction on its own are ontologically impossible. A change in its motion would require kinetic matter of one variety to come into existence and another variety would have to go out of existence as time passes, which substances cannot do. Or it would require the variety of kinetic matter to change its essential nature, which no form of matter can do on its own. Or it would require space to contain kinetic matter in a different way at different locations, which is not compatible with the uniformity of space.

To be sure, in order to explain motion as a form of matter that connects material objects to space in a certain way, the objects must have an absolute velocity, that is, a certain velocity in absolute space. That may seem doubtful in contemporary physics, but it is just what spatiomaterialism entails about the nature of space and that is what is at issue in this ontological explanation of physics.

Notice that the assumption that an object’s velocity is due to its kinetic matter solves a problem that motion otherwise poses for any ontology that that postulates only substances enduring through time. The problem was first posed by Zeno as a paradox about motion. He pointed out that, at each moment, an object must be at rest (as we assume by holding that nothing exists but the present), and he asked, How is motion even possible in that case? If motion is simply how location changes as time passes, motion does not really exist, because the object always has only one location at each moment as it is present. This is not just a puzzle about the continuousness of time and space, because holding that to move is just to have a location that varies continuously with time leaves a problem about why the moving object has a different location the next moment, whereas the object at rest does not. What makes the object in motion different from the object at rest at each moment? To be sure, it is possible to simply assume that the essential nature of all material objects includes the temporally complex property of changing locations again, if it did so the last moment. That is what materialism does in this case (as in the case of every other basic law of physics), and it is not very satisfying, because there is nothing to distinguish the moving object from the one at rest at any moment except where each was the previous moment (which is not something that exists at that moment). If, however, motion is constituted by a bit of kinetic matter that exists in addition to the object with rest mass, then motion is actually a substance that endures through time, and thus, what makes the moving object at any moment different from an object at rest is something that exists at that moment (not just the fact that it has a different position the previous moment).

The first law of motion allows for velocity to change when the material object interacts with another object, and given the forms of matter we are postulating, the only way that a material object can change velocity is for kinetic matter to be transferred to it or from it or both. Somehow the object must come to have a different variety of kinetic matter attached to it. That is basically what interactions do to objects with rest mass. In such an interaction, Newton’s laws say that the object is subject to a force, and our working hypothesis implies that the exertion of a force on the object somehow transfers kinetic matter to and/or from it.

Interactions are something that we expect, given our assumption that material objects are a form of matter that cannot occupy the same place at the same time, because if they can move, they can move to the same location at the same time and something must keep them from being contained by the same part of space. The simplest kind of interaction is a collision of material objects that is elastic, that is, in which nothing changes but the velocities of the material objects that collide. Though collisions of ordinary material objects are mediated by electromagnetic interactions, we can, for present purposes, abstract from the nature of the forces and consider only what happens when material objects collide. We know that they exchange kinetic matter. But we do not know how much is transferred or what effect it has on their velocities. The regularities about such transfers of kinetic matter are what is described by Newton’s second and third laws of motion.

Newton’s second law of motion. Newton’s second law holds that the exertion of a force is what changes the velocity of a material object. Since forces are exerted by other objects, the force on any object has some direction or other, which determines in some way the direction in which the object’s speed changes. It also has a determinate strength and its action on the object has a certain quantity. But how much an object’s speed changes in the direction of any given force depends on another factor, its rest mass, or the quantity of matter embodied in it. That is, what changes when a material object is subject to a force is its momentum, or the product of its velocity and its rest mass.

In the case of material objects composed of many parts with the same rest mass, our working ontological hypothesis offers an explanation of the relevance of rest mass in determining the change of velocity. In order for the composite object to move in a certain way, each of objects of which it is composed (each “atom,” if you will) must move in the same way (assuming that the parts have unchanging spatial relations to one another). Since each part must be moved across space by its own bit of kinetic matter, a force can change the velocity of the whole only by changing the velocity of each part in the same way. Thus, the change in velocity caused by a force varies inversely with the total rest mass of the material object. It must be spread out among all the parts, so to speak. For example, an object with twice as much rest mass has half as much change in velocity, if subjected to the same force. In other words, what changes is not merely its velocity, but its momentum, the product of its velocity and its rest mass.

The second law of motion also holds in the case of elementary material objects with different rest masses. But without a deeper ontological explanation of the nature of kinetic matter and material objects with rest mass, that regularity can only be assumed as part of the essential natures of those forms of matter.

Velocity is not a measure of the amount of kinetic matter, because the change caused by the transfer of kinetic matter to or from an object depends on its rest mass. But it might seem that momentum is the measure of kinetic matter, since it is what changes when kinetic matter is transferred. However, momentum, like velocity, is just a property of the material object with kinetic matter, and we can begin to see why by considering the third law of motion.

Newton’s third law of motion. Newton’s third law describes a more inclusive regularity than the second, for it includes the object that is the source of the force, describing how it is affected as well. This law holds that the action of one object on another is opposed by an equal and opposite action of the other object back on the first. That is, every action of one object on another is actually a symmetrical interaction of the two objects involved. And since what the action changes is momentum, this law says that the change in the momentum of one object is equal and opposite to the change in momentum of the other object. Thus, Newton’s third law of motion entails the conservation of momentum. That is, in any interaction, the sum of the products of the velocity and mass of all the objects involved in the interaction does not change in any direction regardless how the objects may interact.

The conservation of momentum may make it seem that momentum must be the measure of the total quantity of kinetic matter involved. Suppose, for example, that two equally massive objects moving toward one another at the same speed were to collide. Given our working ontological hypothesis, we might try to understand why the two objects rebound from one another by thinking of the interaction as each object transferring its kinetic matter to the other, for that would also explain why both objects come out with velocities in the opposite direction. Each acquires the other object’s kinetic matter. And if the objects had different rest masses and different velocities, this would even explain how much the velocity of each changes. 

Momentum cannot, however, be the measure of the amount of kinetic matter, because it is a quantity that depends on the direction of the motion, whereas the quantity of kinetic matter does not. (In other words, momentum is a “vector quantity,” whereas kinetic energy, as a substance, must be a “scalar quantity,” which does not depend on the direction of motion.) To illustrate the problem, suppose that two objects colliding with equal and opposite momentums do not rebound from one another, but simply come to a stop. The latter is compatible with Newton’s third law of motion, because the change in the momentum of one is still equal and opposite to the change in momentum of the other. Each loses an equal and opposite momentum. Action and reaction are symmetrical. But if momentum were the measure of kinetic matter, it would mean that their kinetic matter simply goes out of existence, for their momentums cancel out. And since that is impossible for a substance, momentum cannot be the measure of kinetic matter.

It is no great surprise, of course, that momentum is not the measure of the quantity of kinetic matter on this ontological explanation, for we postulated the existence of kinetic matter in the first place in order to account for kinetic energy. But the foregoing example does bring out the difference between momentum and kinetic energy. It is currently explained only mathematically: in Newtonian physics, momentum is the product of an object’s rest mass and its velocity (mv), whereas its kinetic energy is one-half the product of its rest mass and the square of its velocity (1/2 mv²).

It is a subtle difference, which was not obvious even to classical physicists at first. The difference was not recognized by Cartesians, and Leibniz was so struck by kinetic energy being different from momentum, or mere motion, that he took the existence kinetic energy as evidence of a vis viva, a “force of life” in the object, which helped inspire his belief that atoms are really “monads,” or minds.

The ontological difference between kinetic energy and momentum is that the former is the quantity of a form of matter that can be attached to objects with rest mass and the latter is a quantitative property that material objects have when kinetic matter is attached. Momentum is just an aspect of those two kinds of material substances as they are contained by space, an aspect that depends on the direction of the motion in space. Newton’s second and third laws of motion describe the regularity about how that property changes when material objects interact, including the conservation of momentum. The kinetic energy is, however, part of the substance constituting the object in motion, and so it is conserved because it is a substance.

This is just the beginning of an ontological explanation of the difference between kinetic energy and momentum. Though we can see that they are different, it does not explain the quantitative relationship between them, that is, why kinetic energy varies with the square of velocity, while momentum varies with velocity. That can be explained only later, when we take up a deeper ontological explanation, the quantum theory of matter. There is a more specific nature of kinetic matter that entails momentum being related to kinetic energy as the velocity to the square of velocity.

In the foregoing case, where colliding objects with equal and opposite momentums simply stop, the collision is not elastic, that is, something changes besides the motion of those objects. Instead of dropping out of existence, the kinetic energy is converted into another form of matter (such as potential energy in new forces being exerted among its parts) or transferred to other objects (such as the kinetic energy of the parts of the objects, that is, becoming heat).

Newton’s law of gravitation. Newton’s law of gravitation holds that material objects exert an attractive force on one another that is proportional to the product of their (rest) masses and inversely proportional to the distance between them. But since each object exerts such a force on the other, an object must have a gravitational field around it even when there are no other objects in its neighborhood. There is, in other words, a gravitational force at every location in the space around the material object. Those forces are radially symmetric around the object itself, and their strength declines with the square of the distance from the object.

The gravitational field is explained ontologically by postulating matter in the form of gravitational matter, which is spread out in space around the material object exerting the gravitational force, though its quantity is included, along with matter is some other (yet to be described) forms, as the rest mass of the material object. This affords an obvious ontological explanation of many of the aspects described by Newton’s law of gravitation. Gravitational forces are directed toward the object, since that is the center of the rest mass of the material object that spreads gravitational matter out in space. The forces are radically symmetric, because the object is located in three dimensional space. And the strength to the force falls off with the square of the distance, because that is how fast space spreads out sideways as you move away from the source of the force.

The force of gravity is not given an ontological explanation in classical physics. Instead, it is usually described as just a disposition at each point in space to exert a precise, mathematically described force on any material object (with a certain mass), if it were located at that point. Talk of “dispositions” is a way of predicating regularities of objects as if regularities were just properties of the objects. But that is to leave those regularities unexplained. There is no alternative in classical physics, because it assumed that gravity involves action at a distance (which is implicitly to deny the reality of the space across which it is supposed to act). Talk of gravitation as a disposition is a way of being skeptical about the reality of such forces as anything beyond their effects. This ontological problem was eliminated by Einstein’s general theory of relativity, and that discovery is what we are anticipating by including gravitational energy as a form of matter in this explanation of the truth of classical physics.

Gravitational matter helps explain the truth of the principle of the conservation of mass and energy, however, only by being counted as a negative quantity, that is, as potential energy. The maximum quantity of potential energy is zero, because according to our our ontological explanation of that accounting practice, potential energy is actually part of the matter that is already counted in the rest mass of the material object whose forces are a potential source of kinetic energy.

This theory calls for a deeper explanation of how the matter appears both as a material object, with a definite location and rest mass, and at the same time as force field spread out in the space around that center of mass. We will consider such a theory later, but for now, we must simply recognize that the rest mass includes both forms of matter. And we can use the notion of gravitational potential energy to illustrate further the puzzling relationship between momentum and kinetic energy.

Gravitational forces exist as fields in which forces are exerted continuously over time and material objects change momentum continuously as they move through them. The way in which material objects interact by gravitational forces can be described as a conversion between potential and kinetic energy, and since such conversions are also a way of explaining the interaction of material objects by electric and magnetic forces, I will describe some of its features by considering what happens to a ball thrown upwards in a (nearly) constant gravitational field, such as near the surface of the earth.

The ball has an initial momentum when it leaves the hand that is proportional to its upward velocity. But since its momentum is constantly decreasing as the result of the constant downward gravitational force on it, there is a point at which the ball comes to a stop and starts falling again, after which its downward velocity increases until we catch it. The ball had kinetic energy when it left our hand, but at the top of its trajectory, it has lost all its kinetic energy. And by the time we catch it, the ball has regained kinetic energy. Since kinetic energy is a form of matter, it never simply goes out of existence or comes into existence, but merely changes form. It is converted into potential energy, which the ball has because it is located in a way that enables the gravitational force to accelerate it over some distance, that is, can acquire kinetic energy from those forces as the object moves through the gravitational force field. If we think of it ontologically, we see the ball losing kinetic matter as it rises, but since the distance across which the gravitational force can accelerate the ball increases, it gains potential energy (which increases the rest masses of both ball and earth). And when it falls, it loses potential energy (decreasing rest masses) and acquires kinetic energy. Since the ball has lost all its kinetic energy at the top of its trajectory, when it is at rest, its potential energy at that point must be equal to its kinetic energy at the beginning and end of its trip. The potential energy depends on two factors, the force exerted by the earth on the ball and the ball’s location in that force field. Both are needed to accelerate the ball and give it kinetic energy, and since the force is nearly the same at every location, the potential energy turns out to be proportional to the height to which it rises, that is, to the distance it can fall in the (constant) gravitational field.

This allows us to see, once again, the difference between momentum and kinetic energy. How much faster would we have to throw the ball upward in order for the point at which its stops and starts falling again to be twice as high? It is not necessary to double its velocity, as we would find if we tried. Instead, the initial velocity needs to be increased only by the square root of two (or about 1.4). The reason is that the ball consumes kinetic energy in rising to a certain height in the gravitational field, not momentum, and since kinetic energy varies with the square of the velocity, it is not necessary to double the initial velocity to double kinetic energy). (Likewise the time it takes will also increase only by a factor of the square root of two, since gravity changes its momentum at the same amount each unit of time and the amount of momentum to be changed is only increased by the square root of two.)

The conversion between kinetic and potential energy is basic to classical physics, though the quantities become more complex when we take into account that gravitational forces are not constant, but have a strength that varies inversely with the distance from the center of gravity. But we need not consider all the complexities of the quantitative relations (though these ontological causes must be able to explain them in the end), because we are merely trying to see what is involved in an ontological explanation of the basic laws of classical physics. We have seen how such ontological causes would make Newton’s laws of motion true, and spatiomaterialism is not trivial, like materialism, considering that it implies the existence of kinetic matter (and begins, at least, an explanation of the relationship between momentum and kinetic energy). The one form of matter that has not been described is electromagnetic waves, and that brings us to the explanation of Maxwell’s laws of electromagnetism.

Maxwell’s laws of electromagnetism. The other basic set of laws making up classical physics at the end of the 19^th Century were Maxwell’s four laws of electromagnetism. They describe the electric and magnetic forces and how they interact, and these forces can be explained in much the same way as gravitation, that is, as a form of matter that coincides with space by being spread out spread out in space like a field, and yet contained in the rest mass of material objects with electric charges.

Electromagnetism is more complex than the gravitational force, because there are two forces, electric and magnetic, which interact with one another, and there are two opposite electric forces that material objects can have, positive and negative.

Maxwell’s great triumph was to show how the interaction of the electric and magnetic forces can couple them in a way that propagates both across space at a fixed velocity, that is as electromagnetic waves propagating at the velocity of light. Since electromagnetic waves exist independently of all the other forms of mass and energy (and, thus, the other three forms of matter, on this ontological account), there is less room for doubt about these forces being a form of matter.

It is now known that electromagnetic interactions mediate all the non-gravitational interactions among molecules, among atoms in molecules, and even between electrons and protons in atoms. Even the elastic collisions that we took for granted in discussing Newton’s laws of motion are mediated on the micro level by interactions involving both electric and magnetic forces among objects with electric charges. But all these interactions involve events with a unit-like nature which was unexplained until the discovery of quantum mechanics, and we will take them up later (in Change: Quantum mechanics.)

At this point, I will discuss aspects of the regularities described by Maxwell’s laws in an order that adds up to an explanation of electromagnetic waves, and then I will discuss how spatiomaterialism can explain such waves ontologically.

Electric charge. One of Maxwell’s laws describes the electric forces that can be exerted by material objects. When a material object has an electric charge, it exerts a radial force surrounding the center of rest mass whose strength declines with the square of the distance. This is like the force of gravity, except that the electric force acts on other objects because of their electric charges, rather than their mass. And unlike the gravitational force, the electric force can be either attractive or repulsive, depending on whether the other object has an opposite or same electric charge, respectively. The electric force can give such objects kinetic energy (or become another form of energy, such as an electromagnetic wave), and so it is counted as potential energy. But once again, the maximum potential energy is zero, making it a negative quantity when some of it has been consumed.

Spatiomaterialism can explain potential electrical energy ontologically as some of the matter that is counted in the rest masses of the material objects exerting the electric forces. Thus, when potential energy is consumed, the rest masses of the charged objects are less. If we think of the potential energy as a form of electromagnetic matter that is spread out in space around the objects with the electric charges, we can see why the quantity of potential energy varies with the matter.

Objects with opposite charges attract, and their potential energy is maximum when they are far apart from one another, because their electric fields more nearly approximate a spheres (of forces declining with the square of radius), which requires the maximum quantity of electromagnetic matter to constitute them. But when opposite charges are next to one another, their electric fields are mostly neutralized, and the electric field they jointly set up is deformed in a way that requires less electromagnetic matter. In this case, their total rest mass is less than if they were independent of one another.

Objects with like charges repel, and their potential energy is maximum when they are close to one another, because instead of neutralizing one another, their electric fields oppose one another. Though holding them together yields an electric force that is twice as strong as the radial force field they jointly set up, additional electromagnetic matter is required for the two charged particles to have a force repelling them from one another. In this case, their rest masses are greater than they would be if the objects were at a distance from one another.

In either case, in the equations describing these situations, the potential energy is represented as zero when it is maximum, and thus, what is actually a loss of rest mass, which comes from consuming potential energy and converting electromagnetic matter into other forms of matter, is counted as negative potential energy.

The electric field is also more complex than gravitation in another way because of its interaction with the magnetic force. It affects the motion of a charged object in an electric field. For example, in an electric field is set up by a material object too massive to move much, a charged object that is accelerated by it will increase its velocity not only in the direction of the force, but also in a direction perpendicular to both the electric force and the direction of its own motion in the electric field. That is the work of the magnetic force. The magnetic force on the charged object is a function of its velocity through the electric field as well as the strength of the electric field. This effect of electric forces is not mentioned in this first law, but is a consequence of another of Maxwell’s laws.

No magnetic charges. The second law holds that there is no material object with a magnetic charge, even though there are magnetic forces. A material object with a magnetic charge would have a radial force surrounding its center of rest mass which declines with the square of the distance. Instead, as it turns out, magnetic forces occur in fields in which they are all directed around a closed loop, such as a circle.

According to another law, as mentioned above, the magnetic force can arise because of the motion of a material object with an electric charge. For example, when electric charges are moving in a certain direction through space, they set up a magnetic field in which the magnetic forces are aligned in a circle around their direction of motion. (Such a circular field is set up even when the moving electric charges are neutralized locally by opposite charges, as in a wire in which a current is flowing, and the net strength of the electric force is not changing at any point in space in the surrounding space.)

Coupling of magnetic and electric forces. The two remaining aspects of the regularities described in Maxwell’s equations explain electromagnetic waves. One holds that a change in the magnetic field causes a circular electric force around the direction of the magnetic forces. The other holds that a change in the electric field causes a circular magnetic field around the direction of the electric forces. In both cases, the strength of the field being set up varies with how fast the first field changes (and thus indirectly on the strength of the forces). But the directions are reversed (so that an increasing electric force causes a magnetic force, while an increasing magnetic force causes a electric force in the opposite direction). Furthermore, the change in the strength of each force generates a force of the other kind that is related to it spatially in a certain direction, so that changes in the two forces are coupled as a wave that propagates across space at the velocity of light.

An impression of how electromagnetic waves propagate can be gathered by considering how the motion of electric charges generates them. Consider, for example, a current of electrically charged objects in a wire that is changing direction. The current sets up a magnetic force circling the wire, but as the electric charges slow down, the magnetic force declines (because the rate of change in location of the electric charges becomes lower). The decline in the magnetic force field causes an electric force that circles it. But the change in that electric force causes, in turn, a magnetic field around its direction, which is in the opposite direction of the first magnetic field. And the change in the second magnetic field then causes an electric field, this time in the opposite direction. And finally its change causes a magnetic field that is like the one caused by the electric charges in the wire, except that it is located a fixed distance away from the wire which depends on the velocity of light. Thus, the changes in the two forces are coupled in a way that propagates across space at the velocity of light as an electromagnetic wave. And a steady succession of such waves is generated as long as the current in the wire continues to oscillate. That is basically how antennas send electromagnetic waves.

Electromagnetic waves are a form of energy counted in the principle of the conservation of mass and energy, and though the quantitative details are not relevant here, we should consider what our working hypothesis implies about the nature of "electromagnetic matter." The matter involved in these waves is similar to the matter that makes up the electric field of a material object with an electric charge, except that in the electromagnetic wave, the electric force is changing and the changes couple it with a magnetic force that also changes. The forces interact in such a way that they go through complete cycles, putting them in a position to do the same thing over and over again. But the forces they generate are so related to one another in space that the wave moves across space over time at certain fixed velocity, that is, the velocity of light.

The matter constituting electromagnetic waves may not be as different from the electromagnetic matter constituting electric charges as this contrast makes them appear. According to current quantum theory, material objects with electric charges also have a spin angular momentum. Since that is a magnetic force, it suggests that the electric charge may actually be an electric force that is changing cyclically by somehow spinning around an axis. That possibility will lead us to speculate (when discussing quantum mechanics and the basic particles) that the opposite electric charges (positive and negative) differ from one another by being in opposite phases of their cycles wherever they are located in space.

Inherent motion in space. Maxwell deduced the velocity of light in a vacuum from measurable constants mentioned in his laws, and since classical physics assumed that space is absolute, it could hope to explain this implication as the result of electric and magnetic forces being exerted on an extremely elastic substance that was assumed to be at rest in absolute space. They called it the “luminiferous ether” (or “ether,” for short). Since the ether was supposed to be a kind of matter, it seemed plausible to explain the propagation of electric and magnetic forces mechanically, as an interaction between charged particles and the ether, on the model of waves of forces in ordinary material objects. That project did not work out, but that does not mean that space cannot be playing a similar role in the motion of electromagnetic waves.

In recognizing that space is a substance, spatiomaterialism departs from classical physics as well as from materialism. Though classical physics assumed that space is absolute, it did not take space to be a substance that could interact with bits of matter in any way other than providing all the locations where they are could move or be located. In particular, space was not supposed to affect the motion of bits of matter, at least, not in the way other bits of matter can. But since spatiomaterialism has independent reasons for believing in the existence of space as a substance enduring through time (that is, in addition to presentism, reasons deriving from the recognition of the validity of ontological-cause explanations and inferring to the best ontological-cause explanation of the natural world), it has no reason to doubt that space can interact with bits of matter in ways that are quite comparable to the interactions of bits of matter in space. Thus, spatiomaterialism can use space to explain the velocity of light without having to postulate the existence of the ether as an additional kind of matter that coincides with space. We can take talk about the ether to be referring to an aspect of space as a substance. That is what we will do by taking space itself to be the medium of light transmission.

To be the medium of light transmission, space must have an aspect by which it interacts with electric and magnetic forces and carries them across space as electromagnetic waves at a certain velocity. In order to explain how space does so, I will assume that there is an “inherent motion in space.” By “inherent motion,” I mean a further relationship among the parts of space, beyond the geometrical relations we have already assumed, which involves their endurance through time. We have assumed that the parts of space are particular substances, that is, so that each point has an existence that is distinct from all the others and each point endures, like any substance, through time, never coming into existence nor going out of existence. But since only the present moment exists, only one moment in the history of each part of space exists, and that moment in the history of all the parts of space always occurs at the same time. That is how these substances exist together as a world, and it is the wholeness of space that relates the bits of matter it contains as parts of the same world. This temporal aspect of the nature of the parts of space is the ontological foundation for a further relationship among the parts of space. What I am calling the "inherent motion of space" (as our substitute for the "luminiferous ether") is a spatio-temporal relationship among the parts of space.

Such a temporal aspect to space is not only plausible, but also required by the role of space in constituting what happens. If the parts of space did not have a spatio-temporal relationship to one another, they could not affect one another as time passes. Nor could they enable bits of matter to affect one another.

The geometrical relations among the parts of space explains which parts of space can be affected by any other given part, namely, those nearby, then those next to it, and so on. But in order for a change occurring at any one part of space to affect another part of space, the other part of space must change at a later moment. If the effect were immediate, the effect would not be distinct from the cause, and they could not act on one another like particular substances enduring through time. Space would interact with bits of matter as a whole. Thus, let us assume that the rate at which one part of space can affect another part of space as time passes is finite. That would be a maximum velocity by which one part of space can affect other parts of space. I call it the “inherent motion” in space in order to make clear that it is a temporal aspect of the nature of space as a substance.

I think of the "inherent motion" as a motion sweeping through every part of space at the same velocity, both ways in every direction possible in three dimensional space, at every moment. This is how space is an ontological cause, along with the nature of electromagnetic matter, of the velocity of light. That is, we can explain the motion of electromagnetic waves as bits of matter (or so-called “photons’) being carried along by the inherent motion. But there is an inherent motion, even when there are no photons. Indeed, it would be happening, even if there were no matter in the world.  In other words, the inherent motion is an aspect of space as a substance.

The postulation of an inherent motion may seem ontologically excessive, since all we need to assume is that the parts of space are so related temporally, as well as geometrically, that there is a maximum rate at which it is possible for what happens to matter at one part of space to affect what happens to matter at another parts of space. Thus, it may be urged that the inherent motion is not real, but merely the velocity of possible effects across space. It is merely a spatio-temporal geometry about space, that is, a geometry describing how the present moment of any one part of space is related to the past or future moments of other parts of space because of the maximum velocity with which events can affect one another. Such an account, it could be argued, would be a better ontological explanation in the end.

Though a spatio-temporal geometry to space may be a sufficient ontological explanation, I will continue to speak of it as the "inherent motion in space." I can take this liberty, because I am not claiming that the more specific natures of matter and space that I am introducing in order to explain the truth of physics are the best possible spatiomaterialist ontological explanation of the basic laws of physics, only that they are a possible spatiomaterialist ontological explanation. That is all that is required for ontological philosophy to make the case for using spatiomaterialism as the foundation for its argument about necessary truths. And I allow myself the liberty of postulating an actual inherent motion in space, because that invokes an image (in rational imagination) that makes it easy to think about an aspect of the essential nature of space that will be central in the following explanation of the laws of contemporary physics. I find it preferable to “spatio-temporal geometry,” because talk of motion brings out vividly the temporal aspect of what might otherwise be seen as a static structure (such as spacetime in Einsteinian relativity). And it emphasizes that it is always happening everywhere in space, connecting the parts of space ontologically in a further way than merely having geometrical relations, a way that is central to the existence of causal connections among events in the world.

As it turns out, nothing turns on the difference between saying that space has a an inherent motion and saying that space has a spatio-temporal geometry, as long as we recognize that we are talking about an aspect of a substance that endures through time and has the opposite nature from matter. The motion of electromagnetic waves (or photons) is only one manifestation of this aspect of the essential nature of space. There will be several others as we proceed, and it will be a somewhat more complex aspect of space by the time we are through, variations in its velocity at different locations in space. It is easier to think about these ontological effects of space by thinking of space as having an inherent motion prior to the motion of photons, because the picture is spatial imagination is more concrete.

The the inherent motion in space is the medium of light transmission, and though it may also be called the "ether," as it was in Newtonian physics, it is ontologically important to keep in mind that it is an aspect of space. The ether was supposed to be an ethereal matter that is at rest everywhere in space, and no such thing is needed in a spatiomaterial world, because when space is a substance, it can interact with bits of matter in much the same way as other bits of matter.

It should be noted, however, that just as it made sense to speak of being at rest in the ether, it will make sense to speak of being at rest relative to the medium of light transmission. In either case, it is the reference frame in which the one-way velocity of light is exactly the same both ways in every direction in three dimensional space. It was assumed in Newtonian physics that being at rest in the ether would be at rest in absolute space, because they assumed that the ether was at rest in absolute space. Though we also assume that there is a reference frame that is at rest relative to the light medium, we will not assume that it is at rest in absolute space, because in order to explain ontologically the truth of the general theory of relativity, we will have to assume that the light medium itself can have a velocity in space. That will be to hold that that inherent motion in space can have a different velocity at different locations. But if you prefer, such talk can always be translated into talk about the spatio-temporal geometry of space as a substance enduring though time.

The basic laws of classical physics can, in sum, be explained ontologically by postulating various forms in which matter can coincide with space as a substance. Those forms of matter are material objects with rest mass, kinetic matter, gravitational matter, and electromagnetic matter (including both matter as electric and magnetic forces and as electromagnetic waves). And they explain the truth of the laws of classical physics in the sense that a world made of such substances enduring through time has aspects (properties, relations and regularities about change) that correspond to those laws.

That is, the laws of classical physics are true because they correspond to an aspect of the world that has been constructed from our assumptions about the basic nature of substances, about space and matter as the two opposite kind of basic substances that make up the world, and about the specific forms of matter that coincide with space. There is, therefore, one way, at least, that a spatiomaterialist ontology can make its basic laws true, which shows that spatiomaterialism is possible, as far as classical physics is concerned.

Thus, we have laid the foundation we will need in order to explain the truth of the basic laws of contemporary physics ontologically. The first step in that project has already been made by postulating an inherent motion in substantival space to explain the velocity of light ontologically. In assuming that light has a medium through which it is transmitted, it may seem that we are resurrecting the "luminiferous ether" of Newtonian physics. But if so, it is no longer a strange form of ethereal matter at rest in space, but an aspect of space itself. Space itself is the medium of light transmission.

Contingent laws: Contemporary physics. In the early 20th Century, revolutions in physics have made it seem impossible for spatiomaterialism to explain the basic laws of physics ontologically. There were two revolutions, Einstein’s two relativity theories and quantum mechanics. The first led to the belief in spacetime, and the second made it seem that processes at the micro-level are indeterministic. These new theories were irresistible in physics, because they were justified by the empirical method in the same way as Newtonian physics had been. They were inferences to the best efficient-cause explanations, where the best depends heavily on making surprising, quantitatively precise predictions that turn out to be true when measurements are made. And both revolutions have been extremely fruitful, leading to surprising predictions in new fields.

Two theories are involved in the Einsteinian revolution: the special theory of relativity, which covers phenomena that occur in material objects with velocities approaching that of light, and the general theory, which is a more accurate account of gravitational phenomena. Together with quantum mechanics, the special theory led to quantum field theory, a more accurate account of electromagnetism, which included the discovery of spin and positively charged electrons. As a gauge field theory, quantum electrodynamics became the model for theories about the two short range forces, the so-called weak and strong (or color) forces, which are responsible for the composition of particles in ordinary material objects, and that has exposed more basic particles of nature, such as quarks and neutrinos. Together with the observation that the universe seems to be expanding (Hubble's law), the general theory is now used to support the big bang theory about the origin and expansion of the universe. In sum, our understanding of every kind of physical phenomenon has been radically enriched by these two revolutions in physics.

There is one way, however, in which these two revolutions do not fit well together. It is often characterized as the main theoretical problem of contemporary physics. Einstein’s general theory of relativity explains gravitation, one of the four basic forces, but it is mathematically quite different from the theories describing the other three forces (electromagnetism, the color force and the weak force). The latter three are formulated as gauge field theories, making it possible to fit them together mathematically, but no one has found a simple way of connecting them with Einstein’s general theory of relativity. Attempts to connect them have led some physicists to believe that there are ten or more dimensions to space!

Notice that this theoretical problem in contemporary physics is basically a mathematical problem. It derives from the so called "holy grail" of physics, which is to discover a single law from which all the laws of physics, describing all the basic forces, can be derived. But the incompatibility between quantum theory and the theory of gravitation is very likely intractable as a mathematical problem.

Physics is crying out for a new approach. That is what ontological philosophy supplies. The solution to the main problem of contemporary physics is an extra benefit of its spatiomaterialist interpretation of contemporary physics.

Each of the basic revolutions of contemporary physics poses, however, a challenge to spatiomaterialism all by itself.

Einstein’s two relativity theories pose a challenge to ontological philosophy, as we have already seen, because they seem to describe a world in which space and time are not absolute. Realism about Einsteinian relativity entails the belief in spacetime, which puts time ontologically on a par with space: each moment in time is supposed to exist alongside every other moment in time, just as each point in space exists alongside every other point in space, as equal parts of an eternal four-dimensional world. But the belief in spacetime is incompatible with spatiomaterialism, because spatiomaterialism holds that only the present moment exists and takes space to be one of two opposite kinds of substances that endure through time. Thus, unless there is a way that Einstein’s special and general theories of relativity can be true in a world where space and time are absolute, ontological philosophy cannot use spatiomaterialism as the foundation for its arguments about what is necessary. Showing how the belief in spacetime could be replaced in a spatiomaterial world was one of the mortgages we took out in order to make this argument, and now the time has come to pay it off.

Quantum theory however, may also seem incompatible with spatiomaterialism. In addition to its apparent denial of determinism, it seems to deny that physical processes are constituted by material substances that coincide with space. Quantum mechanics is often interpreted, at least, as denying that the smallest entities have definite locations and as implying that they behave in ways that are incompatible with the principle of local motion and local action.

Quantum mechanics is less challenging than Einsteinian relativity, because the received interpretation of it (the so-called “Copenhagen interpretation, due mainly to Bohr) is more like skepticism about ever knowing the real nature of the smallest bits of matter than a generally accepted ontological belief about what exists on the micro-level that is incompatible with spatiomaterialism. The belief in spacetime is incompatible with the belief in absolute space and time. 

It is possible, however, for spatiomaterialism to explain the truth of both theories. What is more, by explaining their truth ontologically, it solves the problem about how gravitation is related to the other three forces of nature. This ontological solution to the basic theoretical problem of contemporary physics will also provide the foundation for more speculative suggestions about cosmology, both the basic particles recognized by high energy physics and about the origin of the large scale structure of the universe.

Relativity theories. The two theories involved in Einsteinian revolution will be discussed in sequence. The notion of spacetime was introduced with the special theory of relativity as a way of explaining measurements made from objects with very high relative velocities, and Einstein used it as the basis for his explanation of gravitation. In a parallel way, the ontological explanation of spacetime in the special theory of relativity will be the foundation for the ontological explanation of the role of spacetime in the general theory of relativity.

In the case of Einstein’s special theory of relativity, it may not be surprising that it is possible for spatiomaterialism to explain its truth, for even Einsteinians admit that the empirical implications of Einstein’s theory could be explained on the assumption that space is absolute. It is just a matter of assuming that one of all possible inertial reference frames is at absolute rest and explaining the appearance that it is not different from the others on the assumption that absolute space causes certain distortions in material objects that move through it. Such a theory is possible, and it was begun, at least, by Newtonian physicists before Einstein first published his special theory of relativity.

The ontological explanation of Einstein’s general theory of relativity may be more surprising, because contemporary physicists apparently do not even suspect that it is possible to understand the gravitational phenomena discovered by Einstein on the assumption that space and time are absolute. The universal acceptance of the special theory of relativity and its notion of spacetime as a description of the nature of space and time has kept physicists from even considering a very simple, intuitively satisfying, ontological explanation of gravitation.

The spatiomaterialist special and general theories of relativity that result are not ontologically necessary truths, according to ontological philosophy, because they do not follow from spatiomaterialism, but rather depend on what has been discovered empirically about what happens in the world. All that needs to be shown is that it is possible for Einstein’s two theories to be true in a spatiomaterial world.

Once the laws of physics are explained ontologically, the additional assumptions that must be made about the nature of matter and space in order to explain them will be incorporated into the foundation of ontological philosophy as a way of explaining ontologically other aspects of the world, such as the global regularities. That is how we incorporate the laws of physics into spatiomaterialism. But since those further explanations will depend on the more specific natures of matter and space assumed here in order to explain the truth of classical and contemporary physics, their ontological necessity will be only conditional. They hold only of all possible spatiomaterial worlds like ours, that is, in which the laws of physics are true.

As it happens, however, the spatiomaterialist ontological explanation of the truth of classical physics together with its explanation of quantum mechanics seem to entail the ontological assumptions that have to be made in order to explain the truth of the special theory of relativity. If so, the regularities described by Einstein's special theory of relativity have a deeper ontological explanation, even if they are not unconditionally ontologically necessary.

It should be mentioned, however, that the explanation of the global regularities to be given under Change does not depend on this ontological explanation of the truth of contemporary physics. Given that space is a substance, they depend only on matter obeying the regularities described by the laws of contemporary (and classical) physics. Though we shall make further assumption about the nature of space and matter in order to explain ontologically the truth of quantum mechanics, the basic objects of physics, and the origin of the universe, they are required only to show the possibility of spatiomaterialism. They are not relevant in explaining the global regularities.