Contingent laws about local regularities. Though certain kinds of events are ruled out as ontologically impossible by the necessary principles about local regularities, that leaves open many ways for bits of matter to behave. Indeed, it leaves open the possibility that no change actually takes place at all. But if bits of matter in space do change as time passes, they must change in determinate ways, and how they move and interact is what is described by the basic laws of physics. Since that is something that can be known only by observing what happens in nature, those regularities are not ontologically necessary. Assuming that they have ontological causes, they depend on the specific kind of matter and specific kind of space that constitute the actual world. Thus, although spatiomaterialism explains the basic nature of what exists, ontological philosophy needs to make additional assumptions about the specific essential natures of the matter and space it postulates in order to explain the truth of the basic laws of physics.

The properties mentioned in basic laws of physics are called “physical properties,” and as noted in Properties, ontological philosophy takes physical properties to characterize the extrinsic essential aspects of the nature of matter and space. (Intrinsic essential natures, by contrast, are what explain phenomenal properties.) And in the same way that physical properties (and spatial relations) are explained as aspects of the basic substances constituting the world, basic physical laws describing how they change can be explained as aspects of those substances as they endure through time.

If the matter postulated by an ontology were simply assumed to have whatever essential nature is required to make the basic laws of physics true, there would be no genuine ontological explanation of why the basic physical laws are true. That is what materialism does (hence, its other name, “physicalism”). Indeed, that is the only way that physical properties can be introduced by materialism, because when space is reduced to spatial relations among bits of matter (as materialism does, being implicitly committed to spatial relationism), matter is the only possible ontological cause of physical properties and regularities about how they change over time. But a spatiomaterialist ontology recognizes two basically different ontological causes, and so space can work together with matter to constitute properties, relations, and how they change over time. When it comes to explaining the truth of physics, therefore, what ontological philosophy is looking for is a description of a more specific essential nature of matter and space such that, when space contains all the bits of matter, objects have physical properties and spatial relations which change in the ways described by the basic laws of physics.

It may not be surprising that spatiomaterialism can explain the truth of the physics that prevailed at about the end of the 19^th Century, because classical physics afforded an intuitive understanding of the laws of physics, as descriptions of how material substances move and interact in space as time passes and it assumed that space and time are absolute. What cast doubt on the possibility of a spatiomaterialist explanation were the revolutions that spawned contemporary physics. In particular, relativity theory seems to deny that space and time are absolute, as spatiomaterialism requires. Thus, instead of looking for a spatiomaterialist ontology that would make relativity theory (and the other laws of physics) true, contemporary physicists see the “holy grail of physics” as merely discovering a “Theory of Everything,” that is, a single law from which all the other laws can be derived.

At present, there are four basic laws of physics, each describing one of the four basic forces that are now thought to be at work in nature (electromagnetism, the strong force, the weak force, and gravitation), and the task that physics has set itself is to discover a single law that entails (together with suitable initial and boundary conditions) all four of those laws. (That seems possible in the case of the first three, because they can all be formulated as gauge field theories, but attempts to formulate Einstein’s general theory of relativity in a compatible way have been forced to assume that there are as many ten or eleven dimensions to space )

To take the goal to be the discover of a single, basic law is to assume that efficient-cause explanations are the most basic explanations that physics can give. And since ontology itself is not assumed to be explanatory, the only entities that contemporary physics takes to be real are those referred to by the basic law of physics, that is, scientific realism.

Ontological philosophy, on the other hand, assumes that ontology itself is explanatory. That is what led us to recognize that the world is constituted by space as well as matter. Thus, we now expect space and matter to work together is some way to explain the truth of the basic laws of physics and, thereby, the truth of its efficient-cause explanations. Indeed, one of the mortgages we took out in order to use spatiomaterialism as our ontological foundation in proving necessary truths was the promise to give such an explanation of Einstein’s two relativity theories. We promised to show that even though we must take space and time to be absolute, it is possible to describe more specific essential natures of matter and space that would entail the truth of the special and general theories of relativity. But in order to lay the foundation for such a theory, we must first describe more specific essential natures of matter and space that would entail the truth of the laws of classical physics.

The attempt to discover the specific essential natures of matter and space in the actual world is, however, a project resembling empirical science, for it would have to discover which essential nature(s) of matter and space afford the best ontological explanation of the truths of the basic laws of physics in a spatiomaterial world. That is a project of empirical ontology, but nothing so definitive is claimed for what is sketched here. All that is required here is proof that it is possible to give such an ontological explanation of the truth of physical laws, for that will show that spatiomaterialism is not falsified by what is found empirical in nature by physics and, thus, that ontology affords a new approach to philosophy. Thus, though this sketch of how more specific essential natures of matter and space explain their truth will show that a deeper explanation is possible, it may not be the best ontological explanation of physics. That job can be left to ontology as branch of empirical, natural science that is more basic than physics.

Once it is recognized that ontological-cause explanation are prior to efficient-cause explanations, finding the best ontological explanation will become the “holy grail” of the most basic branch of natural science. Unlikely as it may seem now, physicists will eventually welcome substantivalism about space, because it opens up the possibility of a deeper explanation of the world and what physicists really want is the deepest possible explanation that can be supported by the empirical method. As we shall see, for example, it solves the current puzzle about the relationship between gravitation and the other three basic forces of nature.

Contingent laws: Classical physics. We begin with the spatiomaterialist ontological explanation of the truth of the basic laws of classical physics, including Newton’s laws of motion and gravitation and Maxwell’s laws of electromagnetism. If they can be explained ontologically, we can be confident that the rest of classical physics can also be explained ontologically, for the basic physical laws are like the axioms of a formal system and the rest of physics are like theorems that follow from them. That is basically the strategy we used for mathematics, ontologically explaining the truth of the axioms of set theory from which the rest of mathematics follows.

Though classical physicists assumed that space is absolute, they did not try to give an ontological explanation of the truth of the basic physical laws based on space being a substance. They did not recognize the validity of ontological explanations, and so they did not think of space as a substance that works together with matter to make the regularities being described true. Indeed, the action at a distance implied by Newton’s law of gravitation must have made any such project seem hopeless. Instead, their aim was to formulate physical laws mathematically so that they could make quantitatively precise predictions of the measurements that would be made in experimental situations. That method turned out to be a powerful means of seeing into the nature of the world, most spectacularly by revealing the nature of micro-processes, though by leaving out the deeper ontological explanation, it also made the Einsteinian revolution inevitable, as we shall see.

The simplest way to describe the specific natures of matter and space that would explain the truth of classical physics is to start by cataloging all the different entities mentioned by the laws of physics and showing how the forms of matter required to account for them all would, by being contained by space and enduring through time, make the regularities described by the basic laws of classical physics true. That method will leave some aspects of those regularities built into the natures that the kinds of matter and space that are assumed to constitute a spatiomaterial world like ours. But enough of those regularities will be given a genuine explanation to show that an ontological explanation of classical physics is possible -- and to lay the foundation for explaining how the basic laws of contemporary physics could be true in a spatiomaterial world.

Forms of matter. Though we cannot assume anything about the nature of matter or space that contradicts spatiomaterialism, there are many different possible spatiomaterial worlds. It is mainly the more specific nature of matter that we will be concerned with in explaining the truth of classical physics, and in any given spatiomaterial world, bits of matter may come in various forms, each with different ways of moving, interacting and being related to bits of matter in other forms.

Indeed, we will have to assume that matter takes qualitatively different forms, because the basic laws of classical physics mention entities that are as different from one another as material objects and light. Every basic entity mentioned by physics as having a location in space and time must be explained as matter contained by space.

A promising way to inventory all the basic forms of matter required to explain the laws of classical physic ontologically is to take as our working hypothesis that what is conserved according to the principles of the conservation of mass and energy is the quantity of the matter contained by space. Conservation of mass and energy is one of the most basic principles of contemporary physics, and this ontological thesis is a plausible interpretation of it. Indeed, when the principle was first recognized by physics, it was heralded as empirical confirmation of the traditional materialist view that physical processes are made up of substances that endure through time. Let us, therefore, take it as our working hypothesis.

The principle of the conservation of mass and energy holds that in any closed or isolated region of space, there is a certain quantity of mass and energy that never changes, regardless what happens there. That quantity could be the total quantity of matter, for that hypothesis would explain two aspects of the principle.

First, since matter is a substance, it neither comes into existence nor goes out of existence as time passes, and thus, it is conserved. Hence, the quantity of mass and energy could be the quantity of matter.

Second, the principles of local motion and local action explain why the quantity of matter does not change under the conditions described by the principle of conservation of mass and energy. If the only way that bits of matter can change location is by motion, they cannot change their location from inside the closed or isolated region to outside, or vice versa, unless they cross the boundary, and that is excluded. Nor can bits of matter outside the closed region affect what happens to the bits of matter inside, since that would involve action at a distance, contrary to the principle of local action (unless something moved across the boundary between inside and outside to mediate the force, which is excluded).

Let us set aside the peculiar effects that bits of matter may have on one another that are mediated by space itself, since they are not relevant to classical physics. As we shall see, there are always such effects crossing the boundaries, but they do not violate this conservation principle, because, as it turns out, they carry neither energy nor mass.

Thus, it is plausible that the quantity to which classical physics is referring in the principle of the conservation of mass and energy is the total quantity of matter in closed or isolated regions of space.

There is, however, one aspect of contemporary physics that is relevant at this point in our argument. Though mass and energy were thought to be conserved separately in classical physics, Einstein discovered, as a consequence of his special theory of relativity, the famous equation connecting them (E=mc²). That is further evidence that mass and energy are just different forms of the same basic material substance, because if they were different forms of matter, we would expect them to be commensurable.

Indeed, the suggestion that they are basically the same stuff has turned out to be true, for there are actual physical processes in which they are converted into one another, most spectacularly in the nuclear reactions used in nuclear weapons (fission and fusion).

The conservation of mass and energy is now seen as a consequence (or presupposition) of the basic laws of contemporary physics. It is a way of formulating what is called a “symmetry” about those laws, that is, something that is invariant as other things change. But that it to treat it formally, as a basic symmetry principle of contemporary physics, and here, it will be interpreted ontologically, as describing an aspect of the world that is caused by the permanence of the matter that coincides with space.

Furthermore, the conversion between mass and energy will be assumed here in order to explain the various forms of matter ontologically, quite apart from explaining any of the phenomena covered by Einstein’s special theory of relativity. 

The assumption that all the forms of mass and energy described by physics are various forms of matter that coincide with space is just a working hypothesis. It will serve my purposes, because it is a simple and plausible way of laying out an ontological explanation of the laws of physics (classical and contemporary) and, as we shall see, it does show that there is at least one way that spatiomaterialism can explain them all ontologically. Though it may not be the best spatiomaterialist explanation of them, it will suffice to provide an ontological foundation for explaining the global regularities, because it will show that, for all that physics knows empirically, spatiomaterialism could be true.

This ontological explanation of the truth of the principle of conservation of mass and energy implies that there are as many different forms of matter as there are kinds of mass and energy recognized by physics in confirming this principle empirically. And in order to explain the truth of the laws of classical physics, we must recognize four (or, perhaps, six) qualitatively different forms of matter (with varieties of each). They are (1) material objects with rest mass, (2) the kinetic energy involved in the motion of rest masses, (3) the energy due to gravitation, and (4) the energy due to electromagnetism. (Since the latter two each involve two basically different forms of energy, as potential energy and as actual waves, they might better be counted as two forms of matter each, yielding a total of six.) Let us consider briefly how each kind of energy can be explained as a form of matter and then we will see how these forms of matter would explain ontologically the truth of the laws of classical physics.

Matter as material objects with (rest) mass. Material objects with rest mass are the form of matter that is usually intended when people think of matter. Ordinary material objects have definite locations in space and can be at rest. The quantity of rest mass in any such object (at rest) would be the quantity of matter constituting its existence. The endurance of matter through time would then explain the principle of the conservation of mass in classical physics.

Even at the altitude of classical physics, however, material objects have further properties. Since different material objects cannot occupy the same places at the same times, some sort of interaction keeps them from doing so, when their motion would otherwise bring them to the same location. Such interactions are explained in physics by forces that the objects exert one another.

Thus, we will assume that some material objects have electric charges by which they can interact with other charged objects. And we will assume that every material object exerts a gravitational force by which it attracts every other material object. Such forces are, as we shall see, aspects of the matter that exists in the form of rest mass, and since these aspects involve regularities about change, they are dispositional properties.

However, since the forces are spread out in the space surrounding where the material object with rest mass is located, we must assume that some of the matter constituting its existence is somehow spread out in space, for otherwise the matter would not be able to explain the forces that the material objects exert. But as we shall see, all the matter constituting the material object is counted in its rest mass, and the object interacts as if all its (rest) mass were concentrated at its center, where the material object itself is said to be located.

We will also assume, as classical physics did, that ordinary material objects, such a billiard balls and cream puffs, are composed of simpler material objects, such as “atoms,” the parts of atoms (protons, neutrons and electrons), and the parts of parts of atoms (such as quarks), though we will also leave the natures of these particles and the forces binding them together unexplained until we take up contemporary physics.

The simplest parts of material objects are now known to be particles that are quite unlike material objects in various ways, but I will just assume that they can also be explained ontologically by spatiomaterialism until I show that the truth of quantum mechanics can be explained ontologically by spatiomaterialism. (The nature of the basic particles of physics is explained ontologically in Change: Cosmology: Basic objects.)

Kinetic matter. All the other forms of matter recognized by classical physics are classified as energy by physics, and the most surprising implication of this ontological explanation of classical physics is probably that kinetic energy is a form of matter, for it means that the motion of objects with rest mass is itself a form of matter. There is no way to avoid this implication, given our working hypothesis, because even in classical physics, kinetic energy can be converted into other forms of energy (such a light and potential energy), and other forms of energy can be converted into kinetic energy.

To hold that kinetic energy is a form of matter is to hold that the motion of a material object is constituted by a bit of matter that exists in addition to the matter counted in the (rest) mass of the material object. This bit of matter must somehow be attached to (and, therefore, located with) the matter that makes up the rest mass of the material object, and as a result, both must coincide with space in a way that carries it and the material object across space as time passes. Let us call it “kinetic matter.” More will be said about the essential nature of matter in this form when we take up quantum mechanics, but for now we need only recognize that quantitatively different varieties of kinetic matter would propel objects at different speeds or in different directions. Kinetic matter would be like a motor, except that instead of consuming energy, it is just a bit of matter that endures through time as a substance, and thus, as long as it continues to exist in that form, the material object continues to move. There are, however, interactions by which kinetic matter can be transferred to other material objects, supplemented with kinetic matter transferred from other material objects to join it, and converted into other forms of matter.

To treat kinetic energy as a form of matter is to depart from the received understanding of physics. Kinetic energy is usually treated abstractly as just another quantity that is mentioned in the laws of physics and must be taken into account in order to predict or control what happens in particular situations. When we think of kinetic energy as a form of matter, however, we expect to find other properties that it must have, and that is what leads to a deeper ontological explanation. Kinetic matter must be located, as we have assumed, with the rest mass that it is moving, and as we shall see in explaining quantum mechanics ontologically, kinetic matter has other properties that explain the quantitative relationship between kinetic energy and momentum.

The other forms of matter into which kinetic matter can be converted are those postulated in order to explain gravitation and electromagnetism. Gravitation and electromagnetism are forces that material objects exert on one another, and in order to explain the distinctive kind of energy involved in each, we will assume that the forces themselves are a form of matter. That is, the energy (or matter) associated with these forces can exist in two different forms, potential or actual (that is, as forces being exerted by material objects or as waves of forces that exist independently of material objects).

Potential energy. Potential energy is the energy that material objects have when they exert forces on one another. Such forces must be a form of energy, because they can change how the objects involved are moving.

The amount of potential energy that exists in any situation depends on the distance across which the forces can continue to accelerate the objects involved. When the distance is maximum, the potential energy is maximum. But physics sets the maximum quantity at zero. Thus, any subsequent state in which some potential energy has been converted into kinetic energy (or into some other form of energy) is counted as negative potential energy. This is sometimes said to be just a mathematical convention, but according to this ontological explanation of potential energy, it represents the fact that the kinetic energy acquired by objects being accelerated is another form of the same matter that previously existed in the form of potential energy, that is, as forces being exerted by the material objects.

As suggested above, some of the matter making up a material object that exerts a force must be conceived as being spread out in the space around it as a force field, and that matter is counted as part of its rest mass. When potential energy is consumed, objects accelerate, changing the positions of the objects that were exerting the forces. That alters the force field they jointly impose on space, and the result is a reduction in the quantity of matter constituting those forces and, thus, the material objects themselves. That is, the material objects lose rest mass as their potential energy is consumed as kinetic energy, because some of the matter counted in the rest mass is converted from constituting a force field to constituting the motion of objects with rest mass.

On this ontological theory, therefore, the reason that the potential energy that is consumed as kinetic energy is negative (rather than just a smaller positive quantity) is that the kinetic energy must be subtracted from the rest masses of the material objects that were exerting the forces in order to balance the account. The kinetic energy is a different form of the same bits of matter that previously existed as forces being exerted by the objects. Thus, at the end of such a process, when as much kinetic (or other) energy has been actualized as possible in the situation, the material objects are in a position where their forces cannot accelerate one another and more, and the potential energy is some negative quantity. And since the total quantity of energy (or matter) involved in the process does not change as time passes, the principle of the conservation of mass and energy is true.

Though the equivalence of mass and energy is entailed by Einstein’s special theory of relativity, it is assumed here, as I warned earlier, in order to explain ontologically the conversion of energy between kinetic and potential forms. 

The matter that explains potential energy is, therefore, included as part of the matter that explains the (rest) masses of material objects, and as we shall assume, it is the matter that constitutes the forces exerted by the object. Since those forces are spread out in space like a field, this is to take the force field to be a form of matter that coincides with all those parts of space. Likewise, the strength of the force at any point in space will be taken as a measure of the “thickness” of the matter coinciding with space at that point. And the total potential energy that can be converted to kinetic energy (or other forms of energy) depends on the total amount of matter in this form that exists along the pathway of the object being accelerated (which depends on the length of the path and the “thickness” of the matter at each point along the path)

To be sure, this ontological assumption will seem empirically unwarranted from the point of view of inferring to the best efficient-cause explanation. What happens in the relevant situations can be predicted with laws describing the forces and descriptions of the locations of the kinds of objects involved, without any need to refer to matter making up the forces involved. In the received formulations of physics, force fields are usually explained as spatially variable dispositions, that is, in terms of regularities about how material objects of certain kinds would be accelerated, if they were located there. But ontologically speaking, there must be a substance located there to accelerate the body, and though this description of matter in the form of potential energy does not tell us much more about it than is described by the relevant laws of physics, it does make us look for further properties of such force-field matter. Such properties will be described in the ontological explanations of Einstein's general theory of relativity and quantum mechanics.

More generally, furthermore, remember that we already have empirical reasons for believing that space and matter are substances, and what is at issue is whether the laws of physics can be descriptions of regular changes in the aspects the basic substances we have postulated. This is not an attempt to show that physics must recognize matter in these forms in order to predict what will happen, but only that it can and, thus, that physics provides no reason do doubt that spatiomaterialism is true.

Energy as waves of forces. If forces are a part of the matter constituting the rest mass of a material object that is spread out in space around it, then references to that matter by way of rest masses and as negative energy are indirect, and they obscure its real nature. Moreover, there is other evidence that forces are a form of matter, for such forces can also exist independently of material objects (that is, when they are not counted as part of their rest masses). They exist as light waves, in the case of electromagnetism, and as gravitational waves, though the latter were not recognized until Einstein’s discovery of the general theory of relativity. In both cases, the waves propagate across space on their own, and since they act on objects that they encounter in their paths like forces of the appropriate kind, those waves are best explained as matter existing in much same form that helps constitute the rest masses of material objects, except that it now exist independently of material objects. But given the difference between its form as part of the rest mass of material object and its form as an independently existing wave, we should probably postulate two different forms of matter for each kind of energy, gravitational and electromagnetic (yielding six forms of matter in all).

Gravitational matter. The nature of the force of gravity was problematic in classical physics, because it was supposed to enable material objects to act on one another at a distance, and an adequate ontological explanation of it cannot be given here until we take up the spatiomaterialist interpretation of Einstein’s general theory of relativity. According to Newton, gravity is a universal force of attraction among material objects whose strength is in proportion to the products of their masses and inversely proportional the square of the distance separating them. When material objects (and energy) have accumulated at a certain location in space, as in planets and stars, the gravitational force is strong enough to make an enormous difference in what happens in the surrounding space.

According to contemporary physics, the mass that is responsible for gravitation is not just the rest masses of the material objects, but also includes the mass equivalent of their kinetic energy and electromagnetic energy. That is readily explained by this ontological theory, if matter in all forms exerts gravitational forces, and it will be assumed here.

Without giving a deeper explanation of its nature, we can think of the gravitational force field as a form of matter that is spread out in the space around the center of gravity and has the power where it is located to accelerate towards itself other material objects that coincide with the same part of space. The strength of the force at any location as described by Newton’s law can be thought of as varying with the amount (or “thickness”) of matter in this form spread out in that part of space. But since the quantity of gravitational matter is already counted in the rest mass of the matter accumulated at that location, the force field is just an aspect of the accumulated matter (or an extrinsic property of the matter located there).

Though we are assuming that the gravitational force field is a form of matter in order to explain how classical physics is true, I promise to give a deeper ontological explanation of gravitational matter and how it is related to other forms of matter in making up the rest mass of a material object when we take up contemporary physics. But for now, spatiomaterialism leaves us no option but to recognize the gravitational force itself as a form of matter in some sense, for otherwise there would be nothing to exert the forces involved. Space by itself cannot exert gravitational forces, because they vary with location, whereas space is uniform throughout. But as we shall see, gravitational matter can be a condition of space that is imposed on it by the accumulation of matter at a nearby location.

Gravitational potential energy is the matter that can be extracted from material objects because they are so located relative to one another in space that the gravitational forces that they exert on one another can accelerate them toward one another. When gravitation accelerates material objects to the some location, they acquire kinetic energy, and when they collide, some of it may be turned into other forms of energy. Though that means, on this ontological explanation, that the material objects involved have less rest mass than they did when they were still attracting one another across the distance separating them, there is no violation of the principle of the conservation of mass and energy, because the missing rest mass is now counted as the kinetic (and other forms) of energy of the objects at the center. The reason that classical physics does not recognize that the rest masses of the material objects at the center of gravitation have become less than they were before they accumulated there is that it assumes that any potential energy that is less than the maximum possible is a negative quantity.

In particular, it is possible to hold that the kinetic (and other forms of) energy that material objects acquire as they accelerate toward one another comes from the gravitational matter that was spread out in the space between them, because the motions of the objects so alters the force field between them that less gravitational matter is required for them to exert a gravitational force on one another.

The total matter, both rest mass and forms of energy, accumulated at the center of gravitation determines the strength of the gravitational field around that center, and the field is stronger than it was when the material objects were still separated, even though some gravitational matter has been converted to kinetic (and other forms of) energy, because the accumulation of bits of matter at the same location makes their gravitational fields coincide more completely with the same parts of space, so that the gravitational matter at any location in the field they jointly impose on space is spread more thickly.

Though gravitational matter is just part of matter counted in the rest mass of a material object, gravitational matter can also exist independently, as gravitational waves. But we can leave that until we take up the ontological explanation of Einstein’s general theory of relativity.

Electromagnetic matter.  The electric force is another kind of force that we will assume that material objects can exert. It has a more complicated structure than gravity, because material objects can exert two opposite electric forces, positive and negative, and in either case, the electric force interacts with another force, the magnetic force. How material objects interact by these forces is what is described by Maxwell’s laws, and they will be explained in more detail later. For now, let me merely suggest how electric forces can be explained as a form of matter, by analogy with gravitational matter.

Material objects that exert an electric force are said to have an electric charge, either positive or negative. In order to explain ontologically how Maxwell’s laws are true, we will assume that the matter making up such a material object coincides with space in a way that makes its total rest mass seem to have a determinate location at the center even though some of its constituent matter is spread out around it like a force field. Since the strength of the forces in this field fall off in proportion to the square of the distance from the center, their strength at any point can also be explained as the “thickness” of the electromagnetic matter spread out in that part of space, though it must have a more complex structure to explain the direction of the force, because it depends on the sign of the charge and its motion.

The electromagnetic matter making up the electric field is already counted as part of the rest mass of the material object in balancing the mass and energy books. Thus, the electric field is actually an aspect of the material object, that is, an extrinsic property of the material substance that has the electric charge.

Electromagnetic matter in this form is electrical potential energy, because the force field can accelerate material objects affected by it, namely, other material objects with electric charges. Like gravitational potential energy, electromagnetic matter is converted to kinetic (or other forms of) energy, and such conversions change the rest masses of the objects exerting the electric forces appropriately, because material objects are actually either acquiring or losing matter. But once again, the changes in rest mass may not be recognized as such, because any amount of potential energy less than the maximum possible is counted as a negative quantity.

In the case of electromagnetism, the interaction of electric forces with magnetic forces makes it necessary to recognize that matter of basically the same kind can also exist independently of material objects as waves, such as ordinary light.

When these two forces are coupled, as described below, they propagate across space as a wave of electric and magnetic forces. Since those forces interact with charged objects in much the same way as the electric (or magnetic) forces exerted by material objects directly, electromagnetic waves are basically another form of electromagnetic matter. But since the electric (and magnetic) forces exerted by charged material objects directly are so different from electromagnetic waves, it is probably best to think of electromagnetic matter as existing in two different forms. In one form, its quantity is included in the rest masses of the objects (and the negative potential energy of the situation), and in the other form it is added to the rest of the mass and energy in calculating the total quantity that does not change over time in a closed or isolated system.

Electromagnetic energy is not portrayed as mere waves in contemporary physics. There are two reasons, one that we will accept in the end and one that we won’t.

The first reason is that electromagnetic waves are now known to have a particle-like nature, which has given them the name “photons.” The discovery of their particle-like nature is at the very foundation of quantum mechanics, and it will not be disputed here. We shall see how spatiomaterialism can explain their particle-like when we take up the ontological explanation of quantum mechanics.

The second reason for avoiding the notion of electromagnetic waves is that the notion of waves requires a substratum or medium in which the waves occur, such as the water in which ocean waves occur and the air in which sound waves occur. In classical physics, electromagnetic waves were thought to occur in the “luminiferous ether,” which was assumed to be at rest in absolute space. But when absolute space was rejected with the rise of relativity theory, the notion that light propagates in such a medium was rejected with it. Spatiomaterialism entails, however, that space and time are absolute, and so we do not have that reason for denying the reality of the ether. And since our reason for accepting absolute space and time is that space is a substance (not merely a way of thinking about references to locations and times in the equations of physics, as classical physics did), we have the option of explaining the ether ontologically, that is, as an aspect of space itself.

In other words, we will take the motion of electromagnetic waves to exhibit an aspect of the nature of space. Much the same is true of any form of matter, because the properties of any bit of matter are an aspect of something constituted jointly by the bit of matter and the part of space with which it coincides. But in the case of electromagnetic waves, we will hold that their velocity, that is, the velocity of light, manifests a basic aspect of the nature of space (what will be called the “inherent motion” of space or the “ether”).

It may seem that there are other kinds of energy, besides kinetic energy and the energy that is due to electromagnetism and gravitation, recognized in classical physics, but they all turn out in the end to be reducible to these basic forms.

Chemical energy, for example, is a form of potential electromagnetic energy that depends on how charged particles are configured in atoms and molecules. Heat turns out to be the kinetic energy in the random motion of the smallest material objects. Kinetic energy can also be stored internally in molecules as vibrations of parts of atoms.

There are, of course, other forms of energy associated with the short range forces that are involved in the constitution of more basic material objects, such as the strong forces exerted by protons and neutrons (or the color forces exerted by quarks) and the weak forces that are apparently involved in the constitution of quarks and electrons (and show up observationally in radioactive decay). But we are leaving them aside until we take up contemporary physics, taking the internal structure of material objects with rest mass for granted.

The reason we are taking all these kinds of mass and energy to be forms of matter is that they can be converted into one another without changing the total mass and energy in the region, that is, because the total mass and energy is conserved. Electromagnetic waves interacting with charged particles can convert them into kinetic energy. But this ontological explanation of classical physics takes the conversion between potential and kinetic energy to be an instance of the convertibility of mass and energy into one another. How these forms of mass and energy are converted into one another is described by the basic laws of physics.

To hold that these kinds of mass and energy are basically different forms of matter which move and interact in the ways described by the laws of physics is to hold that matter has a temporally complex nature. What is assumed about the essential nature of matter must include how each kind moves and interacts, including how they change from one form of matter to another.

However, spatiomaterialism opens up the possibility of a deeper ontological explanation of how these forms of matter are related to one another, which might explain how they can be converted into one another. Since ontological philosophy takes space to be a substance, it may be possible to describe the essential nature of matter in a way that makes it possible to explain ontologically why it takes these different forms by how generic matter coincides with space and other bits of matter. That is to suppose that the same material substance could have the properties defining any special form depending on its current relationship to space (and, perhaps, other bits of matter at its location).

For example, if there were a geometrical aspect to generic matter, differences in the forms mentioned above (or some of them) might have an intelligible ontological explanation as different ways in which generic matter engages with the geometrical structure of space. An explanation of the nature of some forms of matter along these lines will be suggested by a theory about the nature of matter that will be offered as an ontological explanation of the truth of quantum mechanics, and it will explain the simplest particles recognized by physics (in Basic Objects under Cosmology under Change.) It illustrates a research project that would be promising, if ontological philosophy is on the right track.

To explain the truth of the laws of physics by postulating a kind of material substance that can change from one form to another with different essential properties is to make the forms of matter similar to Aristotle’s basic substances. Aristotle believed that the simplest kinds of substances (earth, air, fire and water) could be converted into one another, for example, as fire gives its form to other substances, such as wood, changing its essential form to fire. As the essential properties (or essential form) of the substances change, the substratum (or material cause) was supposed to endure unchanged. There is, however, a difference. Spatiomaterialism does not assume, as Aristotle did, that (essential) forms of matter and their substratum are basic principles. Spatiomaterialism is a variety of materialism, in Aristotle’s sense, because it denies that individual substances necessarily involve his two principles (or ontological causes), substratum (material cause) and essential form. Bits of matter are independent substances, and their capacity to change from one form of matter to another is just part of the essential nature of material substance. However, since spatiomaterialism does recognize another basic kind of substance, besides matter, with which it coincides, it is possible that those regularities have a deeper ontological explanation.

Leaving aside for now deeper ontological explanations of these forms of matter, our project here is to show that classical physics can be explained ontologically by spatiomaterialism. That is to explain the truth of the laws of classical physics by their correspondence to aspects of a spatiomaterialism world, and it will be accomplished here by assuming that the bits of matter that coincide with space have these basic forms: material objects with rest mass, kinetic matter, gravitational matter (as part of the matter making up objects with rest mass) and electromagnetic matter (both as part of the matter making up material objects with electric charges and as electromagnetic waves).

The laws to be explained are Newton’s laws of motion and gravitation as well as Maxwell’s laws of electromagnetism. That will suffice to show how the physical properties mentioned by the basic laws of classical physics can be aspects of these forms of matter, and it will explain the regularities among them as temporal aspects of a world constituted by such substances enduring through time.

Since what is at issue is the correspondence between these laws and aspects of substances, what is crucial is not the quantitative aspects of those laws, which are generally the focus of attention in physics, but how those quantities can be explained ontologically by substances of the kind postulated by spatiomaterialism. I will describe how aspects of these forms of matter would explain the properties mentioned by the laws of physics, and I will show that they can explain the quantitative relationships among them and how they change over time. But I will merely show that the quantities can all have the right signs, change in the right directions and have the right orders of magnitude. It is not a matter of making any new, quantitatively precise predictions of what will happen, because any more precise quantitative correspondence can be made to come out right simply by making the right assumption about the essential nature of matter. It is enough to explain them ontologically.

Not every aspect of those physical laws will be given a genuine ontological explanation. But enough will be explained to show that it is possible for spatiomaterialism to explain the truth of classical physics. That will put us in a position to show how spatiomaterialism can also explain the truth of contemporary physics, both relativity theory and quantum mechanics. We begin by sketching an ontological explanation of Newton’s laws of motion and gravitation and then take up Maxwell’s laws of electromagnetism.