Cosmology. By “cosmology,” I mean the ontological explanation of those parts of the cosmos having to so with the extremes of the very small and brief and the very large and long-lasting. We have already explained ontologically the truth of the basic laws of physics governing the middle range involving ordinary material objects and their electromagnetic interactions. But as we recognized when we inferred to spatiomaterialism as the best ontological explanation of the natural world, the simplest and best form of any such ontology would hold that time, space and matter are infinite. Though we left open the possibility that a more complex ontological assumption may be required to explain certain phenomena, the ideal from of spatiomaterialism would hold that the universe is infinite.

The kind of infinity in question is twofold. Starting with the finite, there are two ways there could be an infinite series of steps, one by division into smaller and smaller finite units, and another by multiplication into larger and larger finite units. And there are three basic assumptions of spatiomaterialism to which it could apply: space, time, and matter. Let us consider where we stand on each of them. 

Space. Space seems to be infinite in both ways, as we noted in Spatiomaterialism. There must be finite distances in space, for otherwise space would not have a geometrical structure at all. To hold that space has three dimensions is to hold that distances in it (and lengths of the objects coinciding with it) can be measured in three independent dimensions, say, by placing measuring rods down one after another. Each measuring rod is a unit, and since units that are parts of the same world can be counted [as established in Relations (Math)], distance measurements must obey the theorems of arithmetic, including division and multiplication. Thus, space can be infinite in two way, by an unending division of finite distances or by an unending multiplication of them.

If the division of finite distances in space is without end, space is continuous. That is what we have assumed, and we have found no reason to doubt that space is continuous.

If the multiplication of finite distances in space is without end, space is infinite in extent. That is the kind of spatiomaterialism that empirical ontologists must prefer, because it is the simplest assumption. Since the essential  nature of each part of space includes its geometrical relations in three dimensions to every other part of space, an end to space in any direction would mean that every part of space has a different kind of essential nature from the rest, rather than the same kind of relationship to different particular parts of space. Not only would that complicate the nature of each part of space almost beyond recognition, but it would also be difficult, to say the least, to explain what happens at the end of space. As the ancient Greeks asked, What happens at the end of space? Does a spear thrown toward the edge of space bounce back?

Thus, we assumed that space is infinite in extent. But we acknowledged that we might have to revise that assumption, for that is the prevailing belief among bit gang cosmologists and a spatiomaterial world in which space is not infinite is possible.

Time. Time seems to be infinite in both ways as well. There are finite periods of time. There must be, because there are cyclic processes involving real change. Since such cycles are units that can be counted, the theorems of arithmetic must be true of measurements of time, including division and multiplication.

If the division of finite periods of time is without end, time is continuous. There is every reason to believe that time is continuous, because space is continuous and space has an inherent motion. If the division of time were not as unending as the division of space, there would be no explanation of motion, because objects could not occupy continuously connected parts of space as they endured through time. (And the original and still most basic employment of the calculus to represent motion in a way that overcomes Zeno’s paradox about motion would be a misrepresentation of the world.)

Furthermore, spatiomaterialism is committed to the continuousness of time, because it is entailed by the assumption of an inherent motion in space as an aspect of its essential nature. Each distance in space corresponds to a period of time, and thus, if space is continuously divisible, time must also be. (To be sure, it is not possible to measure space by the velocity of light because of the Lorentz distortions, and even if we could, it would not necessarily tell us about space itself because of the acceleration of the inherent motion in gravitational fields. But the relationship between space and time, though complicated in these ways, requires time to be continuous, if space is.)

If the multiplication (or addition) of periods of time is without end, time is infinite in extent, or what is called “eternal.” The eternity of the world is entailed by spatiomaterialism, because it assumes that existence is in time. That is, spatiomaterialism assumes that the world is constituted by substances of kinds that never come into existence nor ever go out of existence, but rather endure through time. That is what enables it to explain change as really occurring as time passes. Given its view of time and existence, spatiomaterialism cannot believe that there was a beginning to the world, because that would be to hold that something comes from nothing. Nor can spatiomaterialism hold that the world stops existing at some point, for that would be to hold that what exists can become nothing.

Matter. Given our ontological explanation of quantum mechanics, however, matter can be infinite in only one way. The existence of ordinary material objects shows that there are finite accumulations of matter, and since they are units that can be counted, theorems of arithmetic are also true of matter.

If the multiplication (or addition) of matter is without end, matter is infinite in extent, that is, the total quantity of matter in the world is infinite. There is no reason to doubt that the quantity of matter is infinite, if space is infinite, because there is no reason to believe that only a finite region of space has bits of matter coinciding with it. On the other hand, if space were not infinite, matter could not be infinite, at least not ordinary matter, because there would be no room for all of it.

We know, however, that the division of matter cannot go one without end, because the theory of quantum matter holds that each bit of matter is constituted by a series of cyclic quantum events, each with the size represented by Planck’s constant, h. The spatiomaterialist explanation of quantum mechanics is based on the assumption that quantum events have a unit-like nature in which they either exist as a whole or not at all.

To be sure, force-field matter, such as electromagnetic and gravitational fields, may be infinitely divisible. But that is because force field are just properties or conditions that are imposed on space by quantum matter, and the quantity of matter they contain is already counted in the rest masses of the material objects exerting them (except in the case of gravitational waves, which are eventually converted in quantum events as they accelerate bits of matter). Quantum matter is the basic form in which matter endures through time as a substance.

At this point, therefore, spatiomaterialism still takes space and time to be infinite in both ways and matter to be infinite in extent, though only finitely divisible. The final question in this ontological explanation of physics is, therefore, whether spatiomaterialism can keep this simple form. Do its assumptions about space have to be more complicated in order to acknowledge that space and matter are finite in extent? Can its assumption that matter is not infinitely divisible be squared with what physics knows about the basic objects? And do we have to accept that time is not eternal and admit that spatiomaterialism is just an effect of a deeper, theistic ontology in order not to give up ontology altogether? These are the cosmological questions that spatiomaterialism must answer. The issues to be addressed can be separated into two sets, one having to do with the finite divisibility of matter and the other having to do with the infinite extent of space and time.

Finite divisibility of matter. Though spatiomaterialism has assumed that matter is constituted by cyclic quantum events in order to explain the truth of quantum mechanics, it had to take for granted that electrons and the nuclei of atoms can be explained in as a form of quantum matter. This is clearly not the deepest truth about nature, since physics has found other particles like electrons that are much heavier, and some that are massless and carry not electric charge at all. And it has discovered not only that the atomic nucleus is composed of protons and neutrons, but also that such nucleons are composed of quarks, not to mention the two short range forces involved in the interactions of its basic objects.

The main question is not whether the rest masses of the basic objects of physics can be explained ontologically as forms of quantum matter. There is not much reason to doubt that it is possible to give such a spatiomaterialist ontological explanation, though some might find it reassuring to see how it works out in more detail. But there is a reason to take up the issue of the nature of the most basic objects here. It is another opportunity to show the fruitfulness of an ontological explanation of the world based on spatiomaterialism. 

Physics now recognizes some 38 different kinds of basic particles (counting antiparticles, but not the three colors of each quark), and though they are a far less unruly lot than the particles recognized by physics thirty years ago, they are still an odd lot. Part of the problem is that the four basic forces of nature have not yet been fully unified. Even if we count the so-called electroweak force as the unification of the electromagnetic and weak forces, the strong force still resists assimilation as part of a single gauge theory, and as we have noted, physicists are at wits ends about how to represent gravitation as another force of the same kind. Particle physicists believe that there must be a deeper theory, but the dramatic progress of high energy physics during the 1970’s and 80’s has come to a halt in the 1990’s. And they are still pursuing the “holy grail” of physics, a single mathematical law from which the laws describing all the forces of nature can be derived.

The possibility that is not even being considered in this effort is explanatory ontology. As we shall see, by recognizing that space is a substance, it is possible to reduce all the basic particles of physics to nine or ten kinds of particles (including antiparticles). Indeed, it may even be possible to formulate spatiomaterialism in a way that reduces everything to just three basic particles — and space, of course, as the substance with which they coincide.

Infinite extent of space and time. In the direction of very large and very long-lasting, spatiomaterialism must be false, if contemporary cosmogony is correct, because it is currently assumed that the universe began with the big bang and has been expanding ever since. Indeed, the prevailing theory implies not only that the universe had a beginning in time, but also that space and matter are finite in extent. And some even interpret it as imply that the universe might simply drop out of existence at some time in the future (if it collapses because of gravitation), implying that time is also finite in the direction of the future. There are both theoretical and empirical reasons for believing that the universe began with a big bang and continues to expand, though as we shall see, spatiomaterialism can be defended against both.

On the theoretical side, Einstein showed how his general theory of relativity could be used to represent the universe as a whole, and with a relatively minor revision, that approach can be used to represent the expansion of a universe being contracted by gravitation in a mathematically precise way. That is the Einstein-de Sitter model, as it is widely accepted by cosmologists as explaining the expansion of the universe.

The empirical reasons are Hubble’s discovery of a correlation in galaxies between their red-shift and distance which suggests that galaxies are all rushing away from one another, the discovery that the proportion of hydrogen and helium in the universe is explained by their synthesis shortly after the big bang, and the discovery of a cosmic background radiation that seems to be the left over from the big bang (with wavelengths elongated by the expansion of space in the interim).

Spatiomaterialism can, however, be defended against both kinds of reasons. Its critique of Einsteinian cosmology is based on the spatiomaterialist explanation of the truth of Einstein’s general theory of relativity and its explanation of the relationship between gravitation and the other basic forces of nature. And spatiomaterialism offers another way of explaining all the empirical evidence for the big bang and the expansion of the universe. It is an approach to cosmological issues that is not even being considered these days. Not only is it a plausible defense of spatiomaterialism, but it also illustrates the fruitfulness of spatiomaterialism in opening up new ways of explaining natural phenomena.

Let me emphasize, however, that it is not necessary to defend such a cosmological theory in order to spatiomaterialism as the ontology for our new way of doing philosophy. What physics has discovered about the basic particles does not even suggest that spatiomaterialism is false, and like quantum mechanics, we could simply take it for granted that a spatiomaterialist  theory can be formulated. To be sure, big bang cosmogony does contradict spatiomaterialism. But scientists generally are not confident enough of its conclusions to use them as a reason for dismissing spatiomaterialism out of hand. Popular culture seems to be confident of the big bang, and the Church has welcomed it warmly. But among scientists, cosmology is still a matter of hot dispute.

There is, however, a point in carrying this project to the extremes of the very small and brief and to the very large and prolonged, because it turns up certain advantages of recognizing that space is a substance. There are straightforward ways of elaborating spatiomaterialism into an ontological explanation of cosmological phenomena, and hopefully it will do not harm to suggest them here.

This part the spatiomaterialist ontological explanation of the world is even more speculative than its explanation of quantum mechanics. It is included here in the spirit of exploration. By offering an ontological explanation, I do not suggest that these problems can be solved in the end without the use of mathematics to calculate quantitatively precise predictions and the attempt to make the appropriate measurements. Ontology is a deeper explanation than the efficient-cause explanations of empirical science, but it is not a substitute for them. An ontology must be able to explain why those efficient-cause explanations are true in order to be adequate.

Physics is, however, so dependent on the use of mathematics for representing the world that it has given up the intuitive insights that would come from recognizing that the world is constituted by space as well as matter. In explaining the truth of the special theory of relativity, the general theory, and quantum mechanics, we have seen how ontology offers a more intuitive explanation of these phenomena, one that uses our capacity to imagine space and time to think of space and matter as substances enduring through time and, thereby, constituting the natural world. Thus, it would not be surprising at this point, if, together with the enormously powerful constraints that mathematical theories impose on what is possible, the attempt to formulate an ontological explanation illuminated possibilities in the vague darkness that lies beyond what is firmly in the grasp of experimental physicists that turn out to be true.

Though I claim that the following theories are true, I am not claiming that the following explanation is the only possible spatiomaterialist explanation of cosmological phenomena, nor even that it is the best. My only claim is that it is a spatiomaterialist ontological explanation, and it does enable us to discuss these issues in a new and illuminating way. It explores an avenue that physics will travel, when it acknowledges that ontology is explanatory and uses the empirical method to infer to the best ontological-cause explanation, not just the best efficient-cause explanation. But even before it proves itself in that more demanding arena, it is possible to get a glimpse of how how the world is whole even at the extremes of the very small and the very large.

Basic objects. Let us first extend this ontological explanation in the direction of the very small and the very brief. The place to begin is with the so-called “Standard Model” of physics and the inventory of the basic forces and particles included in it. (A history of the history of particle physics by one of the participants that I would recommend is 't Hooft (1997)).

Basic particles of physics. In order to set the scene for inventorying the basic particles of physics, I will first describe more fully a basic difference that physics recognizes between two kinds of basic objects, fermions and bosons. Gauge field theories hold that forces are mediated by bosons, the so-called gauge particle of the underlying field, and the next step will be to describe the two forces of nature in these terms. That will put us in a position to list all the kinds of basic particles currently recognized by contemporary physics.

Fermions and bosons. The most fundamental difference among basic objects in space is that between fermions and bosons. (It is basic to the Yang-Mills field theories which are currently used to explain the basic forces.) This difference is exemplified by electrons and photons. As a first approximation, fermions, such as electrons, are the material objects on which forces the work, whereas bosons, such as photons, are the forces that work on them. Though the difference is more subtle, this contrast points to the basic difference in their roles.

Fermions are basically particles that exclude one another from occupying the same quantum state, whereas bosons are particles that tend to fall into the same quantum states. To put it more precisely, fermions obey the Pauli exclusion principle, while bosons do not. They behave according to Bose-Einstein statistics, as opposed to Fermi statistics.

The difference between them is the kind of intrinsic spin they have. Spin is the quantum mechanical version of a rotating object with an electric charge. It is a measure of the magnetic moment exerted by the particle when a magnetic field is imposed on it. But there are two different kinds of spin, distinguishing fermions and bosons.

The Pauli exclusion principle holds of any particle with some multiple of ½ spin (. .-5/2, -3/2, -1/2, 1/2, 3/2, 5/2, , ,) whereas Bose-Einstein statistics hold of particles with an even number of spin (. .-2, -1, 0, 1, 2, . .). The spin indicates the number of different forces the particle might exhibit when a magnetic force is imposed on it from a certain direction. The number is equal to 2s + 1. Thus, a particle with 1/2 spin can exert one of two possible forces when placed in a magnetic field, either positive or negative (up or down), whereas a particle with spin of 1 can have one of three values, positive, negative, or zero. Among the basic particles, however, there are only three kinds: particles with ½ spin, particles with a spin of 1, and particles with a spin of 0. The other values of spin come from combining basic particles. (Actually, Yang-Mills field theory recognize only particles with a spin of ½ and 1, but it has been necessary to add particles with 0 spin in order to explain the rest masses of particles.)

Fermions have the nature that makes them most like ordinary material objects, for they exclude one another from occupying the same place at the same time. The structure of the atom, for example, depends mainly on the Pauli exclusion principle. The various electron orbitals are distinct quantum states, and since electrons are fermions, only one electron (of each kind) can occupy each orbital. (The reason that there are usually two electrons in each orbital is that there are two opposite kinds of electrons, spin up and spin down, and one of each kind can fit into each orbital.)

Bosons are the particles that mediate the forces of nature, and they are called particles of the underlying field. Whereas basic fermions are point-like in the sense that they are located at each moment at a certain point in space, bosons have a nature more like space itself, because they emerge from the underlying field to mediate its forces.

Particles susceptible to a force are said to have a “charge,” but in order to conserve the charge so that it does not disappear (or multiply) as the particles move and interact, the force field laid out in space associated with the charge generates bosons, or forces, that act on the particle in certain ways, changing its motion or even its kind. This is called “local symmetry,” but it is basically the regularities about the particle that must hold in order for the “charge” to be unchanged.

One basic difference between electrons and photons does not, however, hold generally for fermions and bosons. Electrons have a rest mass, whereas photons are massless particles. But this contrast in rest mass crosscuts the distinction between fermions and bosons. There are massless fermions and massive bosons.

Though most fermions have rest mass, there is one set of fermions that, as far as physics can tell, do not have any rest mass at all. They are called “neutrinos,” which are affected only by the weak force (see below). Theory does not require them to have a rest mass, and experiments have made it clear that the maximum mass they can have is about 12 eV.[1] With a spin of ½, neutrinos should have two possible orientations of spin, but in this case, having opposite orientations of spin is what distinguishes each kind of neutrino from its antineutrino. Normally, antiparticles have opposite electric charges, but neutrinos have no electric charge, and the opposite orientation of spin is equivalent to having an opposite weak charge. The neutrino has left-handed spin in the direction of its motion, and the antineutrino has right-handed spin. They are mirror images of one another. (As massless particles, the fact that each kind of neutrino has only one orientation of spin, despite having a spin of ½, could be explained in much the same way as it is explained in the photon: one orientation of spin is lost because they move at the velocity of light, because they cannot stop to turn around so that they can interact from the other direction.)

Though photons are massless, there are bosons with mass. Mass would be expected in bosons that are merely fermions locked together in a way that neutralizes (or combines) their opposite orientations of space so that they have a net spin that is an even number, such as the helium atom. But bosons that are basic particles mediating the forces of some underlying field are expected to be massless, and thus, the discovery that the bosons mediating one of the basic forces of nature have rest mass (the weak force) posed a problem that had to be overcome. Let us turn, therefore, to the basic forces of nature.

Basic forces of nature. Physics recognizes four forces in nature (gravitation, electromagnetism, the strong nuclear force, and the weak force), and attempts to knit a mathematical description of them into a single, uniform deductive system have used the mathematics of gauge field theory (Yang-Mill gauge invariance). Since bosons are the kind of particle that emerge from the underlying field to mediate those forces, they can be called gauge bosons. 

Electromagnetic force. We have already seen how the electromagnetic force can be explained ontologically, and in passing, I have mentioned the gauge field theory of electromagnetic interactions.

Basically, the electric charge is represented as having an orientation in a complex field, and the electromagnetic forces affecting it are what is required for local symmetry, that is, for the charge to keep the same orientation in the complex field as the particle changes location in space.

What I have described as the force field matter of an object with rest mass is a way of referring to the electric charge of such a particle, and the gauge field theory about how it works can be explained ontologically by thinking of the force field matter of an electric charges as something that is imposed on space in a cyclic way as time passes, as if the force were sent out from the object in regular pulses. If the pulses of all negative charges throughout the universe were synchronized, it would be possible to explain what is meant by “orientation in a complex field,” for it would be the phase in that cycle. Negatively charged particles would all be pulsing at the same time, jointly setting up the force field in which they are located. The pulses would propagate at the velocity of light, since they are mediated by the inherent motion in space. And since the force field that acts on the charged object is pulsating, its charge must remain synchronized with the field, even though the particle may be changing locations in space. Gauge bosons emerge from the field to keep the charge synchronized, but they can do so only by exerting forces on the particle that can change its motion, accelerating it in one direction or another. Those forces are the electric and magnetic forces described by Maxwell’s equations, and the gauge boson is the virtual photon mentioned in explaining the quantum structure of the atom. Virtual photons carry momentum and kinetic energy between charged particles and the force-field matter the particles jointly spread out in space by their pulses. They are the spin 1 particles that mediate the electromagnetic force. 

The difference between positive and negative charges could be explained on this ontological explanation as having pulses with opposite phases in that universally synchronized cycle. Particles that pulsate in phase would repel one another, whereas particles that are pulsing out of phase with one another would attract one another. This dependency of the direction of the force on the phase of the universal pulsation is the reason that there must be virtual bosons to keep charges synchronized with the universal pulsation as the charged particles move across the force field they help set up (the force-field matter that comes from all the particles).

Partial electric charges could likewise be explained as phases relative to the universal electromagnetic pulsation (or as orientation in the complex field) between the extremes of negative an positive. But in order to take account of the magnetic force, the complex field in which charges are oriented may be twofold, and the pulsation correspondingly compounded.

[The mathematics of quantum electrodynamics, and gauge field theories generally, makes it difficult to figure out how a particle will move and interact in the field. Richard Feynman discovered a relatively simple way of doing so by identifying the path of least action from all the possible paths the particle could follow (which is ontologically, the path requiring the fewest quantum cycles). He showed how it could be identified by rules for canceling out more complicated, symmetrically opposite pathways and seeing what remains. This was the foundation for his famous “Feynman diagrams,” which depict electromagnetic interactions between particles as being mediated by the exchange of photons. But the mathematics involved is suspect in the minds of many, because the calculations lead to infinite quantities, which can be eliminated only by hand, canceling out those that are opposed symmetrically, in a process called “renormalization.” There must be a deeper explanation of what is going on.

[This aspect of quantum electrodynamics and other gauge field theories can be explained ontologically, I believe, in a way that involves the waves we have assumed are sent out in the inherent motion by quantum kinetic cycles. The symmetries that Feynman uses to determine the path of least action can ultimately be explained ontologically by the constructive and destructive interference of such waves (much as I have used them to explain Bohm’s “quantum potential”). But it is more complex, because the particle is carrying an electric charge through the force field, and if the force field involves a universal pulsation which constitutes the difference between positive and negative charge, the virtual photons must be synchronized with it in order to conserve the electric charge. I suspect there is some such ontological explanation, but it would take a better grasp of the mathematics than I have.]

Strong force. The strong force is the force that accounts for the nucleus of the atom. Being is about 100,000 times stronger as the electromagnetic force, it holds protons and neutrons together despite the strong repulsive forces among the positively charged protons. The strong force does not affect electrons or neutrinos (or other particles of their kinds).

The particles involved in the strong force are called “hadrons,” both the particles affected by it and the particles whose exchange mediates it. The strong force that holds the nucleons together is mediated by the exchange of mesons (such as pions). But protons and neutrons are only a two of many kinds of “baryons” that have been discovered by accelerating particles to collide with one another at very high energies, and various kinds of mesons have also been found mediating interactions among them.

The neutron, for example, decays into a proton, an electron, and an electron antineutrino, and there are many other kinds of baryons that decay into protons or neutrinos, with similar kinds of debris. The negatively charged pi meson (pion) decays into a negative mu lepton (a heavier cousin of the electron) and an mu antineutrino. Again, there are many kinds of mesons with various decay patterns, so of which decay by way of a pion.

The attempt to explain the diversity in the kinds of baryons and mesons has led to the recognition that hadrons are all composed of simpler objects, called “quarks.” Baryons are constituted by triplets of quarks, and that mesons are constituted by quark-antiquark pairs. There are some six different kinds of quarks, each with an antiquark, though only the two lowest energy quarks (u and d quarks) are found in the nucleons of ordinary matter. Half the quarks have a negative electric charge of 1/3, and half have a positive electric charge of 2/3 (with their respective antiquarks having electric charges with the opposite sign).

Interactions among quarks are mediated by the "color" force. That is, quarks have a “color charge” which makes them susceptible to the color force, and quarks interact with one another by exchanging gluons, the gauge particles of the color force. Gluons are, therefore, bosons with an intrinsic spin of 1. They are massless particles, like the photon. But unlike the photon, gluons are themselves subject to the color force, that is, they exert color forces on one another as well as on quarks. Photons, by contrast, do not interact at all, except for their tendency as bosons to fall in step with one another.

The color force has an unusual strength that keeps quarks confined in triplets to baryons. When quarks are very near one another, the color force is not very strong. But when the distance is increased, the color force increases along with it. And if the distance increases enough for the potential energy (or force-field matter) to constitute a quark and antiquark pair, matter takes that form. The quark of the new quark-antiquark pair replaces the quark that was being moved out of the baryon, and the antiquark combines with the original quark from the baryon to constitute a meson, which quickly decays.

In order for three different quarks of the same kind to help constitute a single baryon, there must be three different “colors” of each kind of quark. And according to the symmetry of the theory, eight kinds of gluons are needed to mediate all the forces that hold among three different kinds of quarks in constituting baryons.

Weak force. The weak force has long been recognized because of the need for some force to explain the radioactive decay of natural substances, such as radium. Natural substances send out particles with rest mass from time to time which can be detected, and since that suggested that they were somehow coming apart, a force was needed to explain how it could happen.

The weak force was soon also used to explain the decay of hadrons (baryons and mesons) into more common particles, such as neutrons, protons, electrons, and neutrinos, which were observed in high energy collisions of particles in accelerators. Indeed, there are also higher energy particles like the electron, such as the muon and tau particle, which decay into the electron and an antineutrino (or if they are positively charged, decay into a positively charged electron, or positron, and neutrino), and those decay patterns were also attributed to the weak force.   

In order to explain these decay patterns on the model of gauge field theory, it was recognized that every kind of particle carries a “weak charge,” which makes it susceptible to the weak force. The weak force is mediated by a kind of particle, which was originally called the “intermediate vector boson,” but is not referred to as the “weak boson” or “weakon.” As the gauge particle of the weak force, the weakon is a boson with spin 1, and in order for electric charge to be conserved in decay by the weak force, there had to be two different kinds of weakons, one with a positive and one with a negative charge (W^- and W⁺⁾.

It is called the weak force, because it is so much more difficult to make particles interact in this way than by the strong force (or even that the electromagnetic force, which is about 100 times weaker than the strong force). (The weak force is about 10^-6 times the strength of the strong force, whereas the electric force is 10^-2 times the strong force.) According to recognized principles, the weakon could still actually be a force comparable in strength to the photon, if the weakness of the weakon were due to having a considerable mass. But the assumption that the weakon had such a mass spoiled the gauge theory: the weakon could no longer represented by Yang-Mills mathematics.

In one of the most famous discoveries of the past few decades, Weinberg and Salam independently discovered a way to give the weakon a mass without spoiling its role as the particle of a gauge theory. This was to postulate the so-called Higgs boson and to assume that such particles exist everywhere in space. The Higgs boson has a spin of 0, lacking any orientation at all in a magnetic field. But to postulate their existence everywhere in space was to postulate the existence of a new field that has minimum energy when it is exerting a force everywhere in space. That force could be used to explain why a boson, such as the weakon, that is otherwise massless has a mass.

Weinberg recognized that this explanation of the mass of the weakon implied that, in addition to the negatively charged and positively charged weakons, there is a weakon that does not carry an electric charge at all (Z⁰). Interactions involving the Z⁰ would not change the electric charges of the particles, but only their motion, as in an elastic collision, and when evidence for such “neutral currents” was found, it was recognized that Weinberg had discovered a theory that explained both electromagnetism (how charges interact by way of virtual photons) and the weak force (how particles generally interact by way of virtual weakons). It is sometimes called the “electroweak force.”  (The color force, however, resists assimilation to that theory. Though it is possible to construct the appropriate equations describing gluons as the gauge particle mediating interactions among quarks (and gluons), it has not been possible to figure out what the equations imply.)

Gravitation. The success of gauge field theories in representing the other forces of nature has led to attempts to represent gravitation as force that is likewise mediated by the exchange of particles from an underlying field. The “charge” on which the gravitational force works is mass, and the gauge particle that mediates the gravitational force is called the “graviton.” However, in order to serve this function, it must be a boson with a spin of 2, and the attempt to integrate this force with the other three forces of nature what has led to superstring theory and the belief that there are as many as ten dimensions to space.

Though the mathematics of superstring theory is supposedly elegant, the need to recognize additional dimensions of space, if nothing else, makes it suspect. And it can be avoided, as we have seen, by recognizing that space is a basically different kind of substance from matter. Assuming that there is an inherent motion in space by which bits of matter coincide with parts of space (and that is possible, as we have seen, by the spatiomaterialist explanation of the truth of Einstein’s special theory of relativity), gravitation can be explained as an acceleration of an inherent motion in space. That is the spatiomaterialist explanation of Einstein’s general theory of relativity. 

This is a radical departure from contemporary physics, because without recognizing that space is a substance, it has no other way to explain gravitation than as just another field that holds among particles. That is what leads to the belief that gravitation is mediated by gravitons and poses what is the most formidable problem for contemporary physics: connecting gravitation with the other forces of nature.

Substantivalism about space makes it possible, however, to explain basic particles in a way that may be similar to superstring theory, but without the extra dimensions.

Catalogue of basic particles. Let us catalogue the basic objects that are currently recognized by physics, and then we shall see how we might account for all of them quite simply, given our ontology. The objects that are currently taken to be basic include both bosons and fermions.

The bosons are the particles mediating the forces. According to current gauge theories, there are bosons for each of the four forces, including the graviton to mediate the gravitational forces. (See diagram of Basic Particles of Physics.)

Current explanations of the weak force requires the postulation a Higgs boson, with a spin of 0, to give weakons (and other particles) their rest masses.

Three weakons mediate the weak force: W⁺, W^-, and Z^0, each with a spin of 1. 

The photon is the gauge boson that mediates the electromagnetic force. It also has a spin of 1.

Eight gluons mediate the color force, each with a spin of 1.

The graviton is the boson that is supposed to mediate gravitational forces, but it can be set aside, since I have already explained gravitation without the need for any such particle.

Fermions are particles that obey the Pauli exclusion principle and have a point-like location in space. There are two broad classes, leptons and hadrons. The hadrons are distinguished by their susceptibility to the strong force, while leptons are immune. Electrons are the most famous members of the lepton group. Their masses are well defined, and their name, meaning “light ones,” comes from being so much lighter particles than hadrons (and even than quarks). But some physicists suspect that neutrinos may not be quite massless. There are six leptons in all, and each has an antiparticle.

The first family of leptons includes the electron and the electron neutrino. The electron has a charge of –1 and a mass of 0.5 MeV/c², whereas the electron neutrino has no charge and there is not much reason to believe it has any mass at all. The antiparticle of the electron is the positive electron, or positron, with a charge of +1, and the antiparticle of the electron neutrino is the electron antineutrino, with neither charge nor rest mass.

The second lepton family is composed of the muon and the muon neutrino. The muon has a negative charge and a mass of about 106  MeV/c²,whereas the muon neutrino has no charge and no rest mass. Again, both members of this family of leptons have an antiparticle, the positively charged muon and the muon antineutrino, without any charge or rest mass.

The third lepton family is composed of the tau particle, with a negative charge and a mass of 1784 MeV/c² and the tau neutrino. Both have antiparticles with properties similar to the first two families of leptons.

Hadrons are the objects affected by the strong force, and they are made of quarks, as we have seen. (Baryons have three quarks each, whereas mesons are made up of a quark and antiquark.) Let us inventory the quarks, since hadrons have already been reduced to them. Most commentators are struck by how the quarks also fall into three families, with two particles each, both with antiparticles.

The first family of quarks includes the d and u quarks, and an antiparticle for each. The d quark has a charge of -1/3, while the u quark has a charge of +2/3, setting the pattern for all three families. The masses of quarks are not well defined, because they cannot be released from confinement in baryons or mesons, but the d and u quarks do not appear to be over 100MeV/c² (and may be considerably less). Their antiparticles are antiquarks, with opposite electric charges, that is, anti-d, with +1/3 and anti-u, with –2/3.

The second family includes the s quark and the c quark, and their antiparticles. The s quark, with a charge of –1/3, resembles the d quark, but it has a mass of about 200 MeV/c². The c quark likewise resembles the u quark, except it has a mass of about 2000 MeV/c². Their antiquarks have the same masses, but opposite electric charges.

The third family includes the b and t quarks. The b quark resembles the d and s quarks, with a charge of –1/3, while the t quark, with a charge of +2/3,  resembles the u and c quarks. Again the main difference is in mass. The b quark has a mass of about 5000 MeV/c², while the t quark has  a mass of about 175000 MeV/c². Their antiquarks have opposite electric charges.

The accompanying diagram listing all the basic particles recognized by physics suggests the deep symmetry that is believed to hold between the quarks and leptons. Each has three families; two members have different electric charges; all particles have antiparticles, and all are subject to the weak force. Together with the bosons required for the three forces of nature, including gravitation, there is a total of 38 particles. (But there are only 37 to explain, since gravitation has already been explained by the nature of space as a substance.)