What forced us to promise to explain how Einstein's special and general theories of relativity could be true in a world where space and time are absolute was the commitment of contemporary physics to the belief in spacetime. We had to take out that "mortgage" on spatiomaterialism as the foundation for ontological philosophy, because spatiomaterialism is committed to absolute space and time. This section will pay it off by showing how how the special theory of relativity can be true in a spatiomaterial world.
Let us recall, first, our reason for believing that space and time are absolute. We were inferring to the best ontological explanation of the world. That is not the method of empirical science, because an ontological theory is a theory about the nature of what exists, not only about what happens to it. The first basic issue about the nature of what exists has to do with the nature of time, and we concluded that we had to prefer presentism to eternalism because it alone could explain our observations about how the present moment is different from the past and future. Presentism holds that only the present exists. The past and the future do not exist. To be is to be in time.
We know by reflecting on ourselves as agents that the future does not exist, because if it did, we would not be able to control what happens in the world. We act as we do in order to make the future different from what it would be otherwise, and that would simply not be possible, if the future already existed. Every event must aleady be determined, if eternalism is true,
Reflection should be considered relevant evidence about the nature of what exists in the world, since the beings who do the reflecting are clear;y parts of that world. But contemporary physicists cannot escape this empirical falisfication of the belief in spacetime. There is also plenty of evidence for those who insist that only peception can supply the empirical data for choosing among theories. It is found in our perception of change. To perceive change, for example, to see a book falling from a shelf, is the recognize that certain spatial relations are going out of existence and other spatial relations are comming into existence. Defined as properties coming into existence and going out of existence, change might be called "presentist change," in order to distinguish it from "eternalist change," or change defined merely as objects having different properties or relations at different times. Anyone who perceives presentist change has plenty of observational evidence that only the present exists because properties (and spatial relations) cannot go out of existence, if the past still exists. Nor can properties (or spatial relations) come into existence, if the future already exists.
If eternalism were true, the present would not be different from the past or the future in this basic way, and thus, eternalism cannot explain what we observe about the nature of existence in perceiving persentist change.
Presentism is an indispensible assumption for any ontology that hopes to be explanatory, for it allows one to hold that what exists are substances that endure through time and, thereby, to explain what is found in the world as being constituted by basic substances and the manner in which they exist together as a world. All truths about the world, including truths about the past and the future, are thereby reducible to facts about what exists now.
On the other hand, if eternalism were true, one would have to postulate many more basic entities in order to explain the world, because one would have to postulate distinct basic entities for every moment in the history of every material object found in the world. Though such basic entities would not be substances in our sense, they would serve as the basic ontological causes in an eternalist explanation of the world, because they would constitute substances in our sense. The spacetime events that make up the world-lines of ordinary objects in Minkowski spacetime diagrams would be basic entities in this sense.
Eternalism is what makes the belief in spacetime unacceptable to empirically minded thinkers who want to know the truth about the nature of what exists. Empirical ontology seeks to discover the theory that corresponds to the basic nature of what exists, and since we have observational evidence that existence is what makes present different from the past and the future, any ontological theory that denies that fact is not very likely to be true. Indeed, it is empirically falsified by our perception of presentist change and our reflection on ourselves as agents.
Though “change” may be defined in terms of the difference between events located earlier and those located later on a world line, that is not presentist change (since there is nothing coming into existence or going out of existence over time). It is eternalist change. Presentist change entials eternalist change (since propositions about the future and the past can be reduced to propositions about the substances that exist now), but eternalist change does not entail presentist change (since there is no way to distinguish the present from the past and the future). Thus, there are observational facts that a presentist ontology, like spatiomaterialism, can explan that cannot be explained by any eternalist ontology, such as the belief in spacetime.
It is not the case that this problem about the nature of time has gone entirely unnoticed in the literature. Putnam  noticed that substantivalism about spacetime contradicts our ordinary assumption about time (that only the present exists). But he focused on the incompatibility between the future being already determined and our view of ourselves as agents. Since he does not recognize reflection as observational evidence about the nature of what exists, he simply accepts the belief in spaceime as another case of scientific discoveries correcting ordinary beliefs. Putnam's point was also made by Rietdijk .
Worries about having to hold that we are suffering a massive delusion in believing that the present is radically different from all the other moments in time are expressed by John Post (1987, Chapter 3) and Roger Penrose (1989, pp. 442ff). But it does not lead them to doubt that spacetime corresponds to the real nature of what exists.
Maxwell , pp. 23-43, stands out as the only philosopher who sees the incompatibility of substantivalism about spacetime with our observation of how the present is different from the past and the future as justifying our rejection of the belief in spacetime in favor of the belief in absolute time. His view has not gathered support in the literature.
Others, like Stein [1968, 1991], have tried to avoid having to choose between the belief in spacetime and the openness of the future by taking the truth of Einstein's special theory of relativity to be relative to the “here and now.” He uses the velocity-of-light limit on causal influences between distant events to distinguish between spacetime events with a time-like relationship to the here and now (with the past being those events that could affect us here and now and the future being those that we could affect) from spacetime events with as space-like relationship to the here and now (namely those spacetime events that we could not affect and that could not affect us without effects traveling faster than the velocity of light). That allows Stein to take spacetime events that are related in a space-like way to the here and now as neither determined nor undetermined, but “indeterminate.” However, if relativity to the here and now does abandon the requirement that theories in physics be true at the same time for observers located everywhere in the universe, it does give up ontology as a theory about the nature of the substances that constitute the existence of everything in the world, for there is no way to explain indeterminate spacetime events by taking spacetime events to be the basic entities that constitute the world (much less by taking substances enduring through time to constitute the world).
Similar objections hold for the attempt by Smith (, p. 4) to solve these ontological issues by reducing existence to “being real to.” What exists cannot be relative to any particular subject without giving up naturalism and accepting an ontology that makes subjective minds basic and reduces objects in space to them in some way.
Mathematics also obscures this issue in the literature. A logical analysis of the difference between invariant and ontological temporal relations is offered by Rakic , but he apparently does not recognize that in introducing the ontological relation R, he is, in effect, adding Newtonian absolute time to STR. He does not see the ontological significance of his mathematical arugment.
In the face of the prima facie difficulties with accepting the belief in spacetime, it is surprising that there has been so little interest in replacing Einstein's special theory of relativity with an explanation based on the belief in absolute space and time. And it is all the more surprising, because the possibility of a “Newtonian” theory the phenomena covered by special relativity is widely admitted.
For example, it is admitted by Zaher , Sklar , and Dorato , and it is even defended by Maxwell , though for different reasons than will be given here. The equivalence of such a “Newtonian” theory to Einstein’s special theory is recognized by Maxwell  and Smith , shown mathematically by Prokhovnik  and Bell , and explained in a more intuitive way by Scribner .
But commentators on Einstein’s special theory (such as Sklar 1992, pp. 27-30) often dismiss this possibility as a mere “compensatory theory”, as if it were a crutch for those who feel somehow psychologically crippled by the loss of an intuitively intelligible explanation, whereas our reason for believing in absolute space is that it is required by empirical ontology, given the observational evidence for presentism.
Spacetime is not, however, the only possible ontological explanation of the phenomenon described by Einstein's special theory of relativity. It is also possible to explain all those phenomena on the assumption that space and matter are substances enduring through time, even though that entails that space and time are absolute. We need only assume that space and matter are so related as basic substances constituting the world that the velocity of material objects through substantival space causes distortions in them in which clocks are slowed down, lengths are contracted in the direction of absolute motion, masses increase and forcefields are flattend in the direction of motion (all at the usual rate). These are the distortions that are implicit in the conclusions of Einstein’s argument, but in the following argument the order is reversed. Instead of assuming the principle of relativity and deriving the distortions as consequences, we shall assume the Lorentz distortions as basic laws of physics and derive the principle of relativity—that is, explain all aspects of the empirical equivalence of inertial reference frames by the Lorentz distortions.
There is probably an interesting story to be told about why Newtonian physicists did not defend such a theory about the empirical equivalence of inertial frames when it was still a live issue. Lorentz did explain the negative result of the Michelson-Morley experiment by the distortions he discovered, but he did even try to explain the symmetry in the transformation equations he used to describe them, because he thought of them as merely a convenient mathematical device for describing the effects of absolute motion on material objects. The reason that other physicists did not extend Lorentz's basically physical approach to explain why comparisons between inertial reference frames could not detect absolute rest and motion may be the devastating effects of World War I on the talent of that generation. An entire generation of potential physicists was wiped out, and after the war, the relative ease of reaching intersubjective agreement about mathematical arguments may have driven out the more divisive Newtonian arguments. To explain special relativity in terms of absolute space and absolute time requires intutive understanding, and such physical explanations could not be constructed without solving paradoxes about pairs of clocks both going slower than the other and light having the same velocity in different inertial frames. It also seemed ad hoc to postulate Lorentz distortions, since their only role in physics seemed to be making it impossible to detect absolute rest and motion. Einstein's elegant mathematical argument may have seemed superior in the young, abstract minds that picked up the discipline after the war untutored by the lost generation of Newtonian physicists. Thus, most students may simply have been taught Einsteinian equations from the beginning of their graduate careers, and those who demanded a more intuitive understanding of what they meant were weeded out as not being intellectually fit to do physics.
In giving the spatiomaterialist explanation of the truth of the special theory of relativity, I will start by following in the footsteps of Lorentz. But the spatiomaterialist explanation disagrees with Lorentz about what is required to explain special relativity, because it recognizes that it is necessary to explain not only the negative result of the Michelson-Morley experiment, but also why absolute motion and rest cannot be detected by comparing inertial frames with one another.
The inability to determine the absolute velocity of a material object by measuring the velocity of light relative to it is what Lorentz explained by postulating the slowing down of clocks and the shrinking of measuring rods in the measuring apparatus. Lorentz and Poincaré attempted to explain these distortions by the interaction of material objects with an ether, and I will suggest in the final section how they might be explained ontologically (by the unit-like, or quantum, electromagnetic interactions that constitute material objects in a spatiomaterial world like ours). In order to explain not only the kinematic phenomena on which Lorentz focused, but also the dynamic phenomena that make the laws of physics apply the same way on all inertial frames, it is necessary to recognize two additional distortions: an increase in mass and a flattening of forcefields in the direction of motion. But to focus on explaining the Lorentz distortions, even including all four, is to fail to recognize that there is another, quite puzzling aspect of the phenomena described by Einstein’s special theory that needs to be explained.
The puzzling aspect is the symmetry that holds between members of each pair of inertial frames. It is implied by the Lorentz transformation equations, and it is an essential part of the principle of relativity as the empirical equivalence of all inertial reference frames, for it implies that absolute rest and motion cannot be detected by comparting inertial frames with one another. Explaining this symmetry will require a two-step argument. The first step is to show that the effect of following Einstein’s definition of simultaneity at a distance in absolute space is to mis-synchronize clocks on a moving inertial frame in a certain way. The resulting disagreement about the simultaneity of events at a distance is widely recognized, but its role in causing the symmetry between inertial frames is not. Hence, the second step is to show how the mis-synchronization combines with the Lorentz distortions themselves to make it appear that the Lorentz distortions are always occurring symmetrically in the other inertial frame.
The Lorentz Distortions. To hold that space is a substance enduring though time is to hold that space is absolute, and we have assumed that space is the medium of light transmission. There is an inherent motion in space that gives light a constant velocity relative to absolute space. On that basis, the spatiomaterialist theory must explain why inertial frames all appear to be alike, that is, why the velocity of light seems to be the same and why the laws of physics all apply the same way in every inertial frame. This "local equivalence" among inertial frames must be explained as a mere appearance, because motion across absolute space must change the velocity of light relative to the moving object, as suggested by the analogy to the boat moving through ripples in a pond. And the laws of physics describing interactions among material objects (dynamic phenomena) make different predictions for material objects with different velocities. In order for it to be impossible to detect absolute motion, moving material objects (that is, objects with with rest mass) must be distorted in certain ways.
There are four kinds of distortions in material objects with high absolute velocity: a slowing down of clocks, a contraction of lengths in the direction of motion, an increase in the mass of moving objects, and an decrease in the strength of forces in the direction of motion. These are what I will call the "Lorentz distortions." Only the first two were actually discovered by Lorentz, but all of them are required for the same kinds of reasons. Though I will not give a formal mathematical argument, enough will be said about each to explain their quantitative aspects.
The rate involved in all these distortions is , where v is absolute velocity. This is the rate of distortion that is required to explain why Michelson and Morley were unable to detect absolute motion by using an interferometer to measure the velocity of light. This apparatus reflects light from two mirrors lying in mutually perpendicular directions, and the velocity of light in each direction is determined by measuring the period required for each two-way trip (by the interference of the waves coming from the two directions).
Time dilation. Assume that one mirror lies forward in the direction of absolute motion with the other transverse to it. The need for physical interactions to slow down on moving objects can be seen by considering what happens on the transverse pathway as the apparatus moves through absolute space.
The transverse pathway of the interferometer is, in effect, a “light clock”, using the velocity of light to measure time. Since the velocity of light in absolute space is fixed, the light in a light clock with absolute motion must travel farther than in a light clock at rest, and that means that the moving light clock is slowed down. It is slowed down at the same rate that all physical processes must be slowed down in order to keep this effect from being detectable. (See diagram of the path of light on the transverse light clock.)
Light traveling along the transverse pathway must go farther than it would, were the apparatus at absolute rest, because to return to its starting place, the light must also keep up with the apparatus, which is also moving through space all the time that the light is traveling. To observers on the moving object, light seems to travel directly to the mirror and back, but its path in absolute space is actually along the hypotenuse (ct) of the triangle formed by the transverse pathway (L) and the motion of the starting point in absolute space (vt). This increases the period required for the two-way trip.
The period is increased at the usual rate (except as a function of absolute, rather than relative, velocity). The rate is obtained by Pythagoras’ theorem for the right triangle depicted in the diagram (L2 + v2t2 = c2t2) and solving for t. Since L/c is the period it would take light to travel to the mirror at absolute rest, the period required for each leg on the moving apparatus is .
Length contraction. The need for a contraction of the size of material objects in the direction of motion can be seen by considering what must happen to light clocks oriented in the direction of motion in order for absolute motion to be undetectable. Unless their lengths were also to shrink, it would still be possible to detect absolute motion by comparing the longitudinal light clock with the transverse light clock, because the former would be even slower than the later.
In addition to the distance back and forth along the longitudinal pathway, the light on the longitudinal must also cover, as we have seen, all the space that the apparatus itself travels during the period of its two-way trip. But in the longitudinal direction, there is a new factor at work, because the two legs of its trip are unequal. Light must travel farther in absolute space on the outward leg in the direction of the apparatus’ motion than on the return leg, because of the motion of the apparatus in absolute space.
That means that, relative to the apparatus, the effective velocity of light toward the (forward) mirror is slower than when coming back. On the outward leg, the velocity of light relative to the apparatus is c - v, and on the return leg it is c + v. But light spends more time traveling slower in the outward direction than it does traveling faster on the return leg, and since the effect on the total time of travel depends on how long it travels at each velocity, it does not make up all the time lost during the outward leg on the return leg. The whole period required would be longer than the period required on the transverse pathway, because with equal distances to cover to the forward mirror and back, it spends a longer time going at the slower (at c-v) than it spends going faster (at c+v). That would make absolute motion detectable, unless the measuring rod were contracted.
If material objects also shrink (at the usual rate), the measurements made by the interferometer will be the same regardless of its absolute motion and the principle of relativity will seem to be true. The required rate is easy to calculate because the new length, L', must be such that the period for the two way trip, L'/(c - v) + L'(c + v), is equal to the period for a two-way transverse trip derived in the foregoing discussion of time dilation. Simply solve for L'.
The two remaining distortions follow from the temporal and spatial (or “kinematic”) distortions, for unless there were further distortions, Newton’s laws of motion, notably his second law (F = ma), would be false and the deviation from what it requires would be a measure of absolute velocity. Time dilation and length contraction are both relevant to dynamic phenomena, because both are involved in the acceleration of material objects, which Newton’s law says is proportional to the force exerted on them. Thus, there are two dynamic distortions, an increase in mass and a decrease of the force field in the direction of motion, corresponding to the kinematic distortions.
Mass increase. The necessity of an increase in mass follows from the temporal distortion, because unless the masses of material objects increase at the usual rate with absolute motion, Newton’s second law of motion (F = ma) will be false and physical processes will not take place the same way in absolute motion as at rest.
For example, dynamic clocks, such as pendulum clocks and wind-up alarm clocks, which depend on the acceleration of material objects to measure time, would disagree with light clocks, and the difference between the two kinds of clocks would be a measure of absolute motion.
Consider a dynamic clock oriented in the transverse direction of the inertial frame’s absolute motion. Since light clocks are slowed down, the dynamic clock would seem to be speeded up, since the pendulum (or whatever) would be accelerating over the whole distance just as quickly as it does at rest. The only way the dynamic clock can be slowed down to match the slowing down of the light clock is for the mass being accelerated to be increased at the same rate the light clock is slowed down. Thus, mass must increase at the rate as a function of absolute velocity as time is slowed down.
Longitudinal decrease in the force field. The necessity of a decrease in forces exerted in the direction of motion follows from the spatial distortion, the shrinkage of measuring rods in the direction of motion, for unless the longitudinal force field decreases with absolute motion at the usual rate, Newton’s second law of motion will still be false and deviations from its predictions will be a measure of absolute motion.
Consider a dynamic clock oriented in the direction of the inertial frame’s motion. Although the mass of the pendulum (or whatever) will be increased at the usual rate and, thus, slowed down, it will still be accelerating under the force at the same rate for the same period as the transverse dynamic clock. But since measuring rods are contracted in the direction of motion, the pendulum would still seem to be accelerating faster, because it would seem to be going farther in the same length of time. In order for absolute motion to be undetectable, the pendulum in the longitudinal direction must accelerate more slowly over space. But it is not possible for this acceleration to be slowed down by a further increase in mass, since mass is a scalar quantity, which does not depend on the direction of motion, and only acceleration in the direction of motion has to be slowed down. The only way the acceleration of the pendulum could be slowed down only in the longitudinal direction is for the size of the force field in that direction to be decreased at the usual rate as a function of absolute velocity.
Thus, in order to explain the "local equivalence" of inertial frames, that is, why absolute velocity cannot be detected by measuring the velocity of light relative to the moving object and why dynamic clocks do not disagree with light clocks, as if their reference frames were at absolute rest in space, we need only assume that the nature of matter is such that these four distortions occur when material objects are in motion across absolute space. There are two kinematic distortions and two dynamic distortions, all at the same rate as a function of absolute velocity. The first two are the distortions first described by Lorentz, and the latter two are distortions that Einstein showed were entailed by the Lorentz transformation equations when mass and force are also taken into consideration.
In order to show that spatiomaterialism can explain the truth of Einstein’s special theory of relativity, therefore, I will assume that matter has this nature.
I have shown the necessity of these distortions here by following Lorentz and arguing backwards from the Michelson-Morley experiment to what is required for absolute velocity to be undetectable by measurements of the velocity of light on any given inertial frame (or from comparisons of dynamic clocks and light clocks), they are not as ad hoc as that makes them seem. As I will argue in the final section, they are the same distortions that would be caused by the nature of ordinary material objects, if they were constituted by unit-like electromagnetic interactions among its parts (among molecules, among atoms within molecules, and between protons and electrons within atoms).
What made it possible for Einstein to infer the Lorentz distortions from his principle of relativity (and his assumptions that light has the same velocity relative to every inertial frame) is that these are the only distortions in material objects that would make absolute velocity undetectable by measurements of the velocity of light and comparisons between light clocks and dynamic clocks. But since they are merely implicit in the Lorentz transformation equations he derived, they appear in the paradoxical form of symmetrical distortions between any pair of inertial frames, and that is the other aspect of these phenomena that needs to be explained.
 This distortion in longitudinal forces is not widely recognized. It is suggested in a few obscure discussions of the difference between “transverse mass” and “longitudinal mass” that follows from Einstein’s special theory. See Okun (1989). This complication in Einstein’s theory is not usually acknowledged in textbooks in this field (and I thank Howard Reese for bringing it to my attention). But since it makes no sense to suppose that mass is different in different directions, the only possible explanation of the principle of relativity (as opposed to mathematical deduction) is a relativistic decrease in longitudinal forces. Prokhovnik (1985) recognizes it, and he explains it mathematically as a retarded potential. (It is as if the force involved a two-way trip at the velocity of light in order to act).