Spatial global regularities. The basic spatial global regularity is that matter is conserved. The total quantity of matter in any closed or isolated region of space does not change. But under certain circumstances, it entails a less general spatial global regularity, the conservation of energy.

“Spatial global regularity” is an appropriate name, because nothing is assumed about the nature of matter except what is entailed by spatiomaterialism (besides space, the existence of many particular substances, each coinciding with some part of space or other.) This global regularity is the purest ontological effect of the wholeness of space.

The regularities caused ontologically by space are not just global. The structure of space also helps cause necessary principles and contingent laws about local regularities (or the basic laws of physics, classical and contemporary). Since bits of matter have spatial relations to one another because they coincide with parts of space, the way those spatial relations change as a result of motion is partly determined by the structure of space. This might be called the local aspect of space.

The global aspect of space, on the other hand, is its wholeness, or the fact that all the parts of space fit together as a single system of locations that are all related to one another geometrically. The wholeness of space is an ontological cause of regularities about change in entire regions of space, because it requires that all the local changes that occur in any region fit together in space as time passes.

When combined with the assumption that matter has a nature that makes the basic laws of physics true, the spatial global regularity (that matter is conserved in a closed or isolated system) entails that energy is conserved in any closed system. That is an ontological explanation of the first law of thermodynamics in a spatiomaterial world like ours.

Conservation principles are called “principles”, because they are supposed to be too basic to be explained by anything else. But conservation principles can be explained ontologically, though in the case of the conservation of matter, the global regularity is so obvious that it may seem to be trivial.

The conservation of matter. Spatiomaterialism holds that matter and space are substances enduring through time. Since matter is a substance, it neither comes into existence nor goes out of existence over time. That is how matter itself is an ontological cause of the conservation of matter. The total quantity of matter cannot change, because matter is a substance. But space is also a ontological cause of this regularity, because matter is contained by space and it is by coinciding with parts of space that bits of matter have spatial relations to one another. Space is what gives particular substances the relationship that makes it possible for them to add up, that is, to be added together and have a total, as we saw in Relations, where the truth of mathematics was explained ontologically.

The relevance of space as a cause of conservation principles is implicit in the way they are formulated. They hold that some quantity does not change in closed or isolated regions of space. But this reference to a region of space indicates a further ontological effect of space. The reason the total quantity of matter does not change in any closed or isolated region of space is that that is how change of any kind adds up in space as time passes when the bits of matter conform to the principle of local motion.

The principle of local motion holds that the only way that bits of matter can change location is by motion, and since it was derived from spatiomaterialism, it is an ontologically necessary principle. But if it holds of all possible change, then the total quantity of matter in a closed region of space cannot change, because to be closed or isolated means that there is a two-dimensional surface surrounding the matter across which no matter is moving That is how bits of matter must “add up” over time because they coincide with space as a substance enduring through time. “Adding up” is an ontological consequence of the wholeness of the space that contains them.

Change in bits of matter adds up in space in the same way that the bits of matter themselves add up in space, except that change takes their endurance through time into consideration. The bits of matter endure though time, but since whatever happens, they cannot change location except by motion, the total matter cannot change in any closed or isolated region of space.

Though it may be obvious and simple, the lack of change in the total quantity of matter in a closed region of space is a regularity about change over time. It is a global regularity, because it has to do with the properties of whole regions of space. The regularity is not just what is assumed by postulating matter as a substance, but rather is explained ontologically by spatiomaterialism, because it is an aspect of the world enduring through time that depends on both space and matter and how they exist together as a world. Thus, the conservation of matter is an ontologically necessary regularity. If the total matter in a closed or isolated region did change, spatiomaterialism would be false. Matter is conserved, therefore, in every possible spatiomaterial world.

The conservation of energy. The first law of thermodynamics is the principle of the conservation of energy. It is a consequence of this spatial global regularity, if we take into account the forms of matter we have assumed in order to explain the basic laws of classical physics ontologically.

This implication will hardly be a surprise, since we used the principle of the conservation of mass and energy as a guide to ensure the completeness of our inventory of the forms of matter that had to be postulated in order to explain the basic laws of classical physics. But since that was just a working hypothesis for distinguishing the various forms of matter, it is relevant, now that we have shown that the forms of matter we assumed can indeed explain the truth of the basic laws of physics, to consider how those forms of matter make the principle of the conservation of energy true. The ontological explanation is not as simple as it may seem.

It may seem that the principle of the conservation of energy is an immediate consequence of the conservation of matter, because it is usually assumed that mass and energy are conserved separately as long as no nuclear reactions, converting rest mass to energy, occur in the region. The total quantity of matter that exists as energy in the region cannot change, because when the total rest mass does not change, matter does not exist in any other forms and matter does not come into existence or go out of existence.

However, the principle of the conservation of energy is not so simple ontologically, because given our ontological explanation of the nature of potential energy, there is a conversion between rest mass and kinetic energy (or other forms of actual energy) whenever potential energy is being consumed or created, which happens in most ordinary physical processes.

Material objects exert forces that can accelerate material objects, and our theory is that those forces are a form of matter that helps make up the material objects and whose quantity is counted in their rest masses. When potential energy has given the objects kinetic energy, for example, the objects have not only changed their relative positions, but the force field itself has changed. The change in the force field means that less matter is required to constitute it, and that is the source of the kinetic energy, which on our theory is also a form of matter. Thus, it is a conversion of some of the matter counted as rest mass into matter that is counted as kinetic energy. The opposite conversion occurs when kinetic energy becomes potential energy, and the same principle holds for conversions between potential energy and photons (and other forms of matter). Thus, the conversion between potential energy and kinetic energy does not violate the principle of the conservation of mass and energy.

Even though, in these processes, matter is being converted between a form that is counted as rest mass and a form that is counted as kinetic energy, the total quantity of energy does not change. The reason is that potential energy is counted as zero when it is maximum and that any potential energy that is consumed as kinetic energy (or photons) is counted as a bit negative energy in the region. There can be no such thing as negative matter, since matter is a substance. But counting potential energy as negative energy keeps the energy accounts balanced.

Negative potential energy is explained ontologically as a decrease in the rest masses of the material objects. The “rest mass” of a material object is defined, according to our ontological explanation of physics, as its mass when it is at rest in absolute space and the only force field in its neighborhood is the one that it imposes by itself (that is, separate from other material objects).

Thus, when it is (falsely) assumed that the rest masses of the objects involved are unchanged, counting potential energy as negative energy keeps the total quantity of mass and energy the same. The actual loss of mass from the total quantity of rest mass in the region is so small (according to Einstein’s equation, E = mc²) that the change in potential energy is not easily detected as a change in rest mass. Thus, counting potential energy as a negative quantity makes it seem that energy is conserved separately from rest mass in these processes.

But in fact, rest mass is not conserved. An object’s mass changes as its potential energy is actualized. Only the total of mass and energy are conserved even in most ordinary processes (where an object’s mass apart from its kinetic matter is accurately determined by subtracting the potential energy it has given up from its rest mass).

Thus, whereas the conservation of matter is an ontologically necessary global regularity, the conservation of energy is ontologically necessary only on the condition that matter has a nature that makes the basic laws of physics true, and thus, this shows it to be ontologically necessary only in spatiomaterial worlds like our own.