[The material of this chapter can be found in Modes of the Finite, Part 1, Sections 3 and 4, as well as Part 2, Section 1.]
4.1. The basic properties of all forms of energy
The object of this part of the book is to describe, from a philosophical perspective, the objects that physics and chemistry deal with--bodies--and to connect the philosophical description with the descriptions found in physics and chemistry. I think the process will yield some conclusions which might be useful in these sciences.
In this chapter, we want to take a philosophical look at what scientists are dealing with when they do things with what they call "energy." We are not really interested in examining the scientific concept of energy, but rather what is referred to by that concept--what the scientists are talking about when they talk about "energy." Of course, in order to show that what we will be referring to under the name "energy" is the same thing that scientists are referring to, we will have to examine the scientific concept; but this is secondary to our main purpose: what are we (and scientists too) talking about when we talk about energy?
First of all, scientists certainly think they are talking about something real when they are referring to energy; in fact, there is a kind of dogma in scientific circles that if whatever it is you are talking about isn't energy or some confiuration of various forms of energy, then you're just playing games with words and imagining things. If it's real at all, they say, it's really nothing but energy.
As it happens, this dogma is false, for reasons I don't want to go into at the moment; but it does give us a starting-point in that scientists are referring to something real rather than imaginary when they talk about energy.
The second thing that seems always true about energy is that it is (at least in principle) measurable. You may not be able to measure it directly, because you can't get an instrument into the system (as, for instance, the internal energy of an atom); but you can either measure how much energy there is indirectly, or at least the energy would be able to be measured if there was a way to do it. It has, in other words, "what it takes" to be measured: there's always a certain amount or degree of it.
Beyond this, there seem to be all kinds of differences in energy; and there we get into the various forms of energy. All forms of energy are (a) real, and (b) measurable; but one form of energy may be totally different from another except in these two common characteristics. Also, (c) any energy is always some form of energy; there's no such thing as a certain amount of "just plain energy" of no form at all.
In fact, each case of energy is always a given form and a given amount--and the amount of one form of energy doesn't have the same numbers attached to it as the amount of a different form of energy. It sounds as if the ammount "attached" itself to the particular form of energy you are dealing with.
4.1.1. Being and activity
Let us, then, examine these characteristics from the more general perspective of philosophy. What are you referring to or talking about when you are talking about something real?
This is actually a very complex subject, and really belongs in the branch of the science of philosophy called epistemology, which is the study of how we can know what is true. For those who want something more than the flying look you will find here, I refer you to my Knowledge: Its Acquisition and Expression.
For our purposes, we can oversimplify without actually falsifying, if we point out the following:
We are aware that our experiences fall into two general categories: (1) experience-of and (2) spontaneous consciousness.
These would roughly correspond to perception and imagining, if it weren't for the fact that reasoning to the (unperceived) cause of something perceived belongs on the category "experience-of [something real]," while reasonings about what the unicorn knocking at your door wants belong in the category of "spontaneous consciousness."
Not to make a long story of this, when you "experience" a unicorn, you are aware that there's nothing beyond the experience itself; there's no such thing as a unicorn. You "made it up," as you would say; meaning, basically, that you took information already stored in your mind and put it together in such a way that you had this act of consciousness which would be like looking at a unicorn if there were such a thing to look at.
And this is why this is "spontaneous consciousness." You don't need anything more than your mind itself (with what is stored in it) to explain imagining; and that is why imaginary experiences are under your control. Imagine the unicorn. Imagine it to be blue. Imagine it to shrink to the size of a mouse.
Note that that "picture" of the unicorn isn't a little unicorn "in your head." It IS the act of imagining; you are not looking AT anything at all when you imagine a unicorn; you are simply aware of the FORM OF YOUR OWN CONSCIOUSNESS, because you know that there is nothing EXCEPT your consciousness here.
This is important, though not terribly so for our purposes. The reason is that when you actually look at a horse, you aren't "really looking at" your little internal "picture" of a horse. What it is in your "looking" that corresponds to the "unicorn" is the form under which you see the horse. But what you are looking at is the horse itself, not your perception of it.
It is impossible for experiences-of to need nothing more than our minds, because then we would not be able to distinguish the two different categories of experience.
That is, identical causes have identical effects; if all that explained our experiences-of were nothing but what explained our spontaneous experiences, then they would not be able to be distinguishable. But they are. There might be times when we confuse one with the other (as in hallucinations), but we couldn't have two different categories at all if both were caused by the same cause.
Therefore, experiences-of are EFFECTS of some cause IN ADDITION TO our minds and the information stored there.
DEFINITION: The OBJECT of consciousness is the causer whose effect is an experience-of.
The object is the causer, not the cause itself. What it is about the object by which it affects our minds is the cause.
NOTE: spontaneous experiences have no objects.
So the experience "of" a unicorn is not really an experience "of" anything (except in that secondary sense, of itself); and you will notice that we say, "there is no unicorn."
DEFINITION: BEING is the object of consciousness.
But since being is "what exists," then
DEFINITION: EXISTENCE is the cause explaining the fact that we are conscious-of rather than imagining.
That is, when we are conscious of an object, we know that the object exists. It is making us conscious of it, because without it, our consciousness would be a contradiction (i.e. it would be in fact the same as spontaneous consciousness, but it is recognized as different).
And in fact, we recognize this; because we see that we have no control over the objects of consciousness. You can imagine the unicorn as blue; but you can only see this page as white with black letters on it; it forces your consciousness to be the particular perception that you are having.
Now then, since we recognize that in spontaneous consciousness, we are actively creating the particular act of consciousness (and doing it "by ourselves,"), we can take the next step, and say that we recognize consciousness-of by the fact that we are passive; that is, we are acting, but our action is really a reacting to something else.
And since the only thing you can react to is an act, then
Existence is ACTIVITY. This is being as cause of our reaction to it.
Being, therefore, is WHATEVER IS ACTIVE. Whatever has activity as an "attribute" of it is a being. This is the causer, the object.
Being known is the ACTION of existence ON SOME MIND (i.e. on something that can be conscious). This is the causality of existence on the mind. Note that "being known" is stated pasively, as if knowing did something "to" existence; but actually, the causality is the other way round.
Knowing is the mind's BEING-AFFECTED by existence. Knowing is active on our part; but the particular activity is our response to the action of the object on us; hence, it is being-affected, not causality. We don't make the object known; it makes us know it. Of course, if we're not there, no knowing takes place; but knowing is not something we do to something, but the other way round.
Notice that reasoning about unicorns or other imaginary objects is not knowing, strictly speaking--because there is nothing to know about. It's just playing games with your mind and you consciousness.
Existence is NOT AFFECTED by the mere fact that we know it. Remember, the cause is not affected by the fact that it is having an effect.
This is extremely important. What it means is that
BEING is IN ITSELF INDEPENDENT of our knowledge of it. We do not alter the existence of a being by knowing it; it alters our existence (and makes us knowers-of-it rather than ignorant).
"Well, yes," you might say; "but aren't there cases where you have to do something to an object in order to know it? For instance, you have to burn hydrogen to know its spectrum; you have to hit electrons with light to know where they are--which moves them from where they are--and so on. Doesn't this imply that at least in some cases, our knowing being alters it?"
That is true; but here our distinction earlier comes in. We sometimes must alter the being in order to know it; but once altered, the activity it produces (its existence) is independent of our knowledge of it. For instance, when you burn hydrogen, the light it gives off is the existence you know; and this light is independent of the way you see it. If you have jaundice and see it as green, it is still blue of a certain wave length. Or if you bounce a photon of an electron, the photon, rebounding is the existence which you see; and you don't act on the photon by seeing it.
So the causer can be altered; but the causer is not the cause. The activity of being which acts on us is just what it is. Of course, the way we see it depends not only on the activity, but upon ourselves as affected objects; but this doesn't make the act depend on us.
The reason I am belaboring this point is that scientists have lately been bamboozled by certain conundrums in physics to assert that "knowing is doing something to what is known." But this mistakes the cause (existence) for the causer (being), and in fact makes (if you think it through) all objective knowledge impossible, and everything to be "really" just fancy forms of imagining. But this is absurd.
4.1.2. Form and limitation
At the moment, I don't want to concentrate on the object itself (or on the being), which seems to be (and is) a complex of many activities, somehow unified.
For this chapter, we will confine our attention to one single activity, and what can be said of it as energy.
In the next chapter we will consider the implications of systems of energy, and those tightly-knit systems called "things," "bodies," or sometimes "substances." They have their own special problems and effects.
What we know so far, then, about a single example of "energy" is that it is activity or existence. We would generally say that it is the existence or the activity of something (some being, or some body); but there seem to be cases of "free energy" (such as cosmic radiation) that are referred to as if they weren't properties of something else--and so it might be the case that there is such a thing as a single form of energy that "exists by itself," so to speak.
Note that, what is true of energy as energy will be true of it whether it is the energy "of" some body or whether it is something that exists in its own right. So we don't need to worry whether there actually exists "really free" energy or not; we are only interested in what can be said of any energy, "free" or "bound," simply because it is energy.
I mentioned that there are various forms of energy: heat, electricity, mass (yes, it is a form of energy), kinetic energy, and so on. Let us look at the implications of the fact that energy is always some form of energy.
Since energy is existence, or that by which we know being, we get at it through our knowledge (its effect on us). Hence, there is something about our knowledge of the existence we call "energy" that makes us say that there are different forms of energy. What is that?
We have different KINDS of experience-of, allowing us to classify many instances under one category, such as "seeings," "hearings," etc.
That is, there are many examples of hearing, but they are all the same in some respect (as hearing), though a trumpet sounds different from a flute. But trumpet-sounds and flute-sounds as heard belong in a different class altogether from green color and blue color.
Now can this classification into different types or kinds of experience-of simply be due to ourselves and not to a difference in the objects we perceive? After all, any experience-of is a reaction of our mind to some activity; and so the experience is the effect of both the mind and the object. So it is at least in principle possible that the activity might be the same and the difference due simply to the fact that we are different as "receivers."
It might seem that this is true, because we hear sounds with our ears, and see colors with our eyes; we have two different "receiving instruments," and this might explain the difference in the experiences.
But it cannot totally explain the difference, or we would be able to see the sound of a trumpet if we paid attention to it (if the sound in itself was just the same as a color), or hear the color blue. But we can't do this. Therefore, there must be something about any sound that makes it capable of being heard by ears and not seen, and something that all colors have in common that makes them able to be seen but not heard.
DEFINITION: The FORM OF ACTIVITY [FORM OF EXISTENCE] is whatever it is about the activity [existence] that allows it to be known as a KIND of activity or existence.
It is the cause in the activity by which it is "classifiable" by kind.
Now what can be said about this?
The form of activity is NOT AN ACTIVITY.
If it were an activity, it would be an activity different from the one we were considering, and would have to be perceived as a different existence. Hence, it is not itself an activity, but something about an activity.
This is confirmed by the fact that if the form of activity were an activity, then it would be something added to the activity, and then the activity in question would be greater than "activity-itself" (because it would be just "activity" plus something). But this is absurd. We experience a given form of activity as less than what it is to be active.
That is, color is only one form or kind of activity; it is not all there is to "being active," let alone "more than what it is to being active." So the form can't itself be an existence or an activity, because it somehow "makes" the existence less than what it otherwise would be (i.e. what it would be if it were not some form of existence).
The form of activity is not SIMPLY NOTHING.
We have to be careful here. If the form isn't an activity, then it is not existence, and can't be known. And it can't be, really; all that can be known is the activity that has this form. That is, when you know color, you don't know the form "color," you know the act which is green. The form can't act on you without being an act.
But the form can't act on the activity, really, either, "making" it only color. If it could, then it would be an additional act, and the color would be greater than activity, when in fact it is less.
But then if the form can't act on us and can't act on the existence which acts on us, then it isn't anything at all, really.
But this would make the form itself imaginary or subjective; and that isn't true either, because we said that there has to be something about the activity that allows for its being known as a kind of activity.
The form is a LIMITATION of activity; it is THE FACT THAT the activity IS NOTHING BEYOND the kind of activity in question.
So the solution is not that the form is something that somehow "does" something to the activity, limiting it, but is simply a fact about the activity itself: the fact that it is only this kind of activity.
Color, then, doesn't have something (a kind of "real nothing") that makes it just color; it is simply activity that is no more than just color-activity; it is the activity itself that is the color, not the activity + something.
And this is why it is the "form of activity." There is and could be no such thing as a form that wasn't a form of activity, because the form is a description of the activity, not something in its own right. It is to activity something like what temperature is to heat. The temperature of the heat isn't something in addition to or "attached to" the heat; it is simply the description that the heat is no more than this intensity of heat. So the "heatness" of the heat (its form) is simply a discription of the fact that the heat is nothing other than heat-activity. You can't have a temperature that isn't a temperature-of heat, and you can't have a "heat" that isn't a heat-of activity.
Any form of activity, as limited, FALLS SHORT of what it is to be activity, and so "leaves out" some of itself as activity.
That is, the form of activity is nothing but activity; and as such it is the same as any other activity. What makes it different from any other is not something it has, but the fact that it lacks something of what it means to be active: something different from what the other form of activity lacks.
But the only intelligibility or reality it has is that of activity itself; and so it lacks something of what makes it intelligible as itself.
If this sounds confusing, it is because I am describing an effect. Something which is limited leaves something of what it is out of what it is--and this doesn't make sense.
We are not going to pursue this particular effect, except to note that it is an effect, and (since all forms of activity are limited and thus identical as effects in this respect), to point out the fact that, whatever the cause of this effect, it can't be a form of activity or any limited activity (because then it would be the cause of itself, which is absurd--since it would be a limited activity which is and is not an effect).
The fact that activities are limited means that there must be an absolutely unlimited activity as their cause. This unlimited activity is called GOD.
For those interested in investigating this line of reasoning (which can become very complicated, in order to make it rigorous), I refer you to my The Finite and the Infinite.
For those who want a model, consider the surface of, say, a wooden ball. The wood in this analogy would correspond to the activity, and the surface to the form of activity. What is the surface? It is what "makes" the wood a ball and not a cube; but it is nothing but the wood. That is, if you carve off a quarter inch from the wood, you have put a new surface onto the ball that wasn't there before (there was no "surface" hidden under the surface), and so the surface is nothing in addition to the wood; it is simply where the wood stops "wooding." But the wood does stop. The surface is the fact that the wood extends no farther.
So what is the problem? If the surface is identical with the wood, really, then wherever there is wood, there would really be surface. But this is not true; there is no surface an inch below the surface. So the surface is not the wood.
So the surface is either a real nothing or a real lack of woodness in the wood--either of which doesn't make sense by itself. The surface is simply a limitation; but "simply" a limitation is not so simple; the word expresses something that gets more mysterious the more you try to figure it out.
Let us, however, be content with the fact that any form of energy, as a form of activity, is a limited case of activity, and the fact that the forms are different simply means that the activities "lack" activity differently; so heat lacks whatever sound has that makes it active, and sound lacks whatever light has that makes it active, and so on.
But to get to what energy involves, we have to take another step. All energy is not only a form of energy, but measurable. What does this mean?
It is connected with the fact that there are many different sounds and many different colors and many different cases of heat. Let us consider heat, because it is clearest to describe.
Heat of fifty degrees does not differ from heat of seventy degrees as heat. Both of them are "equally" heat, in the sense that you can't describe either of them as anything else but heat. Then how do they differ? Obviously, the heat of fifty degrees is not as much heat as the heat of seventy degrees (or perhaps is not as intense, if you prefer).
DEFINITION: QUANTITY is the limitation of a FORM of activity to being ONLY A CERTAIN AMOUNT of the form of activity.
This is another limitation, and so as such is nothing in itself; it is the fact that heat of fifty degrees falls short as heat of heat of sixty or seventy degrees. Clearly, the temperature (the quantity of the heat) is not, as I mentioned earlier something added to the heat.
To give a model, the quantity is like the edge of a surface that has edges--such as a cube. Unlike a ball, whose surface is, from a certain point of view, continuous, if you go along the surface of a cube, you come to an edge where, to remain on the surface, you have to change direction. Note that at the edge, there is nothing there but the wood, really. But the edge is not just the wood; it is where the wood stops; but it is not just the stopping of the wood, either; it is the stopping of the surface (the stopping) of the wood. It is a limitation-of-a-limitation of the wood; a kind of nothingness of a nothingness of something.
It is, of course, limitation at this level that allows us to measure the form of activity. Clearly, if the form of activity were unlimited as a form, you couldn't measure it, because we compare forms with each other as different kinds of activities, not as different degrees. That is, it doesn't make sense to ask how much more activity heat is than sound--supposing that you aren't talking of a certain degree of heat and a certain degree of sound. Heat as such is just different from sound, but not less than it or more than it. In order to measure, you have to have something in common between the two things measured, so that you can set up your scale of numbers; and this "common element" is the form of activity in question. Heats can be compared with heat and sounds with sounds.
It is not this simple, of course. Since forms of activity can be transformed into each other, indirectly we can compare between acts. The formula for the mechanical equivalent of heat, for instance, says that when mechanical energy is transformed into heat, a certain quantity of the one becomes a definite quantity of the other. Or Einstein's famous equation, E = mc2 says that when mass (a form of energy) is converted into light (another form), then the number 1 of 1 gram of mass becomes the quantity 3,000,000,000 of units of light-energy. But unless you can convert one form of energy into another, there is no way to measure one "against" the other. Note that in the transformation process, it is assumed that somehow the quantity "remains constant" even though the forms have been altered. If the quantity is a limitation (a nothingness) of the form, which in turn is just a limitation (a nothingness) of the activity, this "remaining constant" is really wierd; and we will have to treat it later.
In any case, for our present purposes, it seems reasonable to say that
Quantity (the fact that forms are limited) is what allows for the possibility of measuring things. It is the "aspect" of an activity which is its "measurability."
Since we have now described what all the things that science talks about under the name of "energy" have in common, we are in a position to give a philosophical definition of energy.
DEFINITION: ENERGY is any activity that is limited BOTH in form and in quantity.
Note several things here.
First, energy is not the quantity itself; it is the activity. Energy has forms; quantity doesn't, because it's the quantity of a definite form of activity. Energy is measurable; quantity is the internal cause in an act of its measurability. In one sense, the quantity is measured; but in another sense, the energy is measured. That is, when you measure some energy, you are measuring a causer (the energy) which has characteristics (such as heat) other than the quantity (the cause) you are measuring. So in this respect, the energy can't be the quantity either.
Secondly, activity is called "energy" only if it is quantified (i.e. limited in form and quantity). In order to be limited quantitatively, of course, the energy has to be limited in form, because the quantity is a limitation of the form of the activity, not the direct limitation of the activity itself.
Thirdly, energy is an analogous term. All forms of energy are somehow the same (in that they are activity, and that they are quantified); but they are also somehow different. But, though we can give the "differences" (the forms) separate names, we don't know exactly what they are. This is especially true since the forms are simply the fact that the energy lacks something of itself, and not something the energy really has.
Hence, each form of energy is the same as all others in some real (but not observable) way and different from all others in some real (but not observable) way. But this, as we said two chapters ago, is what you mean by "analogous" rather than "similar."
Fourthly, not all activities are energy. We saw that, since any form of activity needs as its cause an infinite activity, then clearly there is at least one activity that is not limited at all (i.e. is simply the act that is the same as "what it is to be active," and isn't any kind of activity or any degree or amount of activity). But this act can't be called "energy," because it has no quantity.
So the scientific dogma that "if it exists, it is energy" is proved false right at the start. If everything were energy, nothing would exist, because energy in itself is a contradiction (as limited) and there would be nothing that could be its cause.
It might well be that there are forms of activity that are not quantified also--and it turns out that consciousness is one of these. We will not try to establish this here; but there is certainly nothing in principle impossible in something's being a form of activity but not internally limited and so being an unmeasurable form of activity. If you want the evidence for consciousness as not quantified, see my Living Bodies.
DEFINITION: Activity that is NOT limited quantitatively is called SPIRITUAL activity.
So energy is opposed to spiritual activity. Usually, "spirit" is opposed to "matter"; and we will see why energy is "material" later. For the present, let us simply be aware of the distinction, so that we can realize where we stand. It does explain, as you can see, why scientists who subscribe to the dogma that all that exists is energy are "materialists."
Note, by the way, that an activity or form of activity that is not limited is not one that "has an infinite quantity." An "infinite quantity" is a contradiction in terms, because as a quantity it is a limit; and so an infinite quantity would be an "unlimited limit."
This is why mathematicians say that a certain value "becomes infinite" rather than "approaches infinity." The number "infinity" ( ) does not really exist as a number; it is a symbol of something's becoming arbitrarily large.
So when we speak of a spiritual act as "infinite" with respect to quantity, we do not mean that it has an enormous quantity; we simply mean that it cannot be described in terms of quantity, the way "colorless" means that glass, say, cannot be described in terms of color. "How much is it?" is a meaningless question of a spiritual act, just as "What color is it?" is a meaningless question of what is colorless.
Fifthly, if an act is to be called "energy", it will always in principle be able to have a definite number placed on it. The quantity implies a definite limitation, which makes it in principle measurable; and measurement will result in a definite number, indicating that the act is no more than this.
The reason I say that it is in principle able to have a number placed on it is that it might not in practice be possible to do it for either of two reasons: (a) no instrument which can react to this energy is known (as would be the case if whatever causes ESP [extrasensory perception, if there is such a thing] is a form of energy); or (b) it might not be possible to get an instrument in a position to measure the energy without disrupting the object in such a way that measurement is impossible (as when you try to measure the "binding energy" of a body; to get an instrument in there would mean it would have to become part of the body, which would wreck the body). But in either of these cases, if an instrument could be found or if it could be introduced, then it would register a definite number.
In other words, quantity is the cause of the definite number you get when you measure, but not the causality, which needs the effect in order to be what it is.
4.2.1. Energy in physics
Now what is the relation between "energy" as we have defined it and "energy" as science uses the term. Let us take physics as the science to look at. In first-year physics, you learn that "energy is the capacity for doing work"; but as you get along in the subject, you find that this is an oversimplification, and there are all kinds of mathematical definitions of energy.
This would not be at all surprising, if, as we said, energy is an analogous term, and means something different but (in some unknown way) similar each time you use it. So the different mathematical definitions of energy confirm that our philosophical description of it is on the right track. That is, you could have predicted from our philosophical description that there wouldn't be just one cut-and-dried definition in physics--and there isn't, really. Energy in physics is got at indirectly, through work.
This again sounds reasonable, based on our definition. If energy is activity, then (as we saw) it is known as the cause of some effect. In our case, we saw it as the cause of our consciousness of individual objects of a given type (they being the causer). Apparently, physics considers energy (the "capacity") as the cause of the effect called "work."
Well, what is "work" as physics uses the term? It is defined as "force exerted through a distance," and mathematically is the "scalar product" of force and distance. (Don't worry about this; it simply means a kind of multiplication which results in a number without a direction associated with it.)
It sounds as if we are getting wheels within wheels; we need to define "force" before we can define "work." But let us look at the matter qualitatively, using moving a block across a table as our example.
The block tends to remain at rest and to resist a change in its state. The fact that it got to be moved a foot across the table means that something had to be done to it to get it to move. Not only something had to be done, but if it is to be moved two feet, you would have to do more to get it moved the extra foot.
It can now be seen what is going on. You can directly measure the length moved, and you can measure the degree of resistance to the movement, and so on. So you can measure the amount of the effect. It is then argued that the cause will then have the amount necessary to produce this effect.
DEFINITION: WORK is energy AS the effect of some other energy.
It turns out that the work itself is, in a sense, energy; but it is used to find the energy of whatever did the work. The work is something that is for some reason measurable in itself, and it allows you to find the quantity of the energy that did the work.
And here is the difference between the approach of physics and that of philosophy. Philosophy notes the fact that any form of energy has (some) quantity, but it doesn't care what the quantity happens to be in a given case. Physics wants to know what the quantity is, and hence must devise ways of finding it. When the energy is the cause of something, then its quantity will not be directly observable (because you observe the effect and argue to the cause); and hence you have to argue to it based on the quantity of its effect.
And that is why energy is related to work.
Having said this, we then find that there are all kinds of analogous descriptions of work. The heating of the filament in your light bulb (i.e. going from, seventy degrees to several thousand degrees) is a kind of work, though no "motion through a distance" has occurred. But obviously, a measurable change has; and so the total can be arrived at. And this allows you to measure the electrical energy which caused it.
DEFINITION 2: WORK is any complete measurable change.
That is, it has to be "complete" in the sense that you have to be able to give it (even if arbitrarily) a beginning-point and an ending-point. Otherwise, you can't put a definite number on it. Thus, you could consider how much energy is expended making the hand of your watch make a full revolution. True, the watch's motion didn't start at the time you started measuring it, but for your purposes it did; and it ended when the hand came back to the same position. Then, you can measure the tendency it has to stay still, and combine this with the total "length" of the process where it didn't stay still, and come up with a definite number; this will be the work done on it; and it will correspond with the amount of the energy needed to effect this change.
So the two definitions complement each other. Any complete change is a case of "energy-as-effect"; and so any complete change will reveal the amount of the energy which is its cause.
And that is why, in physics, energy is "the capacity for doing work": it is the cause whose effect is some measurable change.
So far, then, we have the effect (work) and the cause (energy). Are there other parts of the cause-effect relation hidden in the concepts of physics?
There are, as it turns out. If we look at Newton's third law of motion (whose integral results in work on one side of the equation and energy on the other), we will see something interesting:
F = ma
This is the equation which "defines" force. It says, mathematically, that the force is equal to the product of the mass (the tendency to resist a change of motion) and the acceleration (the tendency to change one's motion).
So on the right-hand side of the equation, you have two tendencies: tendencies in the object which is about to move. When the movement actually has occurred, of course, what you get is the work done on it. But here, all you have is the tendency to have work done.
In other words, the right-hand side of the equation expresses the being-affected of the object by the energy which is causing it to move. It is expressed, mathematically, as an instantaneous something, which means it is a tendency rather than an actual movement. And what that means is that it is the affected object insofar as it is related to the cause--or it is the "being-affected," as I said.
From this it follows that
DEFINITION: FORCE is the CAUSALITY energy exerts on some affected object.
That is, the left-hand side of the equation is the relation looked at the other way; it is what the causer (the object containing the energy) is tending to do to the resisting object. The right-hand side is what is being done to the affected object by the causer; the left-hand side is what the causer is doing to it. It is the same relation, and so it is not sruprising that there is an equation here.
DEFINITION 2: FORCE is CAUSALITY AS QUANTIFIED.
Once again, what physics is interested in is what the quantity in a given case actually is. And once again, the quantity of some cause cannot be directly got at, nor can the quantity of the causality it exerts. But it can be got at through the fact that it is tending to cause a change--and through the degree of resistance to this change on the part of the affected object.
If we set up the force equation this way:
F = m (vdv/dx)
we can see something interesting. That (vdv/dx) is a mathematical "derivative," which is the instantaneous tendency of the velocity (the motion) to change with respect to the distance over which it changes. Physicists state the equation as the tendency of the velocity to change with time, which masks what is really going on; a little mathematical manipulation will convince them that my equation is the mathematical equivalent of theirs.
If you "separate the variables", then you get this equation:
F dx = mv dv
And if you now integrate, you get
F x = mv2/2
where the left-hand side is the work, and the right-hand side is the kinetic energy.
For those who hate mathematics, what this all boils down to is that the force equation is simply the work-energy equation reduced down to an instantaneous tendency; and when you manipulate it according to the rules of the calculus, you get the work done and the energy that did it. So the work is the effect, the energy the cause, the force the causality and the mass-acceleration the being-affected.
Note that it would have been predictable from our theory of science that, if science is the search for causes from their effects, the key concepts of physics would be in terms of the cause-effect relation. And this seems indeed to be the case.
4.3. Qualtitative mathematics
One of the peculiar things about physics (and chemistry too) is that the mathematics doesn't deal just with numbers, but with what are called "units." That is, the two equations:
F = ma
E = IR
are mathematically identical, since which letters you use to represent what you are talking about make no difference, and neither do upper or lower case. But in physics, they are very different, though they are analogous to each other. The first is Newton's third law and says, as we saw, that the force is equal to the product of the mass and the acceleration. The second is Ohm's law, which says that the voltage-drop is equal to the product of the current (I) and the resistance (R). Resistance is sort of analogous to mass, and current something like acceleration; but even mathematically, to convert the Ohm's law equation into a strict force-equation, you have to take the reciprocal of one of the terms. But let us let that ride.
The point of interest here can be illustrated by looking at an example of Newton's law; say, this one:
1 dyne = 1 gm x 1 cm/sec2
What are those funny words? The "units." Physics teachers get very angry with you if you leave off the units. Why?
Well, if you want to convert it into the form I had before, with velocities and distances, it will look like this:
1 dyne = 1 gm x 1 cm/sec x 1 cm/sec x / 1 cm
dv has the same "units" as v (cm/sec), and dx the same units as x (cm). To show what is going on, notice that there are on the top of the right side two cm's multiplied together; and on the bottom two sec's and a cm multiplied together. The two sec's become sec2 when multiplied, and the cm divides the cm2 on top and leaves only one cm. So the result is the equation above. But what did I do when I multiplied sec's by sec's and divided cm's by cm's? I was doing mathematics with the forms, not the quantities. These "units" aren't numbers; they represent the forms of the energies in question.
What does this mean?
Quantities of one form of energy are only ANALOGOUS to quantities of another. Hence, one must keep track of what FORM the quantity is the quantity of.
As can be seen from the equation above, 2 dynes could be equal to 2 grams x 1 cm/sec2 of acceleration; but what 2 dynes does not equal is 2 of everything on the right side. The units of force vary differently from the units of acceleration or the units of mass, so that 2 of one is not the equivalent of 2 of the other.
What the physical equation expresses is the relation among the quantities of the various forms of energy involved. If, for instance we take the work-kinetic energy equation and "put in the units," we find this:
F x = m v2/2
1 dyne x cm = 1 gm x cm2/2 sec2
The "2" in the equations is a "pure number," not expressing the quantity of some form of energy.
So "work" is ixpressed in dyne-cm, while energy is expressed in gm cm2/sec2. The quantities of work are analogous to the quantities of energy, and the relation is what the equation expresses.
The reason you can do a kind of "mathematics" with the forms themselves (dividing sec by sec without numbers) is that the forms are limitations, and as such are analogous to quantity.
But since the forms aren't really quantities, then the mathematical manipulation of them is pretty primitive and not the same as ordinary mathematics; they are similar somehow (i.e. as limitations) to quantities, but the precise way they are similar is not directly observable; hence, the way they are treated is different from the way the numbers "attached" to them (the actual quantities) can be treated.
In any case, this is an explanation of why, when physics or chemistry uses mathematics, it doesn't do "pure" mathematics (which deals with quantities as such or limitations as such and ignores what is being limited by them), but keeps track of the forms as it manipulates the quantities. If you don't "put down the units" as the science teachers say, then you're doing mathematics, not physics or chemistry or biology, or even economics or sociology.
Energy, once you have got round the strange implications of being limited, seems perfectly straightforward: you have an act which has a form and a quantity. But the real world is rarely as neat as our little categories would like it to be, and I want now to consider a peculiar type of energy: the field.
DEFINITION: a FIELD is a form of energy which has an infinity of quantities all at once.
In a sense, of course, a field has only one quantity of energy (the total energy of the field), and in this respect one field will differ from another of the same type. Thus, for example, the sun's gravitations field is much stronger than the earth's, which is much stronger than the moon's.
But what makes a field a field rather than some other type of energy is that, when it acts on something, the force it exerts on the same type of object differs, depending, as we would ordinarily put it, on the location of the object in the field: how "far away" it is from the object which has the field. And if the force differs, so does the work it does, in the same way; and if the work does, then the energy in the field has different quantities, depending on "where you are" in the field.
Why do I put "far away" and "where you are" in quotation marks? Because these terms are our way of describing the field in terms of its effects, really; and, as I am going to try to show, location, distance, and position are not "somethings" that exist in their own right (and which you can then use for describing the field). The truth is the other way round.
That is, what exists is the field, with its set of quantities. This is the reality, and the only reality involved in spatial relations. The "locations," "distances," "positions," and (the sum of all of these) "space" are descriptions of this same set of quantities in terms of its work or its force (i.e. in terms of its effects on other objects).
To put this another way, there is no "reality" called "space" which is independent of energy and "in which" you can measure distances and so on. We know this both from this philosophical theory and from physics.
From this theory: How could there be a measurable reality which was not energy? Energy is the definition of measurable existence. How could a "measurable non-energy" be known? It would have to act on us somehow for us to know it, in which case, it wouldn't be just "sitting there"; it would be doing something-or it would be energy.
From physics: Einstein's theories of relativity showed that, physically speaking, an "absolutes position in space" is meaningless. You can only talk of position or location (or movement-change of positions-) in reference to some object-that is, at a distance (or change of distance) from some object or set of objects. And, as Einstein showed, the very position is altered by the makeup (the mass) of the object from which you are defining the position, so that it "warps" the space-time around it. His is talking about the gravitational field of the object as what it is that defines the positions and movements in that field, which is just what our philosophical theory demands if you are going to talk about space as a reality.
So we will take it that what is "primitive" isn't space, but the field, with its infinity of quantities; and space, distance, and position are derived from the field.
Now then, the field itself is an abstraction, got at by comparing various objects that have the same type of field and noting how they affect various other objects-and then paying attention to what all the fields of this type have in common.
That is, if one object has a field with twice as much total energy as another, then it will act twice as strongly on a given object as the other one, at "corresponding points" in the field. What this amounts to is that its set of numbers will be just double the other field's set of numbers all along the whole string; and so you can ignore this variation and get at the variation in intensity of the field as such.
It is a little hard to talk about this without using the way we ordinarily look at things to illustrate it. Let me show what I mean, and then make the correction. Let us say we have two objects with electrical fields around them, with A's field being twice as strong as B's.
If we take a little object that can be affected by an electrical field, and put it a foot away from A, we find that the force exerted on it, say, is 200 dynes. If we put it a foot away from B, the force exerted is 100 dynes. If we put it two feet from A, the force exerted drops to 50 dynes; if we put it two feet from B, the force drops to 25 dynes. If we put it three feet from A, the force is now 22.2 dynes; at the same distance from B, the force is 12.5 dynes. At four feet, A's force is 12.5 dynes, and B's is 6.25 dynes. Etc.
Each time, the force exerted by A is twice that exerted by B; but in each field moving the object twice as far results in a reduction to 1/4 as strong; 3 times as far, 1/9 as strong; 4 times as far, 1/16 as strong; n times as far, 1/n2 as strong.
It is this latter set of numbers that is the field as such, because it will be true of any field, no matter what its total energy.
But you will notice that we arrived at the set of numbers by measuring "distance away" with a ruler, as if there were some kind of "space" in which we could figure out the distance first and then get the force based on it.
This is what I contend is backwards. What is real is the set of numbers that varies in a definite way; the "ruler-distance" is what varies in a peculiar fashion with respect to it, not really the other way round.
I am aware that what I am saying is apt to be a bit mind-boggling; but perhaps it will become clearer as we proceed. If you keep in mind that what is real is energy, not something that just "sits there" (space-as-we-imagine-it); and if you are aware that the approach I am taking can make sense out of some things that physicists simply can't make head or tail out of now (because they take the common-sense notion of distance and so forth), then it might be easier to plow through all this.
To take something fairly easy first:
DEFINITION: The POTENTIAL of a field is ONE of its ACTUAL quantities.
That is, here we are talking about the concrete field of some given object (so we are not ignoring the variation due to the different strengths of the sources). In physics, the "potential" of this field is defined as "the work done on a unit object if it is taken from infinity to the point in question."
"Work" should give us the clue that we are trying to define "energy" here; and so the "potential" is the "energy in the field at this point." It is got at through the fiction of "moving" this "unit object" (something that can be affected by the field in question) from infinitely far away to this point--an act, needless to say, which is never actually done.
What the "potential" abstracts from is the differences to which this energy would affect different affected objects. Thus, the potential of the sun's field at the point where the earth is now is the same whether the earth is in it or Jupiter or Mars or some other object. But if you were to replace the sun with some star twice as massive, the potential would be double at this point. So the potential takes into account the variations of the energy as cause and the field variation, but not the variation in actual work due to the varying nature of the affected objects.
So it is the energy "in the field at that point," which, from our peculiar way of looking at it, simply means one of the actual quantities that this field has.
The next easiest concept needs to rely on the abstraction from the different actual energies due to the different total strengths of the fields and consider simply the field variation of quantities (the "inverse-square variation") itself.
So we take an imaginary object with a "field of unit strength" and have it act on an imaginary object of "unit ability to be affected." What do we get?
DEFINITION: ABSTRACT REAL DISTANCE is the CAUSALITY of a "unit" field on a "unit object." Or, alternatively, DISTANCE is the FORCE of a field AS SUCH.
Distance is obviously a relation ("from" something "to" something else); and if it is to be something that is not imaginary, it has to be a relation established by activity; and if it is to be real and measurable, it has to be a relation established by energy, or in other words, a force.
But we have the field and for every quantity of "distance-as-we-know-it" there is one and only one quantity of the force of the field as such. Hence, the reality which causes our reaction to distance (i.e. "distance as it appears to us") must be this force the field exerts on things.
Now this is abstract real distance, because it ignores the actual effect the actual source (with its non-unit strength) is exerting on the actual object (with its non-unit ability to be affected). Obviously, this real causality will be different for different objects in the same abstract position in a field. But it can be useful for physicists to consider distance as it actually exists, and so let us define it:
DEFINITION: CONCRETE REAL DISTANCE is the actual force some object's field is exerting on some real object.
Thus, the concrete real distance from the sun to the earth is how much the sun's gravitational field is affecting the earth at this instant.
Note that EACH FIELD of a given object will have its own CONCRETE real distance to a given other object; and they will not necessarily have the same quantity. But the ABSTRACT real distance will be the same for all fields of the same type.
That is, the sun's magnetic field acts on the earth too; and so its force establishes a magnetic distance of the earth from the sun, while the distance I referred to above was the gravitational distance from the sun to the earth; the two would not necessarily be the same. If you take the abstract distance, however, then (since both are "inverse-square" fields), then they would be the same.
18.104.22.168. Near and far
At this point, some of the peculiarities of this approach emerge. The field's force diminishes in the direction of "far" and increases in the direction of "near" (and, of course, in accordance with the square of the "distance as it appears to us"--what we measure with rulers). Hence, the numbers of distance regarded as we have above will look funny.
Real distance is GREATER the NEARER one comes to the source of the field; it is LESS the FARTHER one is away from it.
So, for instance, when the real distance increases four times, the object is perceived as twice as close; if the real distance decreases to 1/4 as much, the object is perceived as having moved twice as far away.
The point here is that the "twice as close" and "twice as far" are not realities as such, because there is no real activity or force corresponding to them; what they correspond to in the world of activity is the forces and their variation.
Weird? No stranger than Einstein's "warping of space-time."
If you got through that section, this one will be easy. Obviously, distance and position are correlative terms; we know the position of something by the distance it is from something else. And causality and being-affected are the two correlative ways of looking at the cause-effect relation; and so it follows that
DEFINITION: The ABSTRACT REAL POSITION of an object is its BEING-AFFECTED by another's field as such. That is, it is The degree to which it would be being-affected if it were a unit object in a unit field.
Again, we are making an abstraction from the actual (total) strength of the field and the actual ability of the object to be affected, and simply talking about the relation based on the field as a field.
But once again, it can be useful to know the what the relation among the concrete objects is, and so we have the other definition of position:
DEFINITION: The CONCRETE REAL POSITION of one object with respect to another is its ACTUAL BEING-AFFECTED by the field of the other.
The concrete real distance and the concrete real position are what actually exist; the abstractions are just that: abstractions; and "distance as we perceive it" and "position as we perceive it" are not just abstractions, they are abstractions based on certain effects of these field-relations.
22.214.171.124. Non-reciprocal positions
Now we get into a problem that this odd notion of position can solve. If position as a reality is the being-affected by some field, it is not logically necessary that if A is in position with respect to B, B must be in position with respect to A.
What do I mean? In general, if one object is acting on another, it is not necessary for the affected object to be acting on the causer. I mentioned that if you hear the radio announcer tell you bad news, you are affected by him and his words, but he is in no way affected by the fact that you had the radio on and heard what he said.
And this is also true in the physical world. "For every action there is an equal and opposite reaction" is an oversimplification, at the very least. If you just take the radio you are listening to itself, then the transmitter is the causer of the events happening in it (the various electrical impulses going through the transistors), and the varying signal of photons coming out through the transmitter is the cause of this effect in the radio. But what happens in the radio makes no difference either to the transmitted signal or to the transmitter--neither the cause nor the causer is affected in any way by the radio's being on and being affected by the signal.
So in some cases, there is an equal and opposite reaction for an action, but in some others, the causality goes only one way.
But can this be true of position?
It seems it can. Photons (units of light) have no gravitational field, (i.e. have no "rest mass"--this is what that means), and so cannot act on other objects in a gravitational way; but, as Einstein showed, they can be affected by gravitational fields, to a definite degree.
Hence, photons can be in position, but other things cannot be in a position with respect to them.
This sounds very peculiar. All it means is that they can be acted on gravitationally, for instance; but they can't do anything gravitational to anything else, because they have no gravitational field to do it with. They are like radios, which can receive signals but not transmit them. If we have no problem in the one case, why should we have one in the other?
And it turns out that there are certain interference experiments in physics which make sense only if the photons are in position with respect to their surroundings but their surroundings are not in position with respect to the photons.
It isn't that simple, of course. Photons can act on certain things (like photocells); and, though this isn't a field-action, it still is an act of causality; and so you can say that, in a sense, it establishes "where" the photocell is with respect to the photon.
Now then, in the experiments I am talking about [for those interested, they are the Aharonov-Bohm experiment with photons, and an analogous experiment--with interesting sidelights--dealing with electrons by Mullinstedt], photons [or with Mullinstedt, electrons] were made to travel down a path, and then by mirrors [a positive charge], split into two separate paths, and then again by mirrors be brought together into a single beam again. The light was cut down so that it could be known that there was only one photon in the apparatus at once--which would mean that each photon would have to (a) split and go down both paths, or (b) go down only one.
The reconstituted beam at the end was focused on a target, which (not to bore you with the details) made it possible (by what is called "interference" to discover whether the beam was split in two (implying that each photon went down both paths) or not. If each photon went down only one path, even though the right-hand path was used half the time and the left-hand path the other half, the interference pattern would not occur.
Detectors were also placed on the paths during the "split," so that, when turned on, you could discover whether the photon was really in that path or in the other one; or whether half of it was in each path.
What happened turned the world of physics inside out.
A) If the photon-detectors on the paths were not turned on, the interference-pattern indicated that each photon split in two and went down both paths. B) If the detectors were turned on, only one was activated for each photon (randomly, either the left one or the right one), indicating that the whole photon went down only one path; and this ruined the interference pattern at the target--which was consistent with the photon's going down only one path.
So the result seemed to be that if you didn't detect what the photon was doing, it split in two and was in two places at the same time (as a wave can be as it spreads out from its source); but if you detected it it was in only one of the two places.
And since this "splitting" could take place again along one of the split paths, you could put your detectors in a place where the photon would "already have had to make up its mind" whether it was going to split or not (before it came to the second split) but this made no difference to the results. If you turned the detectors on, the whole photon went down only one path; if you didn't, it split, and half went down each path.
Physicists have thrown up their hands at this. Theoretically, you could keep the splitting going on so that the photon would reach the detector a year after it started its journey, and if you started out the experiment as a "split" experiment and six months later changed your mind and decided to make it a "detection" experiment, you would find that the photon was in only one path. But if you started the "split" experiment and changed your mind after six months, and then changed back again a couple months later (before the photon reached the detector), the photon would be in both paths! Where the photon is depends on what you decide; on how you decide to observe it.
And books, like In search of Schroedinger's Cat have been written, based on things like this, saying that "nothing is real," and "observation so alters the observed that what we observe depends on our choice of how to observe it."
But this is even more absurd than the experiment itself.
What is the solution? Simple. When the photon is detected, it acts on the detector. But a photon can only act on something using all its energy; hence, if it activates a detector at all, it will appear to be totally "where" the detector is.
But a photon can be acted on by the fields of its surroundings. And in the case where you focus it into a beam, you are making its surroundings act on it in a special way. Hence, insofar as it is acted on, the photon is in both paths; but insofar as it can act, it can act only on something in one of the two paths.
In other words, the photon is in position with respect to the surroundings of both paths; but objects in only one path can be in that funny kind of "position" with respect to the photon itself.
There's no contradiction here. The contradiction arises because we take the naive notion of position ("position-as-I-experience-it") as sacred. If position actually is as we experience it, then there is a real contradiction in this experiment; but my theory of position explains it. It also makes sense out of Einstein's theories of relativity.
I rest my case for my wierd notion of position.
--Except to say this: The Mullinstedt experiment with electrons also showed that objects not in the paths of the electron could have an effect on it. So the electron could be acted on by something that it was totally incapable of acting on, because it was outside the paths that it was "in." This is perfectly consistent with my view of position, and, as far as I know, makes absolutely no sense with any other notion.
There are a couple more topics before we leave off looking at just single forms of energy and get into systems and bodies. First of all, what happens when there are three or four objects with fields? What about a body that is in position with respect to two or three other objects?
DEFINITION: ANGLE is the COMBINED distance of from two objects to a third.
That is, it is the causality on the object in question by both of the others' fields acting together. It turns out that their effects on it don't just "add up" in a straightforward way, so that if the force due to the first is two units and the force due to the second is two units, the combined force is four units.
Not to get into the complications of this, but you can see that if the fields are attractive, and the object is between the two fields that are attracting it (so that they are on opposite sides of it) the two fields will cancel each other out (it will be attracted equally in opposite directions). If the two fields are on the same side, it will be attracted with the combined force of both; if the two fields are anywhere in between, then the combined force will vary according to the laws of "vector analysis," and the resultant force (the combined one) will--in the naive "as-we-experience-it" view--depend on the angle between the two fields.
All I have done here is what I did with respect to distance and position itself; turned the apparent reality around and defined the angle in terms of the actual effect of the energies in question on the object.
Now then, we can consider space itself. I tried hard earlier to show that that imaginary "receptacle" in which things exist is "space-as-we-imagine-it" and has to do more with the structure of our perceptive mechanism than it does with anything "out there."
There are actually two senses in which you can talk about real space: the "space around" an object (which, for instance, is what "gets warped" in Einstein's theory); or "the whole of space." The definitions are rather simple.
DEFINITION: The SPACE AROUND an object is the object's FIELD.
That is, the field of the object is what it is that allows you to define positions with respect to that object; so it is the set of all possible positions. But positions are "being-affecteds" by that field, degrees to which objects are acted on by it. But that means that the field itself is the reality which is capable of acting-on these possible objects, or is the set of all possible objects around the one that has the field.
So the reality of the space around an object is its field.
DEFINITION: SPACE as a whole is THE SUM OF ALL POSITIONS.
That is, real space is defined by all the objects and their position-relations based on the fields of all the other objects. If there were three objects in the universe, the whole of space would be that triangular interaction of the three objects; if four, the interactions of the four:
Since there are a finite number of bodies in the universe, then it follows that space is finite. That is, it has a finite extent. In fact, this is one of the conclusions of the Theory of Relativity. Einstein says that space is finite but "unbounded" in the sense that there isn't any "surface" to it. This is perfectly consistent with the notion I just gave of space (though Einstein's is on different grounds, based on the "warping" of the "space around" all objects. I would rather not bring up the complications involved in this; bringing them in would not change the conclusion and would only make things more confusing.)
Well, but if space is a finite "size," so to speak, what is outside it? Nothing. Not space. Just nothing. It expands, by the way. What does it expand into? Nothing--meaning it doesn't expand into anything; it just expands. The "space" it would "expand into" is that imaginary space that doesn't exist.
I might point out that, if there are two sets of bodies and each set has field-relations only with other members of that set and not with members of the other set, then there are two spaces, and one is not anywhere with respect to the other. They would have no position-relation with each other. [This might be the case, for instance, if there is a universe of "anti-matter," which, if it interacted with our universe, would blow it up. "Black holes" are another story; they do have position relations (effects) on objects here; but I leave the physicists to puzzle through what is meant on this theory by "where" they are or we are with respect to them.]
4.5. Action at a distance
One final note. There was an old medieval "first principle" that was supposed to be absolutely certainly true: "Action at a distance is impossible." The grounds for that is that an object is supposed to be where it is acting; and so it is simply a contradiction in terms to say that it can act at a distance from itself.
But what we know of fields shows that this is not only not "obviously true," but is even false. If an object is "where it acts," then (since the fields of each one of us extends all through the universe) each object is everywhere in the universe--which makes nonsense out of "being somewhere."
Hence an object is not where it acts; it is where it is acted on by others' fields. But it obviously (by its own field) can act beyond the confines of its location in others' fields.
A magnet, for instance, is on the desk here. That is, it is (gravitationally, say) acted on very strongly by the desk, rather more weakly by the back wall, more weakly still by the front wall, very weakly by the side walls and the ceiling, and so on. This is its position with respect to its surroundings, and it can be defined very narrowly.
But it is acting on the compass over on the other side of the room. If it were an electromagnet, you could demonstrate this by turning it on and off and watching what happened to the compass.
It is clearly acting on something which is at a distance from where it is. And, in fact, as we saw, this type of action establishes the only real meaning to distance.
Hence, action at a distance is not only possible; it gives meaning to distance itself.
...Considering that all we have so far considered is the implications of a single form of energy, we have been able to say a few significant things that might turn out to be useful to physicists. Now let us go on to consider systems and bodies.