Chapter 5

Distance, position, and space

Now then, the distance from one object to another is obviously a relation between the two objects. In our intuitive way of grasping things, it is something "between" the objects; but on the other hand, if all you are talking about is the distance between them, then obviously the distance is the nothing between two objects: it is a certain quantity of nothingness.

Aristotle noticed this, and therefore held that there can't be any empty space; because if there is nothing between two bodies, then obviously they are in contact--unless you want to say that there is a nothing between them, and a quantified nothing at that, which is absurd.

People laugh at Aristotle nowadays, because physicists talk about empty space as measurable; but of course, he was absolutely right. There can't be measurable nothingness between real objects. This sort of "real nothing" isn't like the "real nothing" that is the form of existence or the quantity itself, because forms and quantities are limits, implying something to be limited. But in the case of the "emptiness" between objects, there is supposedly nothing at all there--and not only that, but it has a quantity.

And in point of fact, we know that there isn't nothing between objects; their fields precisely are "spread out" through the whole of "empty space," filling it with various quantities of actual energy. It's only if you assume that the fields "aren't real" that you wind up with space being "empty" and have the paradox of a measurable real nothing--not to mention the fact that material objects actually act on things that they have no sort of contact with at all.

Hence, the distance "between" objects is not in reality a nothing between them that gets measured, it is a real relation between them; and as a real relation, it is obviously the action of one upon the other, or the interaction of the two of them.

And since we know that two objects "at a distance" from one another have fields by which each actually acts on the other, then we have a reality which gives us precisely the separation of each from the other, depending on how strongly the field of each acts on the other.


The real distance from one body to another is the force that that body's field is exerting on the other. This real distance takes into account the actual amount of total energy in the field and the ability to be affected by the other body, and so it is the actual force that is being exerted. So, the real gravitational distance from the sun to the earth is the amount of the gravitational attraction the sun has on the earth. The real distance from the earth to the sun is much less than from the sun to the earth, because (of course) the earth is "pulling" the sun with much less force than the sun is "pulling" the earth--and the "pulling" is the real distance.

While your mind is boggling with the fact that the real distance from A to B can be (and generally is) different from the real distance from B to A, let me further boggle it by observing that a given object can have many fields; and each of these fields will establish a real distance to other objects, which may not be the same as the real distance of some other field.

That is, the real gravitational distance from the sun to the earth is one thing; the real magnetic distance is probably something else, because the sun's magnetic field doesn't have the same quantity as its gravitational field; and similarly, the sun's distance based on its radiation field of light will be different from either--and, of course, the distance from the earth to the sun in each of these cases will be different from the distance from the sun to the earth.

All of this can be made conceptually more manageable, however, if we make this abstraction:

The abstract real distance from one body to another is the causality (the force) one exerts on the other, assuming a "unit source" and a "unit affected object"; or it is the force of the field as a field.

In this case, of course, the abstract real gravitational distance from the sun to the earth would be the same as the abstract real distance from the earth to the sun, since the difference in "total strengths" of the fields is eliminated. It does not necessarily follow, however (if, for instance, different fields have different configurations), that the distance of one type of field will be the same as the distance with respect to some other type of field.

Einstein, in fact, was working on a "unified field theory," and died without being able to come up with one; and that probably is because different sorts of fields establish different distances; and so you can only talk about the distance between two objects if you assume that it is a distance with respect to a certain abstract field.

In other words, distance and position are even more relative than General Relativity supposes; what the distance is depends not only on what you pick as your source, but the kind of field you are talking about when finding the distance.

Notice that in real distance, the quantity is greater the nearer you are to the source of the field, and less the farther you are away. That is to say, "more force" defines what "nearer" means in reality, and "less" what "far" means. And that makes sense; the farther you are away, the less the "influence." Precisely.

But because we are accustomed to measuring distance with rulers and not instruments for registering force, we think of the distance as greater the farther apart the objects are. But the ruler, as I said, is a set of internal fields with internal distances, and so it isn't giving you a true picture of what is really the "between" of two distant objects--which is what they are doing to each other.

The relation between real distance (in a gravitational field) and "ruler-distance" would be expressed by the following equation:

d = (-G m1m2/D)1/2,

where d is the "ruler-distance," -G is the "gravitation constant," m1 and m2 the masses of the two bodies, and D the real abstract gravitational distance (the force). Of course, this is nothing but Newton's Law of Universal Gravitation solved for "r" and using "d" and "D" instead of "r" and "F." The point is that the "ruler-distance" is not what is "out there"; what is on the right-hand side of the equation is what is objective; the left-hand side is, if you will, one way that it is perceived.

Would descriptions of physical interactions be simpler if real distances were taken into account, and "ruler-distances" ignored? This theory would predict that they would be; but it takes a real wrench in a person's customary approach to physics to be able to deal with distances as forces and not to introduce rulers and coordinate systems surreptitiously.

Because of course, coordinate systems--which organize distances and positions in terms of ruler-distances--don't refer to anything at all, as General Relativity shows so well. The only thing that's real about objects at a distance from each other is how they interact; the complications of the tensor calculus are ways of relating this interaction to the observer's coordinate system--and my philosophical prediction here is that you don't necessarily have to do this.

What I am saying is that if you know the forces that objects are actually exerting on each other by their fields, then, based on the quantities of these forces and the tendencies they have toward motion, you can discover the "force-configuration" of the bodies at the end of the process (or at a later stage in it), and from this derive their "ruler-distance" configuration if you want to. Given the fact that the total energy in a system is constant, then how this energy distributes itself within the system will depend on how it is being "traded off" by the various elements in the system (which "trading off" is precisely what the forces are). So you don't really need coordinate systems to know what is really going on in the system, provided you are willing to sacrifice what the activity looks like to an observer sitting somewhere with respect to it.

Obviously, you've got to make observations somehow, to learn what the initial instability of the system is. But what I am saying here is that you can translate (by something like the equation above) this observation into the internal energy-state of the system, after which you don't need to observe what is happening in it as it happens, insofar as the physics of the "happening" is known; and you can then check the results of your mathematical calculations of what happens by another observation at the end of the process. This is actually what physicists do now, except that it seems from things like the calculus that you are "observing" all throughout the change. But the definite integral, for instance, only gives you the results after definite limits are reached, and what happened "in between" is not really known from the calculation itself.

But let us leave this sort of thing to any physicist who might be interested in verifying our theory of philosophy and take the next philosophical step: Since distance is a relation between two bodies, and we have defined real distance as being the relation called "causality"; and since we saw that this same relation can be looked on the other way as "being affected," it should follow that there is some kind of reverse distance-term that would refer to the relation looked at in this way. And, in fact, there is:

The position of a body is its being-affected by some other body's field.

That is, it is the same as the distance, only considered passively--which, when you think of it, is what you mean when you are talking about "where" something is, because you can only point out where it is in terms of its distance from something. What it means here is that it is the tendency to do something in response to the field acting on it, which shows up in equations as the "derivative," or the "tendency to change," while the distance shows up as the force of the field that is producing this tendency.

Note, by the way, that if the field does not produce some tendency to change, then as far as the body is concerned, it is nowhere with respect to that field; it is not "at a distance" from the source of the field at all--with respect to that particular field. Thus, glass, which is not acted on by light, is not at a radiation-distance from the source of the light, because as far as the light is concerned, the glass doesn't "know" that the light is there; it's as if, for it, the light didn't exist; and the light just passes through the glass as if it weren't there. Precisely. It isn't there for the light, if our definition of position is true.

So this apparently abstruse definition of position actually makes sense out of physical interactions. To be "somewhere," you must first of all be somewhere with respect to some object which has a field, as Einstein showed so well in both of his theories of Relativity. "Absolute position," or "position in absolute space" is meaningless; and this, on my theory (and Einstein's too, if you look at it) is because position involves an interaction of objects. But secondly--and here I go beyond Einstein, who was still concerned with "observation" and actually the radiation field of the light getting information to the observer--to be "somewhere" you must actually be being acted on by the field; and this means that we can be "somewhere" with respect, say, to the gravitational field of the sun, but nowhere with respect to the light field of the sun (as glass is).

And, of course, this also would imply that you can be in different positions at the same time with respect to the same body, if the body has different fields exerting different forces upon you.

There is no mystery in all of this if you consider position as being nothing but the being acted on by a force, which is the only reality it could have as a passive relation that is measurable; it only becomes esoteric and mysterious if you think of position as we perceive it, as "out there in my visual space"; but this, of course, is your subjective impression that is the effect on your eyes of the field-interactions of bodies, and is not a "copy" of the relation that is "out there" at all. That is, "position-as-you-perceive-it" is no more "like" real position than "red-as-you-perceive-it" is a copy of the electromagnetic radiation.

And that position-as-perceived is not the same as position-as-real is obvious in that two objects almost in the line of sight appear very close together, while if you were to change your viewpoint you would see that they were very far apart; objects closer to you appear farther apart from each other than the same objects seen from the same angle if they are farther away from you--and so on. What's real is what they are doing to each other, not what they look like as "beside" each other.

Position, of course, as being-affected, will also have the same two sorts of definitions as distance:

Real position is the actual tendency to change based on the actual force and the object's actual tendency to respond to the force. Real abstract position will be the tendency to change of "unit objects," abstracting from anything but the fields as such.

I don't think I have to spend many words on this distinction; it is the same one as with distance.

But one of the interesting things is that this notion of what position really "points to out there" is the perfectly simple solution of a dilemma that quantum physics has got itself into recently: that a body can be "in two positions at the same time, but in only one of the positions that it's in," apparently depending on how you decide to observe it.

I am referring to what is called the "Aharonov-Bohm" experiment dealing with interference of light. A beam of light is split into two beams, each of which is then bounced back off a mirror back to the place where they are combined into one beam again. When they are combined, the two parts then "interfere" with each other, and the resulting pattern on a screen is a series of bright and dark stripes or circles. The actual pattern you get will depend on whether the paths after the split are the same length or not, and what the difference in length is.

Now it turns out that it is in principle possible (if not in practice, but analogous experiments can be done) to dim the light so much that a single photon (unit of light) is in the apparatus at a time; and so if the interference pattern occurs after you've been running the experiment this way for a while, this has to mean that each photon split in two, and half of it went down each path.

But this sounds anomalous, because a photon is supposed to be a unit; and so if you put a detecting instrument on the path after the split (to see if you can detect half a photon because it will have half the energy), something interesting happens. First of all, what you detect is the whole photon in one or the other of the paths at any given time, but never in both; and secondly, the fact that you have introduced the detecting mechanism into the path interferes with what we can call the "dynamic length" of the path just enough to make it "vibrate," as it were, so that the interference pattern is messed up.

So what this means is that if you detect where the photon is, it is in only one of the two possible paths, and there is no interference pattern (which is consistent with the photons' being in one or other path at a time at random, but not both); but if you don't detect the photon (if you turn off your detecting apparatus), then you get the interference pattern, which is possible only if each photon went down both paths at once.

To complicate things, you could put another beam-splitter in the place of one of the mirrors and split the split beam, bringing the split parts back together into the path of the original split, and then the two together again at the target; and you could do this as many times as you want, so that it took five minutes, say, for the photon to make its complicated journey. And if in this case, three minutes after you started the apparatus, you changed your mind about the experiment (deciding to make it now a detecting experiment and not an interference one), you would get the same results as above; it would now not have an interference pattern, and the photon would be in only one of the paths it could be in. On the other hand, if you turned off the detecting apparatus, you would get the interference pattern, which means that the photon went down all the paths and split itself four or eight or however many ways.

But what is fascinating about this is that in principle you could make your decision long after the first "split" into separate beams, where the photon had to make its "decision" on whether to go down one path or both. So the decision itself after the fact determines, apparently, what the photon did in the past.

No wonder physicists find this incomprehensible.

But, as I say, the answer is simple. What do you mean by "going down both paths"? That the photon "bounces off" the mirrors at the ends of the paths, or in other words is affected by the surroundings of the paths. But what happens when you detect the photon? You make it act on something in the paths, and give up energy to it. So in the one case, the photon is reacting to the surroundings, and in the other the photon is acting on them.

It may very well be that a single photon cannot act on anything without using all of its energy somehow, in which case, it can't act on the instruments in both paths, but only one of them. But it is quite possible that a photon can be affected by more than one thing.

And to put this in the perspective of position, what this means is that the photon is in position with respect to the surroundings, but not all the surroundings can be in position with respect to the photon.

That is, if you want to know where the photon really is during the experiment, it is in both paths, because they are doing something to it. On the other hand, if you want to know which path is actually in position with respect to the photon, then you have to make it act on something in the path; but that action it performs prevents it from being acted on in the same way as if it is not using up its energy in affecting the surroundings.

There was an actual analogous experiment by Mullinstedt using electrons, in which he demonstrated that a solenoid between the two paths that the electron traveled affected the interference pattern when the interference pattern option was chosen--which, of course, means that the electron was not only in position with respect to the paths but with respect to what was between them too.

And this sort of thing is also consistent with what Einstein showed in the General Relativity Theory, that light can be affected by strong gravitational fields; but because light has no "rest mass," it itself cannot affect (gravitationally) other objects. Hence, light is in position with respect, say, to the sun; but the sun is not in position with respect to the light that is traveling by it.

As I say, there is no necessary reason for saying that if something can be affected by a field that it has to have a field by which it can affect the causer; and if being in position means being affected to some degree by a field, then it follows that A can be in position with respect to B, while B is not in position with respect to A.

So if you want, my theory of position predicts something like the Aharonov-Bohm experiment and Einstein's bending of (massless) light in the presence of very massive objects. And I know of no other theory that doesn't try to solve either of these peculiarities physically; the "solutions" seem always to involve rather silly excursions into the epistemology of how subjective observation is, and a confusion of the act of observing with what is observed.

Let me now say a word about the Aristotelian and Scholastic notion of position. Aristotle, of course, had no notion of fields; and with his idea that there is no such thing as empty space between objects, then it followed for him that everything between objects was filled with some continuous (fluid) body like air, water or "aether." He therefore defined the "place" or position of a body as "the surface of the body surrounding (and touching) it"; as, for instance, your place is the surface of the air that is in contact with your body.

Unfortunately, we know now that, though space may be "filled" with fields, it almost certainly is not filled with any body (or, for one thing, there could be a meaning to the "absolute position" of something, which seems, because of Michelson and Morely's experiments with light, impossible). Hence, his definition (which wasn't very useful for purposes of measurement anyway) doesn't seem to be worth bothering with in the present age.

So it seems reasonable to say that the reality of position is a being affected (to a certain degree) by some field; in which case, we can make the following conclusion about God:

Conclusion 10: God is not in any position.

What? God is nowhere? No; to say that God is nowhere would be like saying glass is black because it is colorless. God is positionless, not "nowhere." But then isn't God everywhere? No. This would be like saying that glass is white because it's not no color and it's not some definite color, but is all colors; but glass is colorless, not white. Besides, if God were everywhere, this would mean that he is affected by everything's fields, and we saw that God can't be affected by anything at all.

Scholastic philosophers and Theologians say that God is "where" his effects are. But if that is the case, then you would have to say that every body that has a field is "everywhere," because its field actually has an effect (however small) throughout the whole universe. But it is silly to say that I am in my back yard where my dog is because my gravitational field is exerting a pull on my dog.

So this "active" notion of position (which would allow you to say that "God is everywhere") actually makes a mockery of what "being in a position" means, because then everything is everywhere.

Hence, God is not everywhere, not nowhere, not somewhere, not here, not there, not up, not down, not in the sky, not in you, not in the earth. Position terms do not apply to God, any more than color-terms apply to glass. And just as to say that glass has no color (is colorless) does not mean that glass doesn't exist, similarly to say that God is positionless does not mean that God doesn't exist. He doesn't exist anywhere, that's all.(1)

But a while ago I brought up the idea of space. What is it?

Obviously, it is not "space-as-perceived": that "volume" in which we see things distributed. As a reality it is one of two things:

The space around an object is its field. This energy would establish a set of potential positions objects could be in with respect to that field. Space taken absolutely, however, is in reality simply the sum of all positions.

That is, space is simply the passive-component of the field-interactions of all bodies. Once you have counted all bodies and seen how they are affected by all other bodies, then you have the whole of any reality that could correspond to what our notion of "space" "points to."

It follows from this, of course, that space is finite--not surprisingly, if it is something measurable; but it also means that the objects that are farthest away from each other (whose field-force-interactions are weakest) are still at a finite distance from each other; and so space is also finite in size. Einstein, for other reasons, said also that space is finite in size (what he meant by space is the set of paths that things could move in--which are curved, and the largest circle defines the size of space in his sense).

Furthermore, space can increase in size or extent, if the outermost objects move farther apart from each other. Both Blair and Einstein, then, hold that space can (and in fact does) expand. But then what does it expand into? Nothing. Of course. It doesn't expand into anything at all; what it seems to expand "into" is that imaginary "receptacle" which is the "real nothing" of space-as-we-perceive-it. Space doesn't expand into anything; it just expands. But what is outside it? There isn't anything outside it, because "to be outside it" would mean that there was a position "out there," which obviously would by definition be inside it if it is the sum of all positions.

Then where is space? It isn't anywhere; and, of course, it isn't nowhere either. You can't use a position-term referring to "where" the sum total of all positions "is." To ask where space is would be like asking how hot heat is (i.e. not how hot some definite case of heat is but what temperature heat itself has). Plato occasionally fell into traps like this.

Having defined position and space, we can also make the following definition:

The place of a body is its positions with respect to the other bodies around it.

That is, the "place" of something would be the total effect all the bodies are having on it at the moment; the "resultant being-affected" or tendency to change based on the combined field-forces of all of them.

Place is this combined field-force looked on passively. If you look at it actively (so that you get a "resultant force"), then you find something interesting:

The angle is the combined distances of many objects to a given object.

The simplest case of an angle is the combined distances of two objects with respect to some object, or the "resultant force" that expressed what the two of them together are doing to it.

Once again, physics tends to look on this backwards, in terms of the observation. In physics, the "resultant force" is said to depend on (a) the force of each body, and (b) the angle between them. What I am saying is that this "resultant force" establishes the angle, because it is the only reality that the angle has; the other angle depends on your arbitrary coordinate system.

What I mean is something like this: a "straight angle" in which the two sources of the fields are on "opposite sides" of the affected body is the angle at which the resultant force is the minimum; a zero angle is the angle at which the combined forces are the maximum. In between, the resultant force defines angles between zero and the straight angle.

But in the real world, there isn't just the angle like those above, since there will be more than two objects acting on the one in question. Hence, the angle will actually be n-dimensional (like the "solid angle" in solid geometry, only with an n-dimensional geometry, which obviously can't be pictured).

Of course, since in the real world there are no coordinate systems, there are as many "dimensions" in the real world as there are interactions; and even in the physics of bodies-as-perceived, there aren't just three dimensions: to describe a moving particle, which can rotate as well as move, you need six dimensions even in "coordinate physics." So I am not going to say anything about dimensions.

Finally, this view of distance and position gives a conclusion which contradicts the so-called self-evident first principle of medieval philosophy that "action at a distance is impossible." In order to hold this principle, you would either have to say that the object with the field is in the place where it is affecting the object apparently at a distance (which as I said earlier about God makes "being in a position" meaningless, because then everything is everywhere), or you have to deny that objects have effects through their fields on objects that are at a distance from them. It seems to me that the latter flies in the face of the evidence, and the former is nonsense; and so action at a distance is not only possible, it happens all the time.

But now it is time to pass on to the complex units that we call bodies.



1. And therefore, if this is right, Leibniz' notion that "everything that exists exists somewhere and somewhen" is false.