A New Foundation for Theoretical Physics
WHAT GEOMETRIC DYNAMICS IS ABOUT
Here is an original and deeper look at some of the wonders of the physical universe. The author, not at all a slave to orthodox physics concepts, explores new possibilities in regard to the underlying workings of our world and those beyond. It is all written in easy-to-understand layman’s language.
ABOUT THE AUTHOR
Most of Johnny Carlton’s books are suspense filled action thrillers; but with his spiritual, philosophical, and scientific bent, such bigger-picture insights are reflected in his fiction, giving his stories a satisfying depth seldom experienced in adventure thrillers.
His non-fiction books, however, intended to be a help to his fellow life-travelers seeking a better understanding of the universe we live in, more directly take on the challenge of seeking truth; and yet, because the search for truth is exciting, these writings are also entertaining.
Johnny Carlton lives in Saskatchewan, Canada, with his wife, Yvonne, and continues to write both fiction and non-fiction.
For a sneak preview of this book read the sample pages below:
PART 1: DEFINITIONS & RELATIONSHIPS OF THE BASICS
I BELIEVE that the word dimension is wrongly used in some of its applications in connection with theoretical physics, and, furthermore, that the presently widely-accepted combining of the concept of time with height, width, and length to bring about a four-dimensional scenario is erroneous. Time certainly figures–who could deny that? However, it is not a sibling of height, width, and length.
I propose that there are three basics of physical existence; I prefer to call them the Three Basic Manifestations.
These three manifestations that make up the physical universe are:
(3) Motion-Time. (I’ll explain later why I’ve labeled motion and time together as one entity.)
And there is one force that brings the three manifestations into existence and goes on from there working with the three manifestations and causing all physical phenomena. The force is what we call energy, and it is a repulsive or separating force.
The three basic manifestations–matter, space, and motion-time–cannot exist without one another. Each of the three needs the other two in order to make up physical reality. The logic behind this conclusion will be given shortly.
Each of the three basic manifestations has three dimensions.
The three dimensions of matter are:
(1) positive height (or depth),
(2) positive width, and
(3) positive length.
(Matter has other characteristics, but the above three are its only dimensions.)
The three dimensions of space are:
(1) negative height (or depth),
(2) negative width, and
(3) negative length.
(Space has other characteristics, but the above three are its only dimensions.)
The three dimensions of motion-time are:
(1) motion of matter moving away from or toward other matter,
(2) motion of matter moving away from or toward the axis of dimension 1, and
(3) motion of matter moving away from or toward the axis of dimension 2 without running parallel to dimension 1.
(Motion-time has other characteristics, but the above three are its only dimensions.)
Still in the category of motion-time, there are some further important categories to be established. Over and above its three dimensions, there are two kinds of motion:
In this kind of motion the actual, physical particles that make up matter move through space in relationship to other actual physical particles.
This is really an abstract motion, and yet, like all abstract concepts is a reality that effects the physical. Artificial motion is that of waves. The wave motion is caused by smaller actual-physical motion within it in which particle-objects move relatively short distances–a bumping action among the physical particle-objects made possible by the basic repulsive force. As is commonly accepted, when a stone is dropped into water and creates a pattern of circular waves radiating outward, none of the molecules of water move the actual distance of the waves; but, rather, in the particular case of water, move in little vertical circles, in the process bumping into its neighbor molecules and causing them to also move in vertical circles. This bumping and circling action creates a temporary crest and hollow on the surface of the water. The crest and hollow move a long distance over the surface of the water even though the actual physical particles the water is composed of move only short distances. Flicking a rope so that a wave passes through it from end to end clearly illustrates that although the particles that the rope is made of stay where they are within the rope and move up and down only short distances in space, the wave created travels the entire length of the rope. So we clearly have two distinct categories of motion: actual-physical, and artificial or abstract. There are, of course, various kinds of waves, such as transverse, standing, and longitudinal, but the basic principle holds for all of them: they are artificial motion created by shorter, actual-physical motion within them.
I propose to demonstrate, in this paper, that the fact of two distinct types of motion, actual-physical and artificial, is extremely important in our understanding of the physical universe we live in–much more important than theoretical physicists have thus far realized.
Motion, both actual-physical and artificial, has three further categories which need to be investigated and defined as clearly as possible. These are:
(a-3) Fragmentation (commonly thought of as time)
Each of these applies to the three dimensions listed earlier.
Definition of Velocity:
Velocity is the motion of one set of matter in relationship with the motion of another or other sets of matter.
A set of matter simply means two particle-objects considered in relationship to each other.
A particle-object is any matter or part of matter taken as a unit. A quark, an electron, an atom, a molecule, a star or planet, and even an entire galaxy, may each be called a particle-object so long as it is working as a single unit within a larger frame of reference. However, to keep from being too straight-laced, I occasionally refer to a particle-object as either a particle or an object.
There are basically two rates of speed:
(1) faster than the motion it’s being compared to, and
(2) slower than the motion it’s being compared to.
To this can be added (3) fastest of the motions it’s being compared to, (4) slowest of the motions it’s being compared to, and (5) second-fastest, third fastest, and so on; or, starting from the other end, second-slowest, third-slowest, and so on.
One more element of definition must be added, and that is: (6) how much faster than the motion it’s being compared to; and, conversely, how much slower.
Whenever we state that a particular speed has been clocked, usually by putting a number to it, we are using one or more of the above six criteria to establish velocity–nothing more.
If there are only two sets of motion considered in comparison with one another, the only facts that can be established about the velocity of either are which is faster and which is slower and which is fastest and which is slowest. The questions, how much faster? and how much slower?, cannot be answered and are, in fact, meaningless questions under the circumstances of the beginning of the above paragraph.
Consider the following mental experiment in which there are only two sets of particle-objects in motion. Set One is made up of particle-objects A and B and Set Two is made up of C and D. A and B are moving toward each other and C and D are also moving toward each other. If we are considering only the motion of Set One in relationship with Set Two, and if there is a difference in velocity between the motion of Set One and the motion of Set Two, then nothing in regard to velocity can be determined except to state which of the two sets has the faster or slower motion. The questions of how much faster or how much slower are meaningless because there is no other motion with which to compare the discrepancy of motion between Set One and Set Two.
But the situation changes if we consider a third possible motion, say that between A and C. Doing this creates a third set, even though there are only four particle-objects. However, a simpler way of arranging the next step of the experiment is to have three separate sets:
Set One: A and B are moving toward each other.
Set Two: C and D are moving toward each other faster than A and B are moving toward each other.
Set Three: E and F are moving toward each other faster than A and B are, but slower than C and D are.
From this we can conclude that:
Set Two is moving at the fastest rate.
Set Three is moving at the second-fastest rate.
Set One is moving at the slowest rate.
We now can legitimately, logically, build and label a speedometer. Its markings will be limited to (1) fastest, (2) second-fastest, and (3) slowest.
If we want more markings on our logical speedometer we’ll need to add more sets of motion to our scenario.
Why is it that a normal speedometer in a car can have so many markings–say from one mile per hour to 120 miles per hour? What sets of motions are being compared?
As an example, let’s think of a car moving at 60 miles per hour. What do we really mean by that? If velocity is the comparison of one set of motion with another or other set(s) of motion, then what are our comparisons in this case?
Well, an hour is the time it takes the long hand to move once around the face of a clock. Hours, of course, are based on the rotation of the Earth on its axis; so that the long hand of the clock moves around the clock’s face 24 times for every time the Earth rolls over once in its relationship to the sun.
The designation mile remains abstract until applied to two particular points in space (usually on the surface of Earth). When we say that a car is moving at 60 miles per hour we are, each in our own minds, and rather unconsciously, gauging the rate of its speed against that of many other rates of speed, such as that of another car in motion, or the average rate of speed of a pedestrian; but, more consciously, we’re comparing the velocity of the car to the velocity of the hands on a clock or wristwatch. Since on speedometers we use an hour as our standard for measuring velocity, and since an hour is what it takes for any particular point on the surface of the Earth to move one-thousand miles, we are really gauging the speed of the car by making a comparison with the speed of any particular point on the Earth’s surface as it moves a thousand miles in its rotational journey. If we think about a car moving at 60 miles per hour we are, in a sense, considering that the car is moving at 6 percent of the velocity of the Earth’s rotation. Therefore all the markings on a normal speedometer are really percentages of the speed of any particular point on the surface of the Earth as it travels in its rotational circle. (We limit the frame of reference to the Earth’s rotation, ignoring other motion such as the Earth’s orbit around the sun.)
Definition of Acceleration/Deceleration
Acceleration/deceleration is the change of velocity in one quartet of particle-objects in relationship with the change of velocity in another or other quartets of particle-objects.
A quartet simply means two sets of particle-objects (each set containing two particle-objects) in relationship with each other.
If there are only two sets of particle-objects then, although velocity is possible, acceleration/deceleration, or a change of velocity, is not possible. This is because there is nothing to relate any change of velocity to. But if we introduce two more sets of particle-objects that have a velocity relationship between them, so that we have two quartets, we can then relate any change of velocity of Quartet One to any change of velocity in Quartet Two, or the other way around.
We now come to what I find a particularly fascinating matter regarding acceleration/deceleration, namely that the two words mean basically the same thing, and that the only factor that sets them apart and makes them seem to be opposites is their frame of reference. This is important enough to warrant an official postulate:
Acceleration and deceleration, both being changes of velocity, are really the same thing but viewed from two different frames of reference.
In order to demonstrate this clearly we need to do another mental experiment. Imagine a cigar-shaped spaceship that looks the same on both ends and has been built to travel equally well in either of those two directions. Imagine that it’s in space and that you’re looking at it from the side. In the middle is the cockpit containing the pilot. He has two seats in there, one facing forward–which we’ll arbitrarily say is to our right–and one facing backward.
Now imagine another spaceship just like the first, complete with pilot, and lying parallel to the first.
Now imagine two more spaceships, just like the first two, with these also parallel to those.
Now imagine a planet, a sphere, visible in space beyond them.
Without even considering the planet or the second set of spaceships, we can imagine the first two spaceships to be in motion simply by imagining them to be in motion either toward each other or away from each other. Let’s say they’re separated from each other, but on parallel paths, and are moving slowly toward each other like two trains on parallel tracks.
Now, if we bring the planet in the background into play for a new frame of reference we could find that although the two spaceships are slowly moving toward each other–the one on the right moving left, and the one on the left moving right–both of them could be moving left according to the planet. In other words, we’ve chosen to imagine that the spaceship on the left and the planet in the background are both moving toward the right at the same speed, and the spaceship on the right is moving left. According to this scenario alone, leaving the other two spaceships out of it, we can logically have no velocity since the left-side spaceship and the planet have in essence become one unit of motion with the right-side spaceship becoming the other unit as it moves left. (Keep in mind that velocity is not another word for motion, velocity deals with rate of motion.)
But what if we decide to have the left-side spaceship and the planet moving toward the right at different velocities? Can this be done? No, because whichever one assumes the lead and the center position in this arrangement, automatically becomes the stationary center point by which we gauge the motion and direction of motion of the two outer objects. However, although we cannot have different velocities of spaceships and planet, we can now have velocity, for we now find that the two spaceships are no longer moving toward each other, but are both moving toward the left, and there is nothing to stop us from having the right-side spaceship move faster than the left-side one. It can also be said that the right-side ship is moving the fastest. Faster and fastest are two of the basic terms that signify velocity.
At this point there still can be no acceleration or deceleration, for there is nothing of that nature to be compared.
However, if we bring in the other two spaceships, the situation is changed. We can now set up enough comparisons among the four spaceships and the one planet to allow us motion, velocity, and acceleration/deceleration.
We have motion because any one of the objects can be moving toward or away from any of the others; we can have velocity because the motion of any two of the objects toward or away from each other can be compared to the motion of any of the other objects moving toward or away from each other; and we can have acceleration/deceleration because a change of velocity going on between any two sets of objects can be compared to a change of velocity going on between any other two sets of objects. The sets can be made up of any two spaceships, or of any one particular spaceship and the planet, as one prefers.
Now we’re getting closer to demonstrating the postulate that acceleration and deceleration are the same thing. Imagine that all four spaceships are moving in the same direction, toward the left for the observer. For this it is necessary that the planet is moving toward the right. We’ll call the spaceships A, B, C, and D. The pilots of all four ships are seated facing toward the left. Ship B begins to gain rapidly on ship A, and ship D begins to gain even more rapidly on ship C. The change of velocity–acceleration–causes the pilots of ships B and D to be pressed back into their seats–the pilot of D being pressed back harder than the pilot of B. We can have all this because the acceleration of D can be compared to the acceleration of B.
Now let’s say that B and D decided rather to decelerate. Anticipating this they would move to the other seat–or swing their chairs around, as you wish–so that they would now be facing toward the right. As they begin to move more slowly than the other ships, they again find themselves pressed back into their seats for as long as the deceleration continues.
But let’s put them back again so they’re once more facing left like the other two pilots, so that we can finally get to the heart of the matter.
We have already described the acceleration, but to reiterate: We have all four spaceships moving toward the left and the planet moving toward the right. Ships B and D begin to move faster than ships A and C, and so the pilots of B and D are pressed back into their seats during this acceleration.
But whether it is acceleration or deceleration is a matter of frame of reference.
By expanding our frame of reference and bringing in another planet, perhaps one larger and denser than all the previous units put together, and imagining that it is moving toward the left, and gaining on all the other units, we find that in this new frame of reference the smaller planet and the four spaceships are now all moving toward the right, but with the small planet moving toward the right more quickly than the spaceships.
Everything else remains the same, including the changing motion relationships among the spaceships and the small planet, so that the pilots of ships B and D are still facing in the same direction and are still being pressed into the backrests of their seats. Only now they’re moving backward instead of forward, and the reason for the pressure is not acceleration but deceleration.
This shows that acceleration and deceleration are the same thing, only viewed in a different frame of reference.
Definition of Fragmentation:
Fragmentation is any perceived segment of a motion in relationship with other segments of that same motion.
Since motion, like space and matter, is theoretically infinite (where are we going to draw the line on them?), a finite mind, such as that of a human being, is unable to perceive it as a whole. Fragmentation of motion allows finite minds to perceive it.
Fragmentation of motion–which is usually thought of as time–is one of the most difficult concepts we can find to grapple with, even though we experience it all the time. In fact, it may be impossible for us, with our finite minds, to learn much more about it than that which we already know axiomatically through simple perception and experience. We do know that fragmentation has three facets:
However, our experience always is of the present–isn’t it? This seems obvious and yet some would debate it. In any case, in regard to past, present, and future, I personally believe that there are no sharp dividing lines between the three, but rather that one blends into the other. I further believe that the blend between past and present, in our experience, is a more gradual blend than the blend between present and future; yet even that is not as sharp a distinction as we normally think it is. This means that we probably never really live just in any fragment that we would later call the past, and earlier the future. Rather, we live in a blend of past, present, and future, in a sense, with the present being predominant, the past being second in predominance, and the future being the third in predominance.
From this it follows that there is no basic difference between an actual happening in the past and our memory of it–insofar as our memory of it remains accurate.
To demonstrate: Sit quietly in a room by yourself and after a moment say one word, any nice word, in a normal tone of voice. Then be quiet again. You will have heard the word you spoke when you spoke it, but you will also continue to hear it in your mind for some seconds after that until it fades away. It has become memory. You can recall it to some extent if you try. But at what point did it become memory? You may say, “It became memory immediately after I finished speaking it, even when it was still ringing loudly in my ears.” But it was ringing very loudly at the start, wasn’t it? Do you really know when you stopped actually hearing yourself speak it and when the ringing memory of it started? You may say, “I know when that was because when I felt my lips close, I knew I was no longer actually speaking.” But wait–the same time-riddle that applies to your sense of hearing applies to your sense of touch. Who hasn’t felt a kiss long after the kissing stopped? Just as the word you spoke rings in your ears as loudly as the real thing at first but rapidly fades, the feel of your lips closing after you speak is also there as an initially sharp but fading memory. And so it is with things we see and taste and smell, and with all our physical perception. The memory of it is so brilliant at first (perhaps only in the first fraction of a second) that we cannot distinguish it from the real thing. I’m suggesting that there may be no distinct line of differentiation between the real experience and the memory of it.
In any case, time, or the fragmentation of motion in our experience, is a great mystery.
One thing that time is not, is a fourth dimension along with length, width, and depth. That is a mistaken concept in which time is taken to be an aspect of matter and space; whereas in reality it is an aspect of motion, and is, in fact, so closely related to motion that it is impossible to separate the two–hence my designation of motion-time as one of the three basic manifestations of physical reality.
MORE BASICS OF MOTION-TIME: CAPABILITIES AND LIMITATIONS IN CONNECTION WITH THE NUMBER OF PARTICLE-OBJECTS AVAILABLE.
Keeping in mind that motion has three dimensions: (1) away from or toward other matter, (2) away from or toward the axis of dimension 1, (3) away from or toward the axis of dimension 2 but not parallel with dimension 1 even if all angles between axes are right-angles when viewed as a two-dimensional image. It will be helpful to consider the following:
All descriptions of motions–e.g., straight lines, circles, ellipses, spirals, zigzags, etc., are made up of either dimension 1 alone (motion describing a straight line), or of a combination of dimensions 1 and 2 (motion describing various two-dimensional curved lines and various two-dimensional angles), or of a combination of dimensions 1, 2, and 3 (motion describing various three dimensional forms).
(a) Motion which is limited to the first dimension–one-dimensional motion–requires two or more objects in space, because if there was only one object it would have nothing to move away from or toward.
According to my definition of matter (the concept of the entity that can exist only in space while in motion), it is not possible for one object/particle alone to exist.
(b) Two-dimensional motion requires three or more objects because two objects are needed to form an axis and a third object is needed to move away from or toward that axis.
Conversely, it would be impossible for two or less objects to describe two-dimensional movement because neither of the two objects would have anything other than each other to relate to and would therefore not be able to free themselves from the straight-line motion axis between them.
(c) Three-dimensional motion requires four or more objects because we need two objects to form the first axis, a third object to form the second axis in relationship to the first, and a fourth object to move away from or toward the second axis in a direction not parallel to the first axis even if all angles between the axes are right angles when viewed as a two-dimensional image.
Conversely, it would be impossible for three or less objects in space to describe three-dimensional movement because whichever object of the three was designated as the third object would have nothing to relate to that would allow it to move in any direction other than away from or toward the axis of the first two objects, thus limiting movement to two dimensions.
In an imaginary abstract universe with only two objects there would be only one dimension. In a universe with three objects there would be only two dimensions. (However, it is not possible for a creature from a three-dimensional world, as we are, to truly imagine a one-dimensional or even a two-dimensional physical world. When we try to avoid giving an object a third dimension, say that of height, we succeed only in thinking of it as being extremely flat; but no matter how flat a thing is, it still has some height. Therefore a one-dimensional or a two-dimensional universe is an abstract concept and cannot even be properly imagined as being physical.) In a universe with four or more objects, such as we live in, there are three dimensions.
It can be seen from this that the number four constitutes a breaking point. At this point we run out of dimensions no matter how many objects we add. However, the addition of more objects allows a greater variety of patterns of motion within the three dimensions. In our real world the numberless particle/objects in motion are able to describe the great multitude of patterns that constitute the innumerable forms and actions that make up the universe.
The Relationships Between Motion-Time and Size:
The twin concepts of shrinkage and expansion are very important to the understanding of the dynamics of the geometry involved in physics. Shrinkage and expansion are combinations of the concepts of motion and direction and are always related not only to size but to changing of size. They are always sphere-oriented and have their motions running along straight lines that meet at an abstract central point, and with points anywhere at equal distances along those lines being increasingly farther apart from one another in direct relationship to the distance of those points from the abstract center–the greater the distance from the center, the greater the distance between the points.
In regard to expansion and shrinkage, the following points are important to Geometric Dynamics:
(1) When two objects alone in space shrink, they must also be moving apart from one another, for there is no other gauge by which to measure their shrinkage.
(2) Conversely, when two objects alone in space move apart from one another, they must also be shrinking, for there is no other gauge by which to measure their motion.
(3) When two objects alone in space expand or enlarge, they must also draw closer together, for there is no other gauge by which to measure their expansion.
(4) Conversely, when two objects alone in space move closer to one another, they must also enlarge or expand, for there is no other gauge by which to measure their movement toward one another.
DEFINITIONS OF THE THREE BASIC MANIFESTATIONS PLUS RAMIFICATIONS
I — Definition of Matter:
The entity that can exist only in space while in motion-time.
II — Definition of Space:
The entity that can exist only as it divides matter in motion-time from matter in motion-time.
III — Definition of Motion-Time:
The change of position of matter in relationship with other matter in space.
OTHER BASIC FACTORS OF PHYSICAL REALITY
As well as the three dimensions of each of the basic manifestations, and the ramifications of those already dealt with, each of the three basic manifestations (matter, space, and motion-time) has five basic factors:
1 — SHAPE
The simplest, most basic shape in a three-dimensional universe is the sphere. This is because straight lines extending from its abstract center in all directions to its surface have the same length.
We have already seen that no less than four objects can exist in a three-dimensional physical universe. In order for objects to have shape other than spherical, however, requires a continuation of the basic force that has separated them. As each of the four particle-objects began their own separation, they would change shape during the transformation.
It is not mathematically possible for a particle-object to divide from one into one, so two parts is the minimum now (since we already have a three-dimensional universe established by the initial appearance of the first four particle-objects, we can now get by with three or two in regard to separation). A particle-object separating into two would transform through a shape that would at first appear as a slightly oblong spheroid with a groove around the center; the groove would widen and deepen, more and more revealing the shape of two spheres except that they would be overlapping into one another; and then the two spheres would be separate. We have now seen two basic shapes: the sphere, and what we can call the double-sphere, which includes a lot of similar shapes that graduate from one to the next as the separating process is taking place. A spherical particle-object separating into three spheres could be called a triple-sphere, one separating into four could be called a quad-sphere, and so on. A quad-sphere, of course, would have quite a different shape than a triple-sphere or a double-sphere.
Shape is an important factor in the geometrical dynamics of the universe. This is because shape, or maybe I should say the state of any particular shape, like any other physical concept, is determined by frame of reference. This means that the shape of an object can be quite different depending on its frame of reference; and, since everything in the universe effects everything else because all things are related in space and time, the shape of an object can be expected, from a geometrical viewpoint, to have an effect on its surroundings.
2 — NUMBER
The concept of numbering objects is relative and involves the following basic comparisons: (1) the same as, (2) more than, and (3) less than. It would be just as meaningless to try to number one object with nothing else in existence as to try to imagine one object moving in space, or, for that matter, one object alone in existence. One object cannot be alone in physical reality because four objects are needed in order to have a three-dimensional universe (this is explained earlier), the only kind we can imagine. Numbering objects is a way of making comparisons between groups of objects, in which we compare a particular group with differing groups, the span of difference reaching from zero to infinity. Zero, however, is an abstract concept, and infinity cannot, by finite minds, be written down, or even imagined as a number. This leaves us with anything between zero and infinity with which to number things–in other words we can start with the number one and count as high as the occasion demands and time and inclination allow, but still always coming up with a finite number. (It makes one wonder what is the highest number any human being has ever come up with, with or without the help of computers, to date.)
3 — SIZE
Size is a relative matter and has meaning only when one object is compared in size to another object. Therefore the basic sizes are: (1) the same as, (2) larger than, and (3) smaller than. After that, providing we have enough objects to be able to compare to one another, we can refine our definitions to the point of saying, this object is twice as large, or five times as small, as this other object. All size measurements that we make, such as “a five-hundred foot high building” are comparisons of this nature. The only physical entity that cannot be allocated a size is the concept of all physical reality, for if all is included in the entity, there is nothing left to compare it to and so there can be no size attached to it. One object alone could also not be given a size, but this is off the board here, because one object alone cannot exist in a three-dimensional universe which is the only kind we are capable of imagining.
4 — DIRECTION
The concept of direction is strongly linked with the concept of motion-time, for direction describes the where-to and the where-from of the motion. Two objects in space, although impossible in a three-dimensional universe, would, theoretically, be capable of limited direction. They could move in two directions: toward one another and away from one another. As more objects are added to the scenario, particularly with four or more objects, the number of directions becomes increasingly abundant. The more objects in existence, the more comparisons can be made in regard to what is going where. Again, the entity of all physical reality can have no direction for there is nowhere for it to go and nowhere for it to come from.
5 — POSITION
Position or place is the concept of where an object is at a particular moment in motion-time. One object alone can have no position. One reason for this is that it is not conceivable for one object alone to move, since it has nowhere to move to; and since position describes the where of an object during a moment in motion-time, it cannot have that moment when there is no motion. But more basically, one object, even if it could exist alone (which it can’t) could have no position because position is always a description of where something is in comparison to something else. The statement that someone lives in the country of Africa on the planet Earth has meaning only because our minds deal with such a statement by automatically comparing the position of Africa in relationship to other areas on the surface of our planet, and by mentally seeing a quick image of Earth as a planet in the solar system within a larger universe. To someone with no knowledge of the solar system or galaxies–such as someone from the year 1000, or someone from a very primitive society today–the description, “on the planet Earth” would be totally meaningless. This illustrates that position is always the relating of one place in relationship to one or more other places and cannot exist as a concept without that relationship. The concept of position ties in strongly with the concepts of numbers and direction, because the position of an object is always so and so far from such and such other objects in such and such a direction from those other objects. The only existing entity that can have no position is the entity of all existence, because there is nothing else for this to relate its position to.
Postulate: All change of matter, when broken down in detail, is change of position of matter in relationship to other matter in space.
That is to say, basically there is nothing else that matter is capable of but to change its position in relationship to other matter in space, just as it came into existence by separating from itself. (A bit more on this seeming contradiction–“came into existence by separating from itself”– later.)
According to the above definitions (I, II, and III):
1.– Motion-time cannot exist without matter and space because without matter there is nothing to be in motion; and without space there is nothing for matter to move through in relationship to other matter.
2.– Space cannot exist without matter and motion-time because without matter there is nothing for space to divide; and without motion-time there can be no matter to be in motion.
3.– Matter cannot exist without space and motion-time because without space there would be nowhere in which matter could change its position in relationship to other matter; and it is only through motion-time that matter becomes separated from matter so that it can be in space.
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