The Nomothetic Theorem offers many insights regarding the structure and operation of the universe. There comes a time in everyone's life when there is a desire to understand where we come from, why are we here, and where are we going. Those questions hinge partly on spiritual issues that go far beyond the mere physical, but some answers come from looking at the basic structure of the universe.
There isn't one straight line approach that encompasses an entire explanation of the universe, so be patient while I take several runs at the subject from different directions. Some of the larger questions are: What is time, and what is space? What are the properties of mass and energy? And how do they combine to make our universe? The general question is, what are the rules that define the way our universe works?
One way to tackle the question of design is to pretend we can build our own universe. Let us go on a trip in our minds where we try to build a universe that has properties similar to those we are familiar with.
Imagine that you do not exist, but that you can observe. You are all-seeing, but you have no position in space so you have no point of view. You have no capabilities except as an observer.
Imagine you are observing a universe that does not yet exist. This is a universe of uniform nothingness. There is no time, no space, nothing. Then along comes a pulse. The pulse can be anything, but it is total and it is uniform in all respects. For the sake of being sure our thinking is together on common ground, let us assume that the pulse changes this universe of nothingness from total black to total white. This is not a measurable event. You are still in a universe of nothing. There is still no time or distance, no size or direction. Because there is no time, you have no memory and no ability to say that anything even happened because you have no reference points. You cannot say that everything is white, because you do not have black to compare to. This event was a non-event because it did not happen in space or time. Realizing how something can perhaps exist (the pulse) but not be recognized or measured demonstrates why contrast is an essential ingredient to have a meaningful universe. Contrast requires a here and a there, or a then and a now. Contrast requires time and it requires position.
Now imagine that your universe of nothing has a tiny spec of something in it. (Or maybe you have a universe of uniform everything and it has a tiny spec of nothing in it.) You now have contrast, but you do not yet have space (position), or time. Suppose this tiny piece of contrast is moving. How can you tell? There is no reference point with which to compare its motion. You cannot say where this piece of contrast is, or how big it is, or define it in any way. (Remember you do not exist and you have no position, so you cannot define things relative to you.) There is no up or down, no side to side, no near or far, no big or small.
Let us introduce the concept of change alongside the concept of contrast. If this contrast appears and disappears, you might be tempted to think now that we have change, we have time. But there is still no time and no space. When the contrast disappears, you do not know where it was, or even that it ever existed, or when or if it will ever come back. Change must occur relative to something else in order to be recognized as change. (Movement relative to a fixed point can be recognized as motion. Movement in the absence of any reference does not constitute motion.) A single point in the midst of nothing conveys no useful information with which to build a universe.
So let us build a universe that has some usefulness and familiarity to us. Imagine that your universe has multiple points in it that define three dimensional space. (Two points define a one-dimensional line, three points define a plane, four points can move us into three dimensions.) If these points of contrast are absolutely rigid and unchanging, we still do not have distance or time. Distance is a product of change (or motion) over time. Time does not exist in a static universe. If we have no motion, we have no distance, we have no time, and effectively we have no useful concept of space. We need to introduce the event of motion in order to obtain distance. Distance is realized when we allow change from one position in space to another. But distance is meaningless if we allow unlimited (infinite) motion. Therefore, distance also requires a rate of change, and that finally means the introduction of time.
Why is it necessary to have time in order to establish distance? Why can't the principle of equivalence be used to establish distance? If one takes a meter stick and measures the distance between A and B and then measures the same distance between C and D, does not equivalence say that the two distances are the same? The answer is no, not necessarily. Suppose you take a meter stick and hold it in front of your eyes as you look at two mountain peaks off in the distance. You measure them to be fifty centimeters apart. You now turn and hold the meter stick up to an automobile near you. The auto is more than one meter long. Should you conclude that the automobile cannot drive between the two mountains? Your measurements need to be adjusted for position. The obvious way to measure accurately is to physically carry the measuring stick to each object being measured. We begin to appreciate that position affects the perception of size, but a change in position requires motion. Thus motion is relevant to three dimensional position and size. But how do you know that when you move the meter stick, its length will remain constant? Measurements may need to be adjusted for temperature and pressure and gravitational effects and light distortion, and all kinds of interfering forces. In the end, equivalence is not very satisfactory.
Let us go back to the question of why it is necessary to have time in order to establish distance, because the answer says a lot about the structure of space. When you drive to work in the morning, you pass trees and fields and buildings and all kinds of things that occupy the space between your house and your office. But what if there was absolutely nothing between those two points? What if there was a complete void? Would you still cover the same distance? Would it still take the same time to get to work if you travel at the same speed? In our universe we are going to answer yes. Space is a place holder. Even if there is nothing there, space represents a place where there could be something, and we have to treat it just as if there were something there. Therefore, when we pass through empty space, we still have to assign it the same time value as if we were passing along occupied space. Even though we don't see any change, even if there is nothing to tell us that we are traveling, the clock is ticking and we cover the same distance between two points whether the intervening space is occupied or not. This means that motion and time define distance, not how many objects are passed between two points. But distance only tells us the relative position of two unique points in space. If all empty space looks the same, the actual identification of each unique point needs some confirmation. Ultimately the question of identifying a unique position in space devolves around the question of whether the position can be occupied, and whether it can be occupied uniquely.
From a practical standpoint, the existence of motion is interdependent with the definition (measurement) of position. It is necessary to face the simple fact that the whole reason for wanting to know distance is because of motion. If there is no such thing as motion, distance is irrelevant as a concept.
So we have a universe of contrast with multiple points in three dimensions and we have motion. Now, as one point moves relative to other points, we can actually recognize change. But there are still some additional rules that are required to make this possible. We know that there has to be motion. But what if there is too much motion? If one point of contrast can move infinitely fast, it could be in numerous places at the same time. The identification of a unique position in space is a factor of distance measured from a benchmark, and distance is a factor of position. Both are relevant only at a specific point in time and only if position is unique at each point in time. Thus we cannot have one point of contrast in more than one place at the same moment in time. Position is defined as unique in three dimensions and time. A simple rule has been introduced: "No one thing can be in two different places at the same time".
Note therefore that the concept of simultaneity is essential to define a universe. Einstein's theories are often generalized to say "time is relative". While there may be situations where your time and my time are different, this does not erase the concept of simultaneity. When it is said that "No one thing can be in two different places at the same time", we must agree on the simultaneous identification of two unique positions in space within a consistent frame of reference for time.
Implicit in our understanding of motion, and the role time plays in motion, is the reality that motion in our universe is variable. The fact that something can move rapidly or slowly requires a correlation between distance and time. Entities of change must exist in order for there to be a correlation between time and distance. Some motivator must exist to cause a change from one state (position or state of motion) to another. And this same motivator must be able to act at variable rates. These entities of change are what we call energy. Without a flow of energy, there would be no motivator of change and thus no time or space. The governor on the rate of change is inertia. Inertia is a property of mass. Thus, the existence of mass with the property of inertia provides the means for variability of motion. Furthermore, what we refer to as points of contrast are in fact a representation of something we call energy, which provokes change.
Let us think for a moment about these points of contrast that have been introduced into our hypothetical universe. How do these points of contrast relate to the concept of change? What is change? Perhaps the points can either appear or disappear. That is change. The points can also move. That is positional change. The points can also grow in size or shrink in size. What happens if they shrink in size so much that they disappear? Imagine the smallest possible size as being one unit. One unit of what? We will call it one unit of change because the next smaller possibility is disappearance. The next larger possibility is an increase in size. If change requires energy (Change is the result of work which is energy in transit.), it is logical to think of one unit of change as the same as one unit of energy. This leads to the conclusion that in order to create change, it is necessary to either add or subtract energy.
Now imagine a larger structure made up of many units of change (energy). This structure may have many kinds of energy units: kinetic energy, positional energy, even mass. As energy is released or taken away from the structure it will lose its kinetic and positional energy and start to shrink. It will increase in density and become smaller and smaller. As almost all the energy is removed, we finally get down to only two units, so small and so close together that they are only barely discernible as different from one unit. The only thing separating this double sized object from being one object is one unit of change. If we take one unit of energy out of the two units (any infinitely small change will cost one unit), then one unit disappears -- or it can be said we have effectively shrunk the two units into one. There is now only one unit of change left. If the object uses its remaining energy to move one position in space (the smallest amount possible to create change), then we will use up the last unit of energy and the unit will disappear. Thus, disappearance is the same as motion or change. It is now possible to think of 1) any change in size, and 2) any movement in space, or 3) an appearance or disappearance as a change in units of energy.
Where has all this thought about an imaginary universe taken us? We have arrived at the necessity of having contrast and the necessity of having motion or change. We see the necessity for having a smallest unit of change below which there is nothing, and we see that zero is an intolerable condition for our universe to exist. Change is really a factor of distance, even if motion over a distance ultimately causes a change in size, density, or even a disappearance. Furthermore, we acknowledge that the rate of motion (speed) must be limited to some finite amount (an amount less than infinity). Change cannot be allowed at infinite speed or there would be no time, no position, etc. Finally we are starting to get a clear picture of how our universe is structured.
Observation of this universe leads us inevitably to the conclusion that energy wants to radiate out to an infinitely diffuse state. And as it does so, the point from which it departs changes in a correspondingly negative fashion.
When we accept the belief that change requires energy, we appear to run afoul of the fundamental principal of conservation of energy. Whenever change occurs, either a new force of energy is brought in as an agent of change from outside any closed system we are contemplating (energy is added), or energy must be released from within the system (energy is subtracted) to continue the process of change. If energy is released from within the system, where does it go? The answer is that it either stays in the system in a new transformed state and/or it becomes a victim of entropy. Becoming a victim of entropy puts a new twist on the principal of conservation of energy. In theory energy can transform, but is always conserved. However when we accept energy as the required agent of change, we are admitting that when there is no more change, there is no more energy. In the previous example when the last unit of energy changes position, it disappears. The unit of energy used itself up to create the change. Where has the energy gone? If the principal of conservation of energy tells us that energy can never disappear, the response has to be what about entropy? Energy may be conserved, but it can be "used up" when it reaches its maximum state of entropy, its maximum state of stability. At that point, our universe becomes static and it essentially disappears -- even though it may still be there!
When one watches a pendulum swing, positional energy (the motionless pendulum at the top of its swing) is transformed into kinetic energy (the moving pendulum at the bottom of its swing). Here we see the traditional example of the conservation of energy. But change is introduced into the regular swing of the pendulum which prevents it from continuing forever. The motion of the pendulum is non-linear so there is the force of acceleration to overcome. The pendulum hits air molecules and transfers energy through these collisions. There is friction at the fulcrum of the pendulum which releases heat energy. As all of this energy bleeds off, the motion of the pendulum will change -- specifically, the energy of the system will diminish. The law of conservation of energy tells us that the energy must still be around somewhere, it is just transformed. The answer is yes, but eventually it flows out into the universe where it is transformed into a useless state as a result of entropy.
Taking once again the smallest unit of change (which we will label Eu for a unit of energy or a unit of entropy), if its potential energy is released to produce change, then it moves, but in the process, disappears. What happens to the energy? I don't know. Either it becomes infinitely diffuse (but still exists) so that it effectively does not exist, or it ceases to exist (contrary to the theory of conservation of energy) because it has found its opposing anti-energy. In either case, the universe is moving from a structured or higher order to an unstructured or diffuse or random order. The diffuse state of random disorganization is the point of maximum entropy that brings us back to a universe of nothingness or everythingness. Either way, it is an undefinable, meaningless void. All is not lost. The Theory of Volatility tells us to expect a new event, but whatever the event, it is beyond a horizon that nobody will be around to see.
With that cheery thought, let us take a further look at our universe and the physical laws that seem to define its structure.
To Be Continued
CONTINUE To Economic Systems (Expanded View)
Note:
. . . This frame was expanded.
You can return to the Home
Page Index by reducing or
deleting this page.