Note: This essay is the eighth chapter of Mr. Stolyarov's new comprehensive filosofical treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, which can be ordered in electronic format for only $2.50 at http://www.lulu.com/content/140855. Free previews, descriptions, and information on A Rational Cosmology can be found at http://rationalargumentator.com/rc.html .

After we have explicated the relationships of position, motion, and acceleration, it would be fitting to offer a cosmological examination of the concepts frequently employed by theoretical fysics, both of the Classical and post-Classical variety. The idea of a force is correctly used by Classical fysics to explain the cause of acceleration within the bounds to which fysics can rightfully be constrained.

The simplest definition of a force is also the proper one: a force is a push or a pull. Of course, there can be no action, such as a push or a pull, without the entities which originate it. Thus, the cosmological implication of this definition is that a force requires an entity to originate. Also, there can be no push or a pull without an entity which is pushed or pulled. Thus, a force requires an entity to be exerted upon. From all these deliberations, it can be inferred, of course, that forces are relationships, since they require multiple entities to be manifested but are not entities in themselves.

In his capacities as a fysicist, Sir Isaac Newton postulated his Second Law, that the net force acting on an object is a product of the object's mass and its acceleration. All entities have mass, as mass is one of the ubiquitous qualities of entities. Cosmologically, this implies that an entity which is accelerating must have some magnitude of force exerted on it. Since a force can only be exerted by an outside entity, this means that an entity requires another entity to accelerate it or to keep it accelerating. While the involvement of other entities is not required for something to stay in place or move at constant speed, acceleration of anything necessarily implies the activity of some entity external to that which accelerates.

This statement applies equally to mechanical systems that, when taken in whole, cause acceleration to occur within themselves. These mechanical systems are always composites, i.e., made up of smaller entities. It is these constituent entities that exert forces on each other to produce the accelerations necessary to such a system's operation. Though, when the whole system is considered to be an entity, it does not necessarily receive an outside force, it is always necessary to remember that at some permissible reference frame, one will encounter discrete entities exerting forces upon one another in any system. For example, a rocket that moves on the basis of expelling its own fuel does so in accordance with Newton´s Third Law. An action force by an entity (the fuel) causes an equal and opposite reaction force to move another entity (the rest of the rocket after the fuel has been expelled). As will be seen in subsequent chapters, this insight concerns systems of every level of complexity, including living, volitional ones.

How Forces Originate

Some might object to this theory for the interpretation of forces by claiming that it explains only what forces result in and what components are involved in their operation. These objectors would claim that there is insufficient explanation of what causes a given force to arise in the first place. Surely, an entity cannot simply spontaneously "decide" to exert a force on another. The beginning of the answer as to the cause of the force's exertion can be found in Newton's Third Law.

Surely, the greatest merit to Sir Isaac Newton's work has been the ruthless consistency that he maintained between his work as a fysicist and filosofical objectivity, such that no absurdity nor violation of common sense can be found in any of his models and discoveries. Similarly, his Third Law illustrates a cosmological implication that we observe every moment of our lives, yet which few have dared to explicitly frase. According to the Third Law, for every force Entity A exerts on Entity B, Entity B will exert an equal and opposite force (i.e., a force in a direction 180 degrees from that of the first force) on Entity A. There is no time gap between these two force exertions; they occur simultaneously with one another, and both forces are initiated at the same time.

This raises the question as to which entity in this pair is the agent of the force, and which entity is the one being acted upon. The answer to both questions is, both of them. A and B are both originators of the force and its recipients. The reason for why the force exists and is exerted needs not be found outside the system of the two entities in question. The cause of all forces between two entities is the interaction of the natures of the two entities involved, nothing else. One entity does not start the interaction, and the other entity does not follow up. Such terms are inapplicable when discussing how forces come about. Rather, the initiation of a force is a single summary action, in which both entities simultaneously partake and which is caused by the combination of both entities´ properties placed in a certain spatial proximity. In the anatomy of an action-reaction pair, one will find that two distinct forces are always involved, the force of A on B and the force of B on A. Each entity, as a result of its distinct nature, experiences a distinct force from that experienced by the other entity (though of the same magnitude), but the exertion of the forces is a process that goes both ways, a single process that, for the purpose of analyzing the effects on the participant entities, can be mentally separated into the component forces of an action-reaction pair. 

The action-reaction force pair between two entities is the most fundamental acceleration-causing interaction there is. Every multi-entity process involving forces, no matter how complex, can always be interpreted as a set of action-reaction force pairs. To illustrate, three similarly charged metal sferes arranged in a triangular shape and touching each other will be repelled simultaneously in what seems to be a single process. However tempting it might be to attribute this fenomenon to a single force "triple," the repulsion will in fact be the result of three force pairs, the pairs involving, respectively, A and B, A and C, and B and C. Thus, it is true of all force relationships that they occur between two entities, that each entity involved both originates a force and is affected by one, and that this mode of interaction is the root of all acceleration in the universe.

There is no "prime mover."

As brilliant and worthy of admiration as the deliberations of Aristotle might have been, they were not error-free. One of the cosmological fallacies espoused by this thinker was the idea that all motion and acceleration in the universe could ultimately be traced to a single "master" entity, the so-called prime mover, which had originated the motion and acceleration of all other entities. Subsequent theologians have made the argument that the Aristotelian prime mover function is fulfilled by God, and have used Aristotle's reasoning to support their theism. While this is one of the least egregiously flawed religious viewpoints, it nonetheless deserves to be addressed here, as it is a cosmological claim, and an analysis of the proper nature of forces will refute it.

We have seen that a system of two entities of a proper nature requires no forces external to it to bring about the acceleration of its constituents. Since the fundamental origin of all forces is within two-entity systems in which action-reaction pairs arise, this is where our causal chain can stop, with no need for the origin of acceleration to be traced to some outside "prime mover." Furthermore, because we observe multiple two-entity pairs originating forces, we can conclude that forces have no single central origin. Rather, the beginnings of all forces are as localized, numerous, and diverse as the amount of two-entity pairs that have ever interacted in a manner that gave rise to acceleration. This is further reinforced by the truth that the universe is not a single entity, nor do all the entities in the universe behave in a coordinated fashion according to some "master plan." Rather, they act in accordance with their own individual natures, and interact accordingly, with neither need nor possibility for a master mechanism that could coordinate such varied and discrete entities so as to have a single overarching effect upon them. 

Force Fields

A common proposition put forth by fysicists with regard to many fundamental forces which occur at a distance, be they gravitational, electrical, or magnetic, is the idea of a "field" created by an entity which is capable of exerting a certain type of force. When interpreted correctly, this idea is quite useful and cosmologically correct, yet great mistakes have been made with regard to it, especially by empiricist-positivist post-Classical fysicists who had decided to ignore filosofy and treat fields in a manner that yields evident logical contradictions. The mistakes in the interpretation of fields are fundamentally filosofical, yet they have resulted in whole absurd fysical theories, including scores of imaginary massless particles thought to be responsible for certain types of fields, invisible lines which cover all of the universe and are more than the paper models they ought to be, and the multiply flawed idea that a single electric charge somewhere can instantaneously bring about a change in the entire "universal fabric."

Before discussing what a field is not, however, we should first discover what a field is. A hint to the answer can be found in the fact that the common derivation of the very concept involves the use of a "test particle," either of a given unit mass or a given unit charge, which is placed a certain distance from a force-exerting entity. The force exerted upon the test particle at this position becomes known as the strength of the field at said position. That is, the electric field idea merely concisely expresses the knowledge that for every unit of mass, charge, etc., at this location, a force of X Newtons will be experienced, where X becomes the magnitude of the field. The direction of the field is also derived by examining the nature of a given test particle. All gravitational forces attract, thus, any test particle's direction in a gravitational field will be toward the other massive entity. For electric fields, the test particle is assigned a charge, usually positive, and the behavior of a particle so charged then becomes the convention for which way an electric field will be directed at any given location. Thus, the direction of the electric field at a given point is merely the direction in which a particle with the same nature as the test charge will accelerate when a force is exerted upon it at the point.

From this can be inferred that even the very process of defining an electric field depends on the use of two entities, the entity which exerts a given force and the entity upon which a force is exerted. (Of course, the test particle also can be described as having its own field which affects the original field-exerting entity.) Additionally, the model of a field only has fysical consequences when an entity is at a given point which the field is said to encompass. That is, when an entity is present "within the field" of another, there is a force exerted. When no such entity is present at a given point "within the field," all that the field model describes is a potentiality, a knowledge that, if an entity of a given nature were there, it would have a given force exerted upon it. This is useful knowledge to have in order to anticipate positions and behaviors not yet in existence, and the field idea provides convenient symbols and shortcuts to expressing it. However, this model should not be mistaken for an actual fysical existent. The only actual existents are the entities themselves and the forces that they exert. When there is no entity for the field-exerting object to act upon, there can be no force, and the field remains only a convenient abstraction without any fysical existence in itself.

A field qua field is neither entity nor quality nor relationship. It is just an intellectual tool for describing an actual relationship, that of force. All the symbols and diagrams associated with fields are also just reliable predictors of entity behavior. The commonly used "field lines" are a visual expression of both the magnitude (via the lines´ proximity) and direction of the force a given test particle will experience at a certain location "within the field," as well as the trajectory that the test particle will follow at that location. Yet these lines are not actual fysical entities. They are not invisible "roads" that a particle will follow; they are not "woven into" the "fabric of the universe." They are just descriptors of a behavior, one made possible by the presence of entities of a certain type in a certain proximity with respect to one another.

The Impossibility of Non-Local Effects

Before continuing our discussion of fields, it will be fitting to explore a broader concept which will then be applied to further analysis. This concept is at the root of nearly all the fallacies which empiricist-positivist fysicists perpetuate about fields; it is the assumption that such a fenomenon as a non-local effect could conceivably exist.

A non-local effect is one that involves not only a limited amount of participating entities, but the entirety of the entities in the universe (and, in the mistaken view of empiricist-positivist cosmologists, the universal "fabric" in which these entities exist). An entity which exhibits such an effect is presumed to thereby affect everything else that exists, instantaneously and simultaneously.

However, as will be recalled from Chapter IV, all change requires time to take place, and any effect an entity creates implies some change in the entities it affects. A non-local effect, concerning everything as it by definition must, must also therefore occur instantaneously, so as to encompass the entire universe at once. Thus, a non-local effect presumes the occurrence of vast changes of a universal scope without any means for the changes to occur, i.e., the accumulation of time. We therefore know the idea to be false, since any change, and therefore any process, requires some amount of time, however small, to accomplish, and the more entities a given process will affect in the same manner, the more time will be thereby expended in the bringing about of the effect, since the entity originating the process must spend some amount of time affecting each of the entities which the process targets. Thus, a process which is to have some impact on every entity that exists will need to take an extremely long time to be completed, as compared to the time in which that process would affect only a single entity.

As soon as we admit that it would take time for a non-local effect to occur, we thereby admit that it must be a local effect! A given entity affects another, then another, then another, and so on for quite some time, and at every instant during which this process functions, the effect is quite local; only a limited set of entities has been affected, i.e., the entities which it is easiest for the process-originating entity to bring about changes in first. It is true that some entities can, under certain circumstances, affect several others simultaneously and in parallel, as a light bulb will do to two objects the same distance from it, but every entity's resources with which to undertake this simultaneous effect are limited. While the light bulb's luminosity allows it to illuminate a large number of objects in its vicinity, its resources are not nearly of the amount to similarly illuminate every entity that exists.

Fallacies about Fields

The idea of a field as an entity in itself inevitably entails the assertion that it exerts a non-local effect. Most force fields are known to be inversely proportional to distance (or the square of distance) between the entity which is said to originate the field and the entity which is said to be affected by it. However, no matter how large the denominator of the field expression becomes, i.e., no matter how large the distance of separation between the two entities, the magnitude of the field never reaches zero. That is, according to the field-as-entity model, the field must exist at all distances from the entity which originates it, no matter how great, and must therefore encompass all of existence instantaneously and simultaneously, as it is assumed that the field would be established as soon as the originating entity acquires a given mass or charge. The field-as-entity would also need to have infinite measurements in all three of the spatial dimensions, since it can produce effects at any distance, no matter how great. Not only is the idea of an entity having limitless measurements of any quality a logical contradiction, as shall be subsequently seen, but this model also brings about the absurdity of trillions of such infinite field-entities occupying the same space, since multiple entities are observed to originate multiple types of fields! But A is A, and it is impossible for multiple entities to occupy the exact same spatial position at the same time. Thus, being contrary to reality and logically in error, the model of a field as an entity in itself must be rejected.

Even if a field is not an entity, how is it possible to explain the seemingly non-local effect of the field-originating entity needing to exert forces of some magnitude, however small, on the entirety of the entities in the universe in order to be in accord with the equations describing the potentialities for force exertion in a field? In truth, it is impossible for a single entity to act on absolutely everything else that exists, and this fact can be accounted for by including certain caveats to the use of field expressions.

A given field expression is accurate only for a given instant; since fields involve the exertion of forces, and forces cause acceleration, the concept of a field is inextricably tied to the movement of a particle said to be within a field. As soon as the particle begins to move, it is no longer at the same position at which it has been previously, and a different expression now applies to describe type of force which it experiences. Similarly, if the entity said to be "within the field" now experiences a different force, so does the field-originating entity, since it, too, partakes in the action-reaction pair. No entity that exerts a force on another can remain static itself. As the field-originating entity changes its location, so does the nature of the "field" it generates change, and this nature is changed to a far greater extent by closer entities to the entity which originates the field than by entities farther away. Ergo, no field which has any actual fysical consequence can remain constant for more than an instant.

Furthermore, the model of a single isolated field presumes that the entities extremely far from the field-originating entity are affected solely by that field. In fact, these entities have many others close to them, which exert far more powerful forces to determine the behaviors of those entities. This is a practical argument which would lead one to think that the exertion of an extremely small force on an entity extremely far away could well be considered negligible, as far as any legitimate human interests are concerned. However, an even powerful argument exists for the impossibility of non-local effects in the exertion of forces.

An entity, depending on its nature, has only so many actions that it can perform simultaneously and in parallel. It cannot occupy itself with an infinite amount of activities simultaneously, since it has limited measurements of all qualities, and is always constrained by those measurements, of whatever magnitude and whatever sort they might be. No entity could possibly have a sufficiently large amount of measurements of any quality required to affect all the other entities of the universe, for the sum of these measurements would need to equal at least the sum of the measurements of the rest of the entities of the universe, and this, by definition, is impossible, since the universe is the sum of all that exists. While we do not rule out that it is feasible for entities to exert extremely small, even negligible, forces on other entities extremely far away, we can by no means interpret this to mean that every entity produces an active, non-local force effect on every other entity. Only under certain circumstances (i.e. those of a given degree of spatial proximity) and given certain natures of the entities involved, can forces result.

One further fallacy about fields that deserves to be addressed here is the idea that non-contact forces (and thus the field models which apply to them) can be explained by the presence of special types of "particles" which are responsible for the motion of entities in an electric field. Apparently, some fysicists have rejected the very possibility of non-contact forces and have instead tried to explain this fenomenon by inventing entities, such as "gravitrons," that make direct contact with the entities they are supposed to exert forces on, and thereby result in acceleration. Cosmologically, this cannot be, as such entities would need to be massless (especially in the case of "gravitrons," which would otherwise themselves be quite significantly affected by the force of gravity), and mass is a ubiquitous quality of entities. Additionally, an entity without mass cannot exert a force, since by Newton's Second Law, a force can only exist where both a mass and an acceleration exist.  Furthermore, this notion ignores the far better verified Classical idea of action-reaction pairs. If the Earth "sends" gravitrons toward an approaching spaceship, the gravitrons´ pull on the spaceship might explain the force the Earth exerts on it; it would not explain the force the spaceship exerts on the Earth. (Unless the spaceship were to send out an equal and opposite stream of gravitrons at the same time as the Earth, wherein the question would arise as to how these two entities were able to coordinate this exchange with such tremendous precision, how their gravitrons are made possible in the first place, and whether each entity has an inexhaustible amount of gravitrons, or whether it spontaneously stops exerting or experiencing gravity once it runs out.) Far more fundamental notions, belonging both to cosmology and Classical fysics, refute the idea of massless "particles" causing non-contact forces, thus rendering the idea false. To add to this, the idea might be declared moot by Occam's Razor, since, as earlier explained, the two entities involved in the action-reaction pair are quite sufficient to account for how forces originate.

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician and composer, contributor to organizations such as Le Quebecois Libre, Enter Stage Right, the Autonomist, and The Liberal Institute. Mr. Stolyarov is the Editor-in-Chief of The Rational Argumentator. He can be contacted at gennadystolyarovii@yahoo.com.

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