Erwin Marquit: Published in German in Europäische Enzyklopädie zu Philosophie und Wissenschaften [European Encyclopedia of Philosophy and Science], Hamburg: Felix Meiner Verlag, 1990. S. v. “Kraft und Feld.”
FORCE AND FIELD
The term force is abstracted from the application of muscular effort to produce the change in position of some material object or to prevent such change. Among early peoples, the ability to produce or prevent changes of any kind that were beyond human capacity was accorded to deities or to natural elements having consciousness, which, in turn, were regarded as the cause or source of such changes on earth that were beyond the abilities of humans to evoke.. Prayers, sacrifices, and other religious rituals were then invoked to induce the use of this power to meet human needs. These rituals were thus perceived as necessary parts of the productive process and other social activities.
When the philosophers of antiquity, through various combinations of speculative, empirical, and logical activity, began to study the relation between force and motion, the principal methodological approaches necessarily reflected the main conflicting elements of the worldviews that were emerging as a consequence of the class division in society, but on the background of the mythological/religious beliefs that had arisen earlier. The separation of motion into physical, biological, and social changes was often obscured.
The Greek Atomists generally sought materialist explanations, attributing changes in motion to collisions among the indivisible atoms as a result of their different speeds, random orientations ( Democritus), and even spontaneous de flections from straight-line paths ( Epicurus).
The idealist view, however, was the dominant one and was carried over into the concept of forces, often in animistic form, so that the cause of motion of physical objects was attributed to desires, wills, affinities, emanations of spirits, sympathy, antipathy, occult power, etc. on the part of the objects experiencing the motion or change in motion or to objects inducing the motion or change in motion.
To the Ionians, nature was alive, conscious, and capable of self-movement. Empedocles saw motion as the result of the interaction between love and strife. Even the Atomist Democritus, despite his overshadowing materialism, thought, like Plato, that like was attracted to like. These views persisted to the end of the sixteenth century, principally through the influence of Aristotle, according to whom the world consisted of four elements: earth, water, air, and fire. Natural motions such as the falling of stones or the rising of hot gases were attributed to the tendency of material objects to seek their own kind. Aristotle considered departures from this natural motion as violent motions, requiring a push or pull from external forces in contact with the object. In his view, what is now considered to be inertial motion, for example, horizontal motion, was violent motion that was caused by the force of air exerted on the moving object.
A major step toward the de-animation and subsequent materialization of the concept of force was taken by Kepler, who expressed planetary motion in mathematical form, including the dependence on the distance from the sun. In 1621 he concluded that an anima motrix (moving soul) could not be responsible for the velocities of the planets diminishing in exact proportion to the square of the distance from the sun. He proposed that the term vis (force) be used in place of anima (soul).
In the study of statics, also begun in antiquity, the weights of physical objects served as the measure of force. The notion of weight was taken to be intuitively understood. Kepler had associated force with differences in motion, not just position, but f ailed to discover the correct form of the law of gravitation. Isaac Newton, with his three laws of motion and law of universal gravitation, integrated the concept of force in statics with the concept of force proposed by Kepler and presented a general theory of the motion of physical bodies in his Philosophiae Naturalis Principia Mathematica (1687).
Newton gave scientific precision to the concept of force by invoking two distinct but dialectically related types of force. The first was t he innate force (vis insita) of matter, which he also called the inertial force (vis inertiae). He defined this force as “a power r of resisting, by which every body, as much as in it lies, continues in its present state, whether it be at rest or of moving uniformly forward in a straight line. This force differs nothing from the inactivity of the mass, but in our manner of conceiving g it.”' In the discussion of this definition, Newton stated further, “But a body only exerts this force when another force impressed upon it endeavors to change its condition.” He then defined impressed force as follows: “An impressed force is an action exerted upon a body in order to change its state, either of rest, or of uniform motion in a straight line.” In his discussion of this definition he stated: “This force consists in the action only, and remains no longer in the body when the action is over.” Newton thus viewed the mass (“every body, as much as in it lies”) as the physical essence of a body in relation to changes of motion. The innate force is the phenomenal manifestation of this property in response to an impressed force. T he impressed force, which vanishes when its action is over, exists only in relation to the resistance of the body to a change in motion, that is, its existence is conditioned by the existence of the innate force. Innate and impressed forces are therefore mutually conditioned and mutually excluding. Then, in his first law (law of inertia), he stated: `”Every body continues in its state of rest, or of uniform motion in a straight line, except insofar as it is compelled to change that state by forces impressed upon it.” In his second law, Newton then postulated: “The change of motion [momentum] is proportional to the motive force impressed, and is made in the direction of the straight line in which that force is impressed.” In his third law, the quantitative and directional relationship between the innate force and its dialectical opposite, the impressed force, is established: “To every action there is always opposed an equal reaction.” The physical content of force as the quantitatively and directionally determined expression of the (external) cause of change of inertial motion of a physical body is established only through the inseparable linkage of Newton’s definitions of impressed and innate forces with his three laws of motion, which together formed the basis of what has now come to be known as classical, or Newtonian, mechanics.
A problem with Newton's concept of force arises in connection with another dialectical opposition on which it is based, namely, the juxtaposition of uniform straight-line motion with a deviation fro m such motion, acceleration. Newton invoked the a priori existence of an absolute space and time independently of his laws of motion, and then postulated that the inertial motion of a physical body inserted into this preexisting space and time was uniform straight-line motion, that is, displacement over equal segments along a straight line in equal intervals of time.
The separation of concepts of space and time from the concept of matter was criticized by Hegel in his Vor lesungen über die Naturphilosophie: “It is the concept of space itself that creates its existence in matter. Often a beginning has been made with matter, and then space and time regarded as forms of matter. . . . Just as there is no motion without matter, so also there is no matter without motion.” In 1915, Einstein, in his general theory of relativity, actually gave the physical basis in mathematical form for the relationship been space and time and the distribution of matter.
Newton's conception of an a priori space and time, as was the case later with Kant, had its origin in the fact that spatial and temporal concepts were needed long before a structured scientific theory of space and time had been elaborated. Considering as a priori the historically evolved notions of space and time and incorporating them into his description o f motion, Newton then postulated his laws of motion with the logical structure of a hypothetico-deductive system. From these laws it would follow that a rope to which a force was applied at both ends (if its mass were negligible) would form a straight line, and that from a water clock (powered by the force of gravity on the water in a vessel with a small opening at the bottom) equal quantities of water would emerge in equal intervals of time, and that earth’s inertial rotational motion about the sun could also form the basis for a unit of time. Without the assumption of an a priori space and time, Newton’s hypothetico-deductive system thus appears, on the surface, to be based on circular reasoning. However, Newton's science of mechanics and the concept of force associated with it are not logically defective. His first law postulates the existence of motion in the absence of external (impressed) forces. It postulates further that this motion is uniform straight-line motion. Therefore, in the absence of a force, a body already set in motion will move along a straight line with unchanging velocity. The straight-line uniform motion established empirically in this way is theoretically a possible template for straightness and for quantitative standards of length and time. In practice, however, the standards of straightness, length, and time a re based on other processes linked theoretically to these laws. Once standards of straightness, length, and time are thereby determined empirically, the subsequent presence of a force can be detected by a deviation from inertial motion. What mathematicians call the flat space-time of a Euclidean world proves to be, for most engineering and scientific applications, an adequate representation of these empirically determined physical spatial and temporal relations in the region of earth and other parts of the solar system sufficiently distant from the stronger gravitational fields near, say, the surface of the sun.
Force and Causality
Newton, in his early drafts of the law of inertia, used the term cause in the same sense that he later used the word force, for example, “a quantity will always move on in the same straight line . . . unless some external cause divert it.” The cause-effect relationship, however, has greater generality as a stage in cognition than the relation between force and change in mot ion—see Causality. The cause for a change in (mechanical) motion of a physical body cannot only be the force impressed on it, but also the object from which this impressed force arises (for example, one object colliding with an other), or the interaction between two or more objects giving rise to the force (for example, gravitational attraction).
Newton' s identification o f force with one particular aspect of the cause of change in motion had the effect of reducing the entire complex of concrete interactions of one body with other bodies to an abstract physical environment representable mathematically merely by a magnitude and spatial direction (a vector).
In its interaction with real physical environments, however, a physical body is, in general, subject not only to changes in its mechanical motion, but also to qualitative changes. Similarly, real physical bodies can undergo qualitative change as a result of interactions internal to the body. For a wide range of practical purposes, however, where such qualitative changes can be ignored, the subsuming of the external environment under an externally applied force provides a powerful means for determining the resultant change in mechanical motion.
Force and Action at a Distance
As long as force was associate d with wills, affinities, desires, and the like, physical contact did not appear to be necessary, just as two people can be attracted to one another without physical contact. Electric and magnetic forces, like gravitational forces, also appeared to act at a distance. Action at a distance, however, conflicted with the intuitive materialism of nineteenth-century physical scientists. In the 1830s, Faraday introduced lines of force as the agent carrying the force of interaction through the space between electric charges and magnetic poles. Maxwell subsequently replaced the lines of force with electric and magnetic fields, which he perceived as tensions and stresses in this intervening s pace. Field concepts provided a welcome alternative to action at a distance.
In general, a field is a physical property that is associated with a magnitude or set of magnitudes (scalars, vectors, or tensors) the values of which depend on the time and position in space. In the mideighteenth century Euler introduced fields to represent velocities and other physical characteristics of fluids in connection with the development of hydrodynamics. In its extension to forces in the nineteenth century, the magnitude of an electric, magnetic, or gravitational field at a given point in space and time is equal to the force on a unit electric charge, unit magnetic pole, or unit mass, respectively, the field having the same direction as the force at that position.
The question immediately arose: Are fields physically real or are they merely mathematical devices for determining the force? If the physical reality of fields is established, there is no need f or action at a distance. The answer to the question depends on what is meant by physical reality.
In his Materialism and Empirio-Criticism (1908), Lenin began his discussion of matter as a philosophical category by considering the dialectical connection between what he regarded as the two most fundamental categories of philosophy: matter and consciousness (see Matter). Among the criteria of materiality that he suggested are existence independent of, but appropriable by, our consciousness, ability to affect the senses (directly or indirectly), and existence in space and time. If objects meet these criteria, they are material objects. Fields giving rise to physical forces satisfy these criteria of materiality and are therefore physically real. A physical field that exerts a force on a physical body (in the Newtonian sense) is acting directly on the body and not acting at a distance.
Forces and Interactions
The term interaction is more general than that of force. Among the possible consequences of an interaction are not only a change in the state of motion, the immediate cause of which is a force, but also a wide range of qualitative changes in the state, such as vaporization, radioactive decay, and chemical changes. When interactions involve individual atoms or subatomic particles, the representation of the motion of a physical object in classical mechanics (macrophysics) as a sequence of precisely defined positions ceases to be generally adequate (see Physics). This inadequacy also applies to the representation of the spatially extended bodies themselves. The physics of the microworld (microphysics) does, however, borrow many concepts from macrophysics, and objects of the microworld (microobjects) are represented alternatively as particles, waves, and fields. Similarly, the macroscopic concept of force as the cause of a change in motion is carried over into the microworld.
In the macroworld, the sources of forces are the gravitational and electromagnetic interactions. In the microworld, however, two additional forces or interactions are known at the present time, the hadronic (or strong) interaction and the weak interaction. The hadronic and weak interactions, take n together with the gravitational and electromagnetic interactions, are responsible for the existence of the smallest objects known, e.g., baryons, leptons, bosons, photons, mesons, quarks.
In the microworld, the absence of sharp boundaries that are used to characterize, say, a macroscopic solid spherical body affects the relationship between the concept of field and the physical body on which it exerts a force. The radius of the proton, for example, does not define a spherical surface marking a sharp boundary separating the “substance” of the proton from the space outside it, but rather a distance characterizing the spatial region in which the short-range hadronic interactions become significant. In this meaning of radius, the proton itself is a relatively (spatially) concentrated field rather than a physical body composed of some underlying substance with a sharp boundary. The change in motion, say, in a collision between two protons can then be viewed as the product of an interaction between fields. The concept of forces arising out of interactions between fields is not, however, limited to microphysics. In fact, Faraday’s original representation of fields by lines of force and Maxwell’s subsequent mathematical analysis of them involved the existence of stresses and tensions within the fields.
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