ENERGY

Energy, from the Greek energeia (en, in; ergon, work), originally a technical term in Aristotelian philosophy denoting "actuality" or "existence in actuality," means, in general, activity or power of action. In the physical sciences it is defined as the capability to do work, as accumulated work or, in the words of Wilhelm Ostwald, as "that which is produced by work or which can be transformed into work." Energy is measured in terms of units of work, to overcome a resisting force of one dyne over a distance of one centimeter. (The joule = 10⁷ erg = the watt-second; the kilogram-meter = 9.81 × 10⁷ erg. In atomic physics the unit is the electron volt; ev = 1.6 × 10⁻¹² erg.

In physics, energy is either kinetic or potential. A body of mass m moving with a velocity v possesses, owing to its motion, the kinetic energy ½mv ², which is the work necessary to overcome the inertial resistance in accelerating the body from rest to its final velocity and which is again transformed into work if the body is brought to rest. The energy that a system of bodies possesses by virtue of the relative geometrical position of its constituent parts, if subjected to gravitational, elastic, electrostatic, or other forces, is its potential energy. If, for example, a stone is raised from the surface of the earth, the potential energy of the system stone-and-earth is increased; if an elastic spring is expanded, its potential energy increases with increase of length. The attribute "potential" thus merely characterizes the latency of temporarily stored energy and does not call into question the reality of this kind of energy. With the recognition of the principle of the conservation of energy, it became apparent that the concept of energy applies to all branches of physics and to all physical sciences. Because of the at least partial convertibility of any energy into mechanical work, the aforementioned units of work also serve as measures of such energies as thermal, electric, magnetic, acoustic, and optical. For thermal energy (heat) it proved practical also to retain as a separate unit the caloric unit of heat, the calorie (equal to 4.18 × 10⁷ erg).

History of the Concept

In spite of its universality, the general notion of energy as a basic concept in science is a relatively recent result of a long and intricate conceptual process. From the scientific point of view this process may conveniently be divided into five consecutive stages: (1) early conceptions of energy as a source of force, (2) the rise of the concept of mechanical work, (3) the recognition of different forms of energy, of their interconvertibility, and of the conservation of their sum total, (4) the emancipation of energy as an autonomous existent, and (5) the mathematization of energy as an integral invariant. From the philosophical point of view—that is, with respect to the ontological and epistemological status of the concept of energy—one may speak of (1) accidental, (2) substantial, (3) relational, (4) causal, and (5) formal conceptions of energy.

energy and force

Aristotle was the first to use energeia as a technical term in his conceptual scheme, where it often signified the progressive "actualization" of that which previously existed only in potentiality. He also seems to have formed, though in an implicit manner, the idea of energy in the sense of accumulated force or accumulation of force. Force, for him, was not only the cause of motion but also the factor determining the duration or extent of motion. In the Physics he formulated the fundamental law of his dynamics, which, in modern terminology, states that the velocity, D/T (distance divided by time), of a mobile is proportional to the ratio of the magnitude of the moving force, A, and the resistance, B, a relationship that he described by enumerating exhaustively all possibilities under which AT/BD remains constant (with the exception of doubling the distance, D, as well as the time, T ). He argued that a given finite force cannot move a mobile over an infinite distance or for an infinite time. Aristotle thus associated with every force a capacitative limitation, or, in modern terms, an energy content.

The implications of this statement for cosmology—in particular, for the motion of the celestial spheres, which derive their eternal motion ultimately from the "first mover" in accordance with the axiom "all things that are in motion must be moved by something else"—called for further clarifications. Thus, for example, Averroes, in his "Commentary on the Physics," distinguished between the primary motive force, the motor separatus, and the secondary forces, the motores coniuncti ; the latter, in direct contact with the spheres, corresponding to the medieval "intelligences," draw finite quotas of force from the inexhaustible supply of the former. By this process, according to which only finite amounts are subtracted from an infinite accumulation of force, Averroes thought he was able to explain both the eternity of celestial motion and the fact that this motion does not occur instantaneously (in instanti ), as motion under the effect of an infinite cause should do.

Considerations of this kind, which engaged Aristotelian commentators until the times of Thomas Aquinas, show clearly that the notion of force signified not only the immediate cause of motion or acceleration but also its cumulative determination, or energy content. Thomas considered the possibility of a finite and yet invariable moving force, which, being immutable, acts always in the same manner (vis infatigabilis ), and thus he conceived of force as a moving agent independent of and separated from a constantly rejuvenating source, a notion essential for the future conception of the universe as a clockwork in action without the need of a constant supply of additional energy. Early in the fourteenth century the nominalist Peter Aureoli, in Liber Sententiarum, distinguished explicitly between two different aspects of force: its velocity-determining property and its capacity of consumption, or measure of exhaustibility. His differentiation can rightfully be regarded as the first ontological distinction between force and energy.

This, of course, does not imply that allusions to particular forms of energy are not found in early scientific writings. In fact, already in the Mechanica, commonly ascribed to Aristotle, the notion of kinetic energy is clearly referred to when it is asked:

How is it that, if you place a heavy axe on a piece of wood and put a heavy weight on the top of it, it does not cleave the wood to any considerable extent, whereas, if you lift the axe and strike the wood with it, it does split it, although the axe when it strikes the blow has much less weight upon it than when it is placed on the wood and pressing on it? It is because the effect is produced entirely by movement, and that which is heavy gets more movement from its weight when it is in motion than when it is at rest.

mechanical work

The modern concept of energy, as the definition shows, is a generalization of the notion of work in mechanics. The concept of work can be traced back to the principle of virtual displacements, or virtual velocities, which, in turn, has its ultimate origin in Aristotelian dynamics. Aristotle's conclusions (in De Caelo ) concerning one single force (under whose action "the smaller, lighter body will be moved farther …; for as the greater body is to the less, so will be the speed of the lesser body to that of the greater") were soon generalized for the case of a force counteracting a load, as exemplified in simple machines such as the wheel and the axle. In particular, the study of the law of the lever, as mentioned in the Mechanica, in Archimedes' On the Equilibrium of Planes, in the writings of Hero of Alexandria, and in the Liber Karastonis, a Latin version of the ninth-century Arabic text by Thabit ibn Kurrah, contributed to the gradual establishment of the principle of virtual displacements for which finally, in the thirteenth century, Jordanus Nemorarius tried to give a theoretical proof. The Renaissance formulation of this law—namely, that the ratio between force and load is reciprocal to that of the spaces (distances) traversed within the same time—as pronounced by Guidobaldo del Monte (Mechanica, 1577), by Simon Stevin (Hypomnemata Mathematica, Leiden, 1608, Book 3), and by Galileo Galilei (Opere 2), formed the basis for the definition of work as force times distance traversed.

Pierre Varignon, in his Nouvelle Mécanique ou statique (Paris, 1725), reported a letter from Johann Bernoulli, dated January 26, 1717, in which the term energy appears in this connection, apparently for the first time in the modern period: "For all equilibrium of forces in whatever manner they are applied to each other, whether directly or indirectly, the sum of the positive energies will be equal to the sum of the negative energies taken positively." Although some historians, referring to this letter, have ascribed to Bernoulli the definition of energy as "force times distance," a critical study of the text shows undoubtedly that he still defined energy as "force times virtual velocity." In spite of the fact that this notion and its derivative, namely, the notion of work defined as "force times distance," played at least implicitly an important part in the establishment of classical mechanics—Joseph Louis Lagrange saw in the principle of virtual velocities the fundamental basis for his Mécanique analytique (1788), the highlight of classical mechanics—energy considerations were rarely found in theoretical or even practical mechanics prior to the middle of the nineteenth century. Before the development of the steam engine and the rise of thermodynamics, industry had little interest in energy calculations: Force, not its integrated form, counted in the use of simple machines. The primary object of theoretical mechanics, moreover, was still celestial dynamics, where, again, energetics was of little avail. This certainly is also one of the reasons why Isaac Newton's Principia contains practically no reference to the concept of energy or to any of its applications.

According to Ernst Mach, in Die Mechanik in ihrer Entwicklung (Leipzig, 1883; translated as The Science of Mechanics, La Salle, IL, 1942), the delay of the development of energetics as compared with that of general mechanics stemmed from what he called "trifling historical circumstances," namely, the fact that in Galileo's investigations of free fall, the relationship between velocity and time was established before the relationship between velocity and distance, so that, as multiplication with mass shows, the notions of quantity of motion or momentum and force gained priority and were regarded as more fundamental than the concept of energy, which thus appeared as a derived conception. Whatever the reason for energetics' lagging behind Newtonian mechanics, it is an indisputable fact that the concept of energy became a subject of discussion among philosophers rather than among physicists or mechanicians.

the measure of "force"

Foremost among the philosophical discussions was the controversy between the Cartesians and Gottfried Wilhelm Leibniz over whether the true measure of "force" (i.e., energy) is momentum (the product of mass and velocity) or vis viva (as defined by Leibniz, the product of mass and the square of velocity). René Descartes, having shown in his Principles of Philosophy that the (scalar) quantity of motion or momentum (the vectorial nature of this quantity was recognized only by Christian Huygens) is conserved, concluded that momentum is the measure of energy. Leibniz, in "A Short Demonstration of a Remarkable Error of Descartes" ("Brevis Demonstratio Erroris Memorabilis Cartesii," in Acta Eruditorum, 1689), opposed this view. Lifting a load of 1 pound, he claimed, to a height of 4 feet requires the same work as lifting 4 pounds to the height of 1 foot. Since, according to Galileo, the velocities (of free fall) are proportional to the square roots of the heights (of fall), the velocity of the first object is twice that of the second before reaching ground, or v ₁ = 2v ₂. Assuming that the "forces" (energies) are proportional to the masses (moles), Leibniz concluded that m ₁ · f (v ₁) = m ₂ · f (v ₂), where f (v ) is an as yet unknown function of the velocity, v. Substituting m ₂ = 4m ₁ and v ₁ = 2v ₂ yields f (2v ₂) = 4 · f (v ₂), which shows that the unknown function is quadratic in its argument, v. What is conserved and hence is the measure of "force," Leibniz concluded, is mv ².

This controversy between the Leibnizians, among them Johann Bernoulli, Willem Jakob Gravesande, Christian von Wolff, Georg Bilfinger, and Samuel König, and the Cartesians, among them Colin Maclaurin, James Stirling, and Samuel Clarke, was essentially only a battle of words, since the Leibnizians considered force acting on bodies traveling over equal distances and the Cartesians considered force acting on bodies during equal intervals of time, as Jean Le Rond d'Alembert in Traité de dynamique (1743) and Lagrange in Mécanique analytique (1788) made clear.

conservation of "force"

The interesting aspect of the Leibnizian-Cartesian controversy is the fact that both sides argued on the basis of the conservation of their respective "measures": for the Cartesians it was the conservation of momentum, for the Leibnizians that of "living force" (kinetic energy). Both contentions, as we know today, were correct, since both measures are integrals of the equations of motion. One of the most ardent supporters of Leibniz was his disciple Christian von Wolff, who in the Cosmologia Generalis (1731) declared: "In all the universe the same quantity of living force is always conserved." Johann Bernoulli, in the essay "De Vera Notione Virium Vivarum" (in Acta Eruditorum, 1735), was probably the first to treat this statement of the conservatio virium vivarum as a fundamental principle in mechanics. The apparent loss of "living force" in inelastic collisions was usually explained away by the hypothesis that the invisible small parts of matter gain in vis viva just as much as the macroscopic bodies seem to lose, a view Leibniz had already expressed in Essai de dynamique and reaffirmed in a letter to Samuel Clarke (Fifth Letter, August 18, 1716), where he stated that "active forces are preserved in the world" and continued: "'Tis true, their wholes (unelastic colliding bodies) lose it with respect to their total motion; but their parts receive it, being shaken by the force of the concourse. And therefore that loss of force is only in appearance. … the case here is the same, as when men change great money into small." Johann Bernoulli, in contrast, explained this apparent loss as an absorption of force required for the compression of the colliding bodies.

transformation of potential energy

What Bernoulli had in mind was obviously the so-called latent force, subsequently to be called potential energy, and his is the earliest description of transformation of kinetic energy into potential. The idea of such "latent force" was soon generalized to nonmechanical processes. Already in 1738 Daniel Bernoulli, in his Hydrodynamica, sive de Viribus et Motibus Fluidorum Commentarii, spoke of the "latent force" of combustible coal, which "if totally extracted from a cubic foot of coal and used for the motion of a machine, would be more efficient than the daily work of eight or ten men." But the measure of this "latent living force" was still mv ².

Strictly speaking, the notion of potential—that is, a function whose space derivatives yield the force components and which therefore equals the potential energy for a unit of mass, charge, etc.—preceded the idea of potential energy. For in 1777, Lagrange, in "Recherches sur l'attraction des spheroides homogènes" (Mémoire de l'Académie, Paris), calculated the potential for an arbitrary discrete distribution of mass particles, and in 1782, Pierre Simon de Laplace calculated the potential for a continuous distribution. Potentials were still spoken of as "force functions"; the term potential function was introduced for the first time in 1828 by George Green in his Essay of the Application of Mathematical Analysis and later (1840), independently, by Karl Gauss.

When, in 1788, Lagrange derived the principle of the conservation of mechanical energy, or what subsequently was generally called the "theorem of the living force," as an integral of the equation of motion, he asked himself how many such integrals exist and under what conditions. The question, however, whether a similar principle exists also for nonmechanical processes did not occur to him.

The first clear and consistent terminology of energy conceptions, still in the domain of mechanical processes, was used by the Paris school of practical mathematicians and mechanicians, not by the purely analytical school headed by Lagrange and Laplace. It was Lazare Carnot who, in his Essai sur les machines en général (1783; republished in 1803 in a revised and enlarged edition under the title Principes fondamentaux de l'équilibre et du mouvement ), declared that the "living force" can manifest itself either as mv ² or as Fd (force times distance), the second being a measure of the "latent living force." Jean V. Poncelet, in Mécanique industrielle (1829), finally introduced for this quantity the term mechanical work and stated distinctly that it is the inertia of masses that serves for the accumulation of work and thus enables the transformation of work into "living force" and vice versa. Poncelet also measured this quantity by the kilogrammeter, a unit of energy universally adopted since then.

We thus see how at the beginning of the nineteenth century the notions of work and living force and their transformability became firmly established within the confines of mechanics proper. Even the energy was used in this connection. In A Course of Lectures on Natural Philosophy (London, 1807), Thomas Young, though an adherent of the Cartesian measure of force, admitted that "in almost all cases of the forces employed in practical mechanics, the labour expended in producing any motion, is proportional not to the momentum, but to the energy which is obtained." But it took another fifty years until the term energy in its present meaning acquired full citizenship within the vocabulary of the physical sciences. This was brought about from quite a different quarter. It derived from the study of those phenomena where heat and chemical change are the characteristic features.

conversion processes

Although Francis Bacon, in his Novum Organum, had already stated that "the very essence of heat, or the substantial self of heat, is motion, and nothing else," and although similar statements had been made even before the seventeenth century, the late eighteenth century, in general, interpreted heat as a fluidum, in the spirit of the phlogiston theory. Still Jean B. J. Fourier, in his Théorie analytique de la chaleur (1822) declared: "Thermal processes are a special kind of phenomena which cannot be explained by the principle of motion and of equilibrium." Although Joseph Black's doctrine of latent heat accounted for the disappearance of heat on the basis of the fluidum theory, the appearance of heat, as Count Rumford's experiments, at Munich in 1796 and 1798, with the boring of cannon clearly showed, was incompatible with this theory. Having eliminated all sources from which the heat produced during the boring could have originated, Rumford concluded that "it appears to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner the heat was excited and communicated in those experiments, except it be motion."

At the same time (1799) Humphry Davy performed at the Royal Institution in London his famous experiment in which two pieces of ice were rubbed together by a clockwork mechanism in a vacuum, the whole apparatus being maintained at the freezing point of water. Davy concluded that heat was "a peculiar motion, probably a vibration of the corpuscles of bodies" (Essay on Heat, Light, and the Combinations of Light, London, 1799). Rumford's and Davy's experiments, though in their quantitative aspects not yet fully explored, suggested the interchangeability of heat and motion and thus led to the more general idea of an interconvertibility, or "correlation," of the forces of nature, previously regarded as disparate and incommensurable.

Approaching this problem from a chemical and biological point of view, Justus von Liebig, one of the earliest investigators of the economy of living organisms, advanced the theory that the mechanical energy of animals, as well as the heat of their bodies, originated from the chemical energy of their food. Such physiological experiments as those carried out in Liebig's laboratory made possible the study of conversion processes and together with increased concern with engines and natural philosophical considerations, seem to have been responsible for the independent discoveries, between 1837 and 1847, of the principle of energy conservation. In fact, Liebig's pupil Friedrich Mohr, adopting the mechanistic view that all forms of energy are manifestations of mechanical force, wrote as early as 1837: "Besides the known fifty-four chemical elements there exists in nature only one agent more, and this is called 'Kraft' ['force']; it can under suitable conditions appear as motion, cohesion, electricity, light, heat, and magnetism."

energy conservation principle

Robert von Mayer, a physician from Heilbronn, Bavaria, who had served on a ship in the tropics, had noted that the venous blood of his patients there was redder than it had been in Europe. He explained this difference by an excess of oxygen due to a reduced combustion of the food that provided the heat of the body. He thus concluded that chemical energy, heat of the body, and muscular work are interconvertible, an idea that he pursued upon his return by a quantitative investigation of the mechanical equivalent of heat. The first enunciation of the energy conservation principle, combined with the determination of the mechanical equivalent of heat, is found in Mayer's article "Bemerkungen über die Kräfte der unbelebten Natur" (in Liebig, ed., Annalen der Chemie und Pharmacie, 1842, Vol. XLII, pp. 233–240). His calculations, as explained in greater detail in his Die organische Bewegung (1845) were based on the difference of the specific heats of air at constant volume and at constant pressure, as measured by F. Delaroche and others, yielding, in modern units, 3.65 joule per calorie; had Mayer employed Henri Regnault's more accurate results he would have arrived at 4.2 joule per calorie, the currently accepted value. The amount of heat liberated by the expenditure of mechanical or electrical work was systematically measured by James Prescott Joule, a Manchester brewer and amateur scientist. In heating liquids by the rotation of paddle wheels, forcing water through narrow tubes, or compressing masses of air, Joule demonstrated that the expenditure of the same amount of work, irrespective of the manner in which this work was done, resulted in the development of the same amount of heat. His measurements of such conversion processes gave a firm quantitative support for the conservation principle.

The discovery of the physical principle of the conservation of energy was soon found to be in full agreement with the principal tenets of the prevailing natural philosophy, the German Naturphilosophie, whose early proponent, Friedrich Wilhelm Joseph von Schelling, had declared in 1799, in Einleitung zu dem Entwurf eines Systems der Naturphilosophie, "that magnetic, electrical, chemical, and finally even organic phenomena would be interwoven into one great association … [which] extends over the whole of nature." Mayer supported his own conclusions by the metaphysical argumentation that forces are essentially causes and "causes equal effects"; since causes are indestructible and convertible into effects, forces must likewise be indestructible and interconvertible. Even the experimentalist Joule, in an article "On the Calorific Effects of Magneto-electricity, and on the Mechanical Value of Heat" (Philosophical Magazine, series 3, 23 [1843]: 442), declared: "I shall lose no time in repeating and extending these experiments, being satisfied that the grand agents of nature are by the Creator's fiat indestructible." In another paper (in Philosophical Magazine, series 3, 26 [1845]: 382) he stated: "Believing that the power to destroy belongs to the Creator alone, I entirely coincide with Roget and Faraday in the opinion, that any theory which, when carried out, demands the annihilation of force, is necessarily erroneous." The conduciveness of the philosophical climate toward the enunciation of the energy principle can most clearly be recognized from the arguments of A. Colding, who arrived at the principle independently of Mohr, Mayer, and Joule:

The first idea I conceived on the relationship between the forces of nature was the following. As the forces of nature are something spiritual and immaterial, entities whereof we are cognizant only by their mastery over nature, these entities must of course be very superior to everything material in the world; and as it is obvious that it is through them only that the wisdom we perceive and admire in nature expresses itself, these powers must evidently be in relationship to the spiritual, immaterial, and intellectual power itself that guides nature in its progress; but if such is the case, it is consequently quite impossible to conceive of these forces as anything naturally mortal or perishable. Surely, therefore, the forces ought to be regarded as absolutely imperishable. ("Nogle Soetninger om Kraefterne," 1843, in Philosophical Magazine, series 4, 27 [1864]: 56–64).

Even the classic paper of Hermann von Helmholtz, the physiologist turned physicist, "On the Conservation of Force" (Über die Erhaltung der Kraft, Berlin, 1847), shows clearly the impact of contemporaneous philosophy, with its renunciation of Hegelianism and its reversion to an idealistic rationalism, when it declares:

The final aim of the theoretic natural sciences is to discover the ultimate and unchangeable causes of natural phenomena. Whether all the processes of nature be actually referrible to such—whether changes occur which are not subject to the laws of necessary causation, but spring from spontaneity or freedom, this is not the place to decide; it is at all events clear that the science whose object it is to comprehend nature must proceed from the assumption that it is comprehensible.

The requirement of referring the phenomena of nature back to unchangeable final causes was interpreted by Helmholtz as reducing physical processes to motions of material particles possessing unchangeable moving forces that are dependent on conditions of space alone. Thus, Helmholtz, starting with the eighteenth-century dynamics of bodies acting under mutual attraction, generalized the Newtonian conception of motion to the case of a large number of bodies and showed that the sum of force and tension (what we now call kinetic and potential energies) remain constant during the process of motion. Applying conventional analytical mathematics, Helmholtz proved that the principle of the conservation of living force not only can be derived from Newtonian dynamics but may also serve as an equivalent point of departure for the deduction of theoretical mechanics.

This fundamental assumption may be formulated as the principle of the impossibility of a perpetuum mobile. When a system of particles acting under central forces passes from one configuration to another, the velocities acquired can be used to perform some work; in order to draw the same amount of work a second time from the system, one would have to restore its initial conditions by expending on it forces or energy from outside the system. The principle now requires that the amount of work gained by the transition from the first position to the second and the amount of work lost by the passage of the system from the second configuration to the first be equal, no matter in what way or at what velocity the change has been effected; otherwise a perpetuum mobile could be constructed on the basis of this cycle, contrary to the principle. So far Helmholtz's reasoning is but a paraphrase of the arguments used by Sadi Carnot and Benoît Clapeyron in their foundations of the thermodynamics of heat engines. By replacing the concept of work by that of "tensions" (verbrauchte Spannkräfte ), which are equal but of opposite sign to the work performed, Helmholtz transformed the equation between living force (kinetic energy) and work into the statement that the sum of living force and tension is a constant, the tension being a function of the instantaneous state of the system. Although prima facie an insignificant change, this reformulation of the mechanical principle of the conservation of living force through the introduction of "tensions" opened up incalculable perspectives in that it could be applied to all branches of physics, not only to mechanics proper. Moreover, the new formulation was strikingly analogous to that of the principle of the conservation of matter, or mass, an accepted axiom in physical science since the times of Antoine Lavoisier. Exploiting the adaptability of the concept of "tension" to nonmechanical phenomena, Helmholtz not only reconciled the new doctrine of heat with the theory of mechanics, heat explicitly being treated as a form of energy, but also demonstrated the validity of the conservation principle for electrodynamics and other departments of physics. The recognition that mechanical work, heat, and electricity were only different forms of one and the same physical substratum—a result that can rightfully be considered the greatest physical discovery of the nineteenth century—found its analytical vindication in Helmholtz's paper.

At first, however, Helmholtz's memoir was hardly recognized, since its argumentation was based on mathematical reasoning, which at this time was accessible to but a small number of specialists. Another fundamental obstacle in the way of a just assessment of the new truth was the indiscriminate homonymous usage of the term force in both its Newtonian and its Leibnizian significations. Once the semantic difficulties had been removed, the principle of the conservation of energy found general acceptance and even popularity, owing to the writings of William Thomson (Lord Kelvin). In a discourse before the Royal Institution in 1856, Thomson distinguished carefully the significance of the Newtonian notion of force from what he called "energy." The term energy —apart from its early usage by Bernoulli and Young—had already been used three years earlier by William Rankine in his "On the General Law of the Transformation of Energy" (Philosophical Magazine, series 4, 5 [1853]: 106), but only Thomson's application led to its universal acceptance. "Any piece of matter or any group of bodies, however connected, which either is in motion, or can get into motion without external assistance, has what is called mechanical energy. The energy of motion may be called either 'dynamical energy' or 'actual energy.' The energy of a material system at rest in virtue of which it can get into motion, is called 'potential energy'" (On the Origin and Transformation of Motive Power, 1856). In 1893, in a footnote to a reprint of his 1856 lecture (in Popular Lectures and Addresses, London, 1894, Vol. II), Thomson wrote: "Shortly after the date of this lecture I gave the name 'kinetic energy' which is now in general use. It is substituted for 'actual' and for 'dynamical.'" Thus Helmholtz's "tension" was renamed "potential energy," and the sum total of kinetic and potential energies, the total energy of the system, was shown to be a constant that is characteristic of the system.

These innovations, however, had still to overcome some opposition. The Rankine-Thomson designation "potential energy" was rejected by John F. W. Herschel ("On the Origin of Force," in Fortnightly Review and Familiar Lectures, 1857) as "unfortunate," being too common a name for such a "great truth." Even the term conservation of force or energy was subjected to severe criticisms, particularly by T. H. Huxley and by Herbert Spencer in his First Principles (1862), on the ground that "conservation" implies a conserver and an act of conserving and therefore the assumption that without such an act, force (energy) would disappear—an idea at variance with the conception to be conveyed. But in addition to the terminology, the conception itself, particularly that of potential energy, was still a matter of debate. An interesting testimony to these difficulties is Michael Faraday's paper "On the Conservation of Force" (Philosophical Magazine, series 4, 13 [1857]: 225–239), in which the following problem is raised: Is there creation or annihilation of force if the distance between two gravitating bodies is changed and the attractive force varies inversely with the square of the distance? "Gravitation," Faraday continued, "has not yet been connected by any degree of convertibility with the other forms of force…. That there should be a power of gravitation existing by itself having no relation to the other natural powers, and no respect to the law of the conservation of force, is as little likely as that there should be a principle of levity as well as of gravity." Rankine's answer to Faraday's objection (Philosophical Magazine, series 4, 17 [1859]: 250) seems to have had little effect, for as late as 1876, James Croll, in his paper "On the Transformation of Gravity" (Philosophical Magazine, series 5, 2 [1876]: 242–254), attempted to solve Faraday's query with the assumption that "a stone when in the act of falling [may] be acted upon by gravity with less force at any given moment than it would be were the stone at rest at that instant."

the emancipation of energy

Although Croll's paper is full of misconceptions, which, interestingly, were clarified in an answer by the Viennese physiologist Ernst von Brücke, "On Gravitation and the Conservation of Force" (Philosophical Magazine, series 4, 15 [1858]: 81–90), it was of great importance for the subsequent development of the concept of energy. It connected the notion of energy for the first time with that of space. That space and change of position are necessary conditions for energy transformations Croll tried to demonstrate by the following consideration: four possibilities of energy transformations are conceivable—a change of potential energy into kinetic, of kinetic into potential, of kinetic into kinetic, and of potential into potential. Since, however, there "is evidently no such thing in nature, so far as is yet known, as one form of potential passing directly into another form" of potential energy and the existence of kinetic energy always implies change of position, the point is proved. Having thus associated energy with space, Croll went on to dissociate it from the material medium. "Our inability to conceive how force can exist without a material medium has its foundation in a metaphysical misconception," an idea he explained in greater detail in his book Philosophy of Theism (London, 1857). Croll's almost casual remarks, though scientifically rather objectionable and philosophically highly speculative, may be regarded as the earliest objection to the prevailing view, which still conceived of energy as an attribute, so to speak, of the dynamic system.

Meanwhile, James Clerk Maxwell's Treatise on Electricity and Magnetism (1873) appeared, opening the way for a field-theory treatment of electromagnetic phenomena. It showed, in particular, that the work necessary to build up an electromagnetic field can be regarded as equivalent to the energy produced in space with a certain density that depends on the squares of the magnitudes of the electric and magnetic fields. In the case of nonstatic fields these calculations lead to the conclusion, as was shown by J. H. Poynting in "On the Transfer of Energy in the Electromagnetic Field" (Philosophical Transactions of the Royal Society 175 [1885]: 343–361), that energy has to flow from one place in space to another in order to compensate for changes that occur in a particular region of space. A transfer of energy, it is true, had been associated with electricity before Poynting, but the energy flow was always considered as being confined to the conducting wires.

But the existence of induced currents and of electromagnetic actions at a distance from a primary circuit from which they draw their energy, has led us, under the guidance of Faraday and Maxwell, to look upon the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, that is, if we believe that when it disappears at one point and reappears at another it must have passed through the intervening space, we are forced to conclude that the surrounding medium contains at least a part of the energy, and that it is capable of transferring it from point to point.

Thus the surrounding medium or empty space became the arena in which energy moves, and energy, disjoined from matter, was raised in its ontological status from a mere accident of a mechanical or physical system to the autonomous rank of independent existence: matter ceased to be the indispensable vehicle for its transport. Mechanics, with its restricted conception of transfer of energy by matter, could proceed only as far as Gaspard de Coriolis's notion of "energy currents," described in his Traité de la mécanique (1844). The complete emancipation or reification of energy could be achieved only by a theory of action-at-a-distance, such as Maxwell's theory of electromagnetism. Here energy could be labeled and traced in its motion or change of form just as a piece of matter is ticketed so that it can be identified in other places under other conditions.

The recognition of the new ontological status of energy led to a result of great philosophical importance: It strengthened the position of those who opposed the prevailing kinetic-corpuscular theory of nature, according to which all processes are reduced to motions of particles and motion is the fundamental concept for physical explanation. Referring to the demonstrated equivalence of all forms of energy, the opponents claimed that kinetic energy is only one of the forms in which this quantity appears. In their view, energy was a much more general conception than motion, a conception that should not be narrowed down to mean only energy of attraction and repulsion of gravitational or electrostatic nature or energy of various forms of motion. One of the earliest exponents of this school of "energetics" was G. Helm, who, in a treatise, Die Lehre von der Energie (Leipzig, 1887), revived the term energetics, originally coined by Rankine, to characterize his position, according to which energy is the basic physical reality responsible for all natural phenomena. Helm referred to Gustav Zeuner, Ernst Mach, Josiah Gibbs, James Clerk Maxwell, A. J. von Oettingen, and Joseph Popper as advocating similar ideas. In particular, he claimed, energy can always be broken down into two factors, an intensity and an extensity factor, which characterize the quantity of energy as well as the direction in which changes of energy take place (the intensity factor always decreases).

In spite of further expositions, Helm's ideas did not attract much attention until Wilhelm Ostwald incorporated Helm's "factorization of energy" into the second edition of his treatise on physical chemistry, Lehrbuch der allgemeinen Chemie (1893), as the foundation of his theory of chemical affinity. In the period between the first and second editions of his treatise Ostwald embraced the new doctrine of energetics, and with his address in 1895 to the German Congress of Naturalists at Lübeck, "The Conquest of Scientific Materialism" (Die Überwindung des wissenschaftlichen Materialismus ), he became the principal speaker of the new movement. In his view, not only was energy the universal currency of physics, but all phenomena of nature were merely manifestations of energy and of its manifold transformations.

In "Lectures on Natural Philosophy" (Vorlesungen über Naturphilosophie, Leipzig, 1901) Ostwald contended that since substance is by definition that which persists under transformations or changes, energy is substance. Methodological as well as epistemological considerations, he claimed, force us to see in energy the only substance—methodologically because the alternative view, scientific materialism, has failed to give an exhaustive explanation in even a single case of natural phenomena; epistemologically because "what we hear originates in work done on the ear drum and the middle ear by the vibrations of the air. What we see is only radiant energy which does chemical work on the retina that is perceived as light…. From this point of view the totality of nature appears as a series of spatially and temporally changing energies, of which we obtain knowledge in proportion as they impinge on the body, and especially upon the sense organs fashioned for the reception of the appropriate energies." Ostwald's conception of a physical object in terms of energy, of its volume in terms of compressibility, and of its shape in terms of elasticity is one of the final stages in a development that began with John Locke's sensationalistic conception and eventually put an end to the substantial conception of matter.

The "dissolution of matter" into energy was particularly welcomed by the adherents of the monistic school of thought in their search for a unified conception of the universe. Gustave Le Bon, for instance, in his L'evolution de la matière (Paris, 1905), spoke of the "dematerialization of matter into energy," a philosophical conclusion that in the same year found a far-reaching and profound scientific foundation. For in a paper titled "Does the Inertia of a Body Depend upon Its Energy Content?" ("Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" in Annalen der Physik 18 [1905]: 639–641), Albert Einstein showed, on the basis of the Maxwell-Hertz equations of the electromagnetic field, that "if a body gives off the energy E in the form of radiation, its mass diminishes by E/c ²," where c denotes the velocity of light. Since then the mass-energy relation, E = mc ², has been of fundamental importance, particularly in nuclear physics, where P. M. S. Blackett, G. P. S. Occhialini, O. Klemperer, and others showed that the total mass of a particle can be transformed into energy.

Whereas in classical mechanics differences of energy alone were of physical significance, so that energy could be determined only up to an additive constant, in modern physics energy lost this indeterminateness and became a physical quantity of absolute magnitude. Moreover, in the theory of relativity the principles of the conservation of energy, or mass, and momentum, the latter being the basis of the Cartesian measure of "force," revealed themselves only as different aspects of one and the same conservation law, the conservation of the momentum-energy four-vector. On the basis of the Einstein equation E = mc ² the problem of the source of solar (or stellar) energy could be solved, the "packing effect" in nuclear physics could be explained, and the release of nuclear energy could be predicted. Energy was released mass, and mass was frozen energy, or as Bertrand Russell, in Human Knowledge: Its Scopes and Limits (New York, 1948), summarized the situation: "Mass is only a form of energy, and there is no reason why matter should not be dissolved into other forms of energy. It is energy, not matter, that is fundamental in physics."

conservation and invariance

Although the theory of relativity threw new light on the conservational aspects of energy, or mass, the relationship between conservation and invariance found its final elucidation in Emmy Noether's article "Invariant Variational Problems" ("Invariante Variationsprobleme," in Göttinger Nachricten [1918], pp. 235–257), which demonstrates the conservation of certain quantities (for example, the canonical energy-momentum tensor) for dynamic systems that are invariant under continuous transformations of the coordinates or, more generally, of the field functions involved. Conservation thus appeared as a consequence of symmetry properties, a fact that was in part known already from the Hamiltonian formulation of classical mechanics. In particular, if homogeneity of space and time is assumed, that is, if it is postulated that the system is invariant under translational transformations of the origins of space-coordinates and time-coordinates, then the conservation of momenta and of energy is but a mathematical consequence. The principle of the conservation of energy of a given dynamic system is therefore ultimately a consequence of the invariance (or symmetry) of the system under changes in the zero-point of the time scale, that is, a consequence of the homogeneity of time.

See also Alembert, Jean Le Rond d'; Aristotle; Averroes; Bacon, Francis; Bilfinger, Georg Bernhard; Clarke, Samuel; Descartes, René; Einstein, Albert; Faraday, Michael; Force; Galileo Galilei; Gibbs, Josiah; Helmholtz, Hermann Ludwig von; Huxley, Thomas Henry; Lavoisier, Antoine; Leibniz, Gottfried Wilhelm; Mach, Ernst; Maxwell, James Clerk; Newton, Isaac; Ostwald, Wilhelm; Peter Aureol; Philosophy of Physics; Russell, Bertrand Arthur William; Schelling, Friedrich Wilhelm Joseph von; Thomas Aquinas, St.; Wolff, Christian.

Bibliography

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M. Jammer (1967)