PHYSICAL THEORIES. — In the broadest sense, a physical theory (t. f.) is a rational explanation of a phenomenon or a set of physical phenomena, where explanation means reducing the unknown to the known, the complex to the simple, and what arouses surprise to a scheme of reasoning that is familiar to us; in short, “reducing a new situation to elements so familiar that they may be accepted as obvious and thus extinguish our curiosity” (P. W. Bridgman, *The Logic of Modern Physics*, p. 50).
In this sense, primitive man constructs a theory by explaining a storm as the capricious act of an angry god. The physicist, however, demands more: he wants the familiar elements to which we reduce the situation to be such as to allow prediction of their future behavior and, as far as possible, to be internal to the phenomenon itself. Ancient Greece already offers examples of theories of this kind, such as the theory of the natural places of heavy and light bodies, Democritus’ atomic theory, and various theories about the nature of light, but above all those of cycles and epicycles to explain the apparent motion of the stars. These latter theories show how, from antiquity, an attempt was made to reduce the explanation of phenomena to geometrical and mechanical elements. However, when one speaks of physical theories, one generally refers to modern theories from Galileo and Newton onward.
In the construction of modern science, physical theories have a well-defined place and purpose. Modern science begins with the observation and measurement of the facts and elements of the physical phenomenon; these observations and measurements are then linked together by logical and causal relations, the laws, which, in the most favorable case, take the form of equations connecting the variables of experience through functions. In turn, numerous empirical laws are linked together into a rational system that allows the deduction, from a few initial propositions, of the laws and facts of concrete experience; that is, the aim is to achieve, with respect to laws, the same goal of synthesis and explanation that a law achieves with respect to direct observations and measurements.
A physical theory, or in general a scientific theory, can therefore be defined as a system of propositions, preferably expressed in mathematical form, whose purpose is to synthesize and explain in the simplest, most complete, and most exact manner a set of experimental laws.
It is necessary to distinguish immediately between two categories of physical theories:
1) Theories that are logical deductions from established experimental facts. For example, the theory of optical instruments, particularly Gauss’ theory of centered systems, and the elementary theory of lenses, are logical deductions from the experimental laws of geometrical optics (rectilinear propagation, laws of reflection and refraction, independence of light rays, etc.). Rational mechanics, a pure logical deduction from the laws of Galileo-Newtonian dynamics, is another example.
2) Theories that are logical deductions from hypotheses not experimentally verified. For instance, Newton’s theory of universal gravitation, which accounts for Kepler’s empirical laws, is based on the untested hypothesis that all bodies attract one another in direct proportion to their masses and in inverse proportion to the square of their distances (E. Perucca, *Experimental Physics*, I, Turin 1949, p. 3).
I. The Value of Physical Theories
One of the central problems of modern epistemology (v.) is the question of the nature and value of physical theories: with regard to theories of the first category, the question arises whether they express objective, universal, and constant relations between phenomena and real things, or whether they are merely expressions of practical and subjective value; with regard to theories of the second category, the further question arises as to the value of the hypothetical, experimentally unverifiable elements with respect to reality.The classical conception, which remained almost unchallenged until the second half of the last century, with a few dubious exceptions, attributes to physical theories the value of a *real*, ontological explanation of physical phenomena; that is, they would constitute a search for the essences of things and the causes of phenomena.
According to the tendency that appears from ancient Greece but became prevalent after Descartes, every real explanation was sought through *mechanistic explanation*, using only elements of quantity and motion; and this reduction has, in recent centuries, formed the ideal explanation, indeed the only truly satisfactory one, in the words of William Thomson (Lord Kelvin): “I am not satisfied until I have been able to construct a mechanical model of the object I am studying; if I can make such a model, I understand; until I can construct such a model, I do not understand at all” (*Notes of Lectures on Molecular Dynamics*, Baltimore 1884, p. 270). The mechanistic intention led, as recent epistemologists (Duhem, Whitehead) have often noted, to a duplication of material reality, sharply distinguishing between sensible appearances, as directly perceived by our senses with all their qualities and qualitative variations, and a hidden reality, endowed only with extension and motion. Examples of physical theories to which real value was attributed in the classical conception include the fluid theories of the 18th century, the wave and corpuscular theories of light, Dalton’s atomic theory, the kinetic theory of gases, and Bohr’s electronic theory of the atom, among others.
The mechanistic explanation easily degenerated, especially among 19th-century English physicists (Lord Kelvin, Lodge, Maxwell), into the *imaginative explanation of mechanical models*: unlike proper mechanism, the construction of models does not claim to discover the true structure of reality but consists merely in imagining a set of mechanical devices—balls, springs, gears, levers, pulleys, etc.—arranged so that the changes in the constructed machine are analogous to natural phenomena. Mechanical models thus have a purely metaphorical sense and are suggested more by imagination and a poetic spirit than by scientific rigor. It is therefore natural that the most rigorous scientists felt the need to purge science of this extraneous baggage, leading to the conception that considers theoretical frameworks (t. f.) as purely logical and formal explanations. Thus, for Poincaré, “mathematical theories of physics do not aim to reveal the true nature of things; such a claim would be unreasonable. Their sole purpose is to coordinate the physical laws that experience makes known to us, laws which, without the aid of mathematics, we could not even formulate” (*Science et hypothèse*, p. 245). For Duhem, “a theoretical framework is not an explanation at all but merely a system of mathematical propositions deduced from a small number of principles... which can be formulated arbitrarily”; and just as “the quantities to which calculations refer do not pretend to be physical realities,” so too the “principles of deduction do not present themselves as statements of true relations among these realities” (*La théorie physique*, pp. 26–27). According to this view, the purpose of theoretical frameworks is solely the pursuit of economy (Mach) or convenience (Poincaré), and at most, they aim to provide a natural classification of physical laws (Duhem). This conception, which arose from Mach’s empiricism and the formulation of thermodynamics in purely energetic terms, gained greater strength among contemporary physicists and epistemologists due to the increasing difficulties encountered by many mechanistic theories; so much so that the most modern theoretical frameworks, such as those of relativity and quantum mechanics, are today generally presented as pure logical syntheses of experimental data. To cite but one example from a contemporary physicist, for Dallaporta theoretical frameworks “possess no intrinsic reality. And this must be clearly understood—not because they are considered as first approximations, due to the fact that science is still relatively undeveloped, approximations that would later be completed and integrated by more refined theories to which, one distant day, we might finally attribute certainty. No. They possess no reality according to the very criteria by which they are constructed, according to the very purpose for which they are built, because those who construct them do not intend, through them, to arrive at reality” (*Valore e finalità della ricerca scientifica*, in F. Selvaggi, *Valore e metodo della scienza*, Rome 1952, p. 128).
These conceptions are often defined as the theory of “as if,” since according to them theoretical frameworks not only do not tell us why things are as they are but do not even describe how they actually are; yet it remains possible to act *as if* things were as the theory describes.
The most extreme formulations of this viewpoint are found in scientific pragmatism (James, Dewey) and absolute nominalism (Wiener Kreis, neopositivism), according to which the only genuine knowledge is empirical knowledge expressed in singular propositions, while laws and theoretical frameworks are not knowledge of the physical world at all but merely enable us to act upon it; and when considered in their abstract form, they reduce to mere verbal statements, indeterminate formulas, and significant nonsense.
Agreement on the value of theoretical frameworks is far from achieved among contemporary physicists and epistemologists; however, a clarification of the problem and a path toward its solution may be reached through careful analysis of the elements of theoretical frameworks and their evolution amid the continuous development of science.
**Elements of Theoretical Frameworks** — Every theoretical framework contains elements of different kinds, which a critical analysis must carefully distinguish in order to arrive at an objective judgment of their value. Indeed, in their initial formation, theoretical frameworks almost inevitably incorporate elements of varying value and utility; the constructive moment cannot be subjected to rigid rules, which would hinder and perhaps stifle the fruitful spontaneity of inventive genius. But at a later stage, criticism must return to the constructed theoretical frameworks—not with a destructive intent but to analyze and evaluate their individual components. From the foregoing discussion, it emerges that every theoretical framework includes mathematical elements and mechanical elements, elements drawn directly from experience and hypothetical elements that can only be confirmed a posteriori by experience.
As for the mathematical elements, it must be noted that they never exhaust the meaning of a theoretical framework, since every theoretical framework contains, beyond the formal mathematical expression, intrinsic elements that have an essential and ineliminable reference to empirical data and elementary concepts, which give different meanings to formally identical or similar mathematical expressions.
Even in mathematical physics, the mathematical expression constitutes only the formal aspect under which the properly physical material is considered—one might say, in Thomist language, that mathematical physics is a mixed science, materially physical and formally mathematical. Moreover, although mathematics constitutes the ideal of a theoretical framework because it allows for a higher degree of intelligibility, it cannot be pursued exclusively; and especially if one adopts the broader sense of scientific theory, it is undeniable that there exist theories that are not and perhaps never will be reducible to mathematical expressions, particularly in the fields of biology, psychology, and the human sciences in general. It suffices to recall, among others, the theory of biological evolution.
As regards mechanical elements, they too offer particular explanatory advantages, since they come closer to the intelligibility of mathematics and lend themselves more readily to measurement and calculation. It is therefore easy to understand the effort of mechanism, since a theoretical framework that reduces phenomena to mere elements of quantity and motion attains the ideal of explanation. Yet even these cannot be considered as the exclusive elements of a theoretical framework. Already by the end of the last century, the development of thermodynamics and electromagnetism had forced physicists to greatly reduce their claims to mechanical explanation and to content themselves all too often with abstract mathematical description alone, setting aside the discovery of occult mechanisms as the ultimate explanation of physical phenomena. The further developments of relativistic and quantum mechanics have perhaps definitively compelled us to abandon the attempt to fashion a mechanical model of every phenomenon. Today it is clear in scientific thought that fashioning a mechanical model is not always possible; indeed, in certain cases it is even dangerous. Many of the criticisms leveled by modern epistemologists against the real value of theoretical frameworks are valid precisely—and only—against the dominant conception up to the mid-nineteenth century, which arbitrarily sought to reduce every real explanation to a mechanistic one.
To construct a theory today means to derive a set of formulas coherent with the essential principles of physics, such as that of the conservation of energy and momentum, of invariance under Lorentz transformations, and so forth. On the basis of these, once the initial data of the problem have been established—that is, once a set of measurements has been performed—the results of another experiment, namely other measurements, can be predicted. This does not, however, exclude the possibility that some mechanical elements may be considered real and effective, as, for example, the motion of gas molecules according to the kinetic theory. Nor should we entirely disregard the value of many mechanical models, which, while not providing a univocal description of reality, are not merely suggestive and useful aids to intuition but also yield a genuine analogical knowledge of reality and thus possess a certain degree of truth.
A second distinction of great importance for judging the value of a theoretical framework is that between elements drawn directly from experience and those obtained through logical generalization of experience itself, on the one hand, and purely hypothetical elements, on the other. The value of the former, as objective expressions of real relations between phenomena and things, cannot be denied except on the basis of philosophical prejudices, whether empiricist or idealist. Such, for example, is the position of Poincaré, who regards all the most universal principles, both of mathematics and of physics, as mere conventional hypotheses or disguised nominal definitions. In many cases, however, principles such as those of classical mechanics and thermodynamics are generalizations, partly idealized or even approximate, but always grounded in empirical observation and scientific induction, which, in the constancy observed, logically reveal real relations existing between phenomena—that is, true laws of nature. Thus even mathematical formulas, though abstract, yield the correct answer to concrete problems and possess not only practical but also cognitive value with respect to reality and its essence.
When, however, we are dealing with hypothetical elements, the judgment of their value becomes more complicated and difficult. It would be unjustified to exclude a priori the possibility that they possess real value; such exclusion has been especially the occasion for the differentiation, already noted, between mechanistic and real explanation. On the other hand, a posteriori confirmation by experience is not logically sufficient to confer certainty upon their truth, in accordance with the logical principle that from the truth of the consequences one may not infer the truth of the hypothesis. Indeed, it is generally possible to construct an infinity of hypotheses from which the same consequences may be drawn. Indirect confirmation by experience therefore cannot render an hypothesis certain, except in particular cases where an experimentum crucis may be established; it does, however, confer greater probability upon the hypothesis in question. Indeed, in some cases the convergence of the most disparate experimental confirmations may be such as to constitute a reasonable ground for certainty regarding the hypothesis considered. Yet whenever one is judging the value of an hypothesis, critical work is required to distinguish within the hypothesis itself independent elements, some of which may prove superfluous with respect to the consequences confirmed by experience—that is, such that even if eliminated they still allow the same deductions to be made. These superfluous elements, obviously, receive no confirmation from favorable experience.
III. EVOLUTION OF THEORETICAL FRAMEWORKS — Another argument advanced by many epistemologists against the real value of theoretical frameworks is the continual and rapid evolution to which even those once thought best established are subject.
Some authors present theoretical physics as a field of ruins, in which theories succeed one another like ephemeral constructions, soon demolished to make way for new theories that soon suffer the same fate. Against such a presentation of the history of physics, all the most authoritative physicists have spoken out, emphasizing the continuity of science even in the construction of theoretical frameworks. Certainly, there are cases in which scientific progress has led to the absolute rejection of theories once held in high regard: consider the theories of phlogiston and caloric, the corpuscular theory of light so fashionable in the seventeenth and eighteenth centuries, and later completely abandoned with the advances of chemistry, thermodynamics, and optics. Generally, however, scientific progress does not lead to the complete rejection of earlier theories but rather to their correction and supplementation.
This can occur, in the first place, through the elimination of elements contained in the original theory that, upon critical reflection, prove superfluous with respect to the consequences confirmed by experience, and through the substitution of new elements suggested by new experiments that do not accord with the original theory. A particularly significant example is offered by the wave theory of light: in Huygens’ original conception, light consisted of longitudinal oscillations of a fluid medium, like sound waves. Subsequently, the phenomenon of polarization led physicists (Fresnel) to eliminate longitudinal oscillations and to substitute transverse oscillations with respect to the direction of the light ray, conceiving the ether as a rigid medium capable of transmitting extremely rapid mechanical oscillations. Even this conception encountered grave difficulties until the advances of electromagnetism led to the rejection of the hypothesis of mechanical vibrations in favor of electromagnetic oscillations (Maxwell). The fundamental hypothesis of Huygens regarding the wave nature of light remained intact through these successive transformations, but purified of superfluous and harmful elements and supplemented by new elements that permit a more adequate explanation of real phenomena.
The theory of light provides an example of another kind of evolution to which physical theories may be subject. For more than two centuries, two theories had been pitted against each other as opposing and irreconcilable, the corpuscular theory, which initially prevailed due to Newton’s authority, and the wave theory, which eventually came to supplant the former. Yet just when the real value of the latter seemed beyond dispute, new phenomena (the photoelectric effect and later the Compton effect and others) forced physicists to reconsider their theories anew and compelled them to reconcile the two opposing theories into a single physical theory capable of accounting for all observed phenomena. The logical possibility of such reconciliation—and thus the new kind of evolution in physical theories—was illuminated by Bohr through the principle of complementarity.
Another type of evolution in physical theories consists in a progressive refinement of theories toward an ever-greater approximation of reality, whose ideal goal is a perfect and total adequation, perhaps never attainable through human knowledge. The principles of the preceding theory are then regarded as a first approximation, a schematic abstraction valid for coarser experiences but insufficient for finer ones, for which it becomes necessary to account for variables neglected in the first theory. An example of evolution in this sense is provided by classical mechanics, which evolved into relativistic and quantum mechanics, taking into consideration the variation of measurements of length, time, and mass as functions of velocity and energy, as well as the discontinuous structure of energy—factors that in a first approximation could be safely disregarded without harm.
The historical evolution of physical theory is unjustifiable—or at least difficult to comprehend—within a rationalistic and aprioristic epistemology of Cartesian, Newtonian, and Kantian type, which regards all principles as expressions of pure rationality independent of any experience. Instead, it demonstrates the necessity of continuous interaction between experience and reason in a form of dialectical progress—not of Hegelian kind—which has recently been highlighted by eminent epistemologists such as Bachelard and Gonseth. This dialectical progress, in no way relativistic or skeptical, is fully justifiable within the empirico-rationalist epistemology of Aristotle and St. Thomas Aquinas. Through this approach, the necessary absolute values can be preserved even as room is made for the continuous evolution of physical theories.
IV. PHYSICAL THEORIES AND REALITY
In conclusion, the problem of the value of physical theories in relation to reality cannot be resolved uniformly for all cases. Indeed, while many modern physical theories have purely formal value and are abstract mathematical formulations that do not explain the cause of phenomena or the nature of reality but merely allow prediction of the outcomes of future experiments, others provide real analogies with the internal structure of reality; some even constitute a true ontological explanation of phenomena, which, though initially appearing as a mere probable hypothesis, gains increasing probability with successive experimental confirmations, a probability that may even become genuine certainty. As examples of theories to which such value cannot reasonably be denied, one may cite the astronomical theories regarding the structure, dimensions, and forms of the solar and galactic systems, and the kinetic-molecular theory of gases, which compelled even Poincaré to regard the chemical atom not merely as a convenient fiction but as a reality (Derrière les pensées, Paris 1913, pp. 196 and 199).Moreover, even the most abstract formulas of mathematical physics are not mere practical recipes or purely formal expressions devoid of content and physical meaning; they always constitute a—albeit incomplete and analogical—knowledge of the real relations prevailing among phenomena and things and of the very essence of physical reality. They do not, of course, provide the ultimate *why* of things, for that *why* can only be found in something that transcends matter and physical knowledge entirely, entering the domain of pure metaphysics; yet they do enable us to know the external real world ever more fully” (M. Planck, *The Knowledge of Physical Reality*, p. 226) and increasingly confirm the conviction “that with our theoretical constructions we can attain reality” (A. Einstein and L. Infeld, op. cit. in bibliography, p. 303).