PHYSICAL THEORIES. - By physical theory is meant, in the most general sense, a rational explanation of a phenomenon or of a set of physical phenomena, where explanation means reducing the unknown to the known, the complex to the simple, what arouses surprise to a scheme of reasoning that is habitual to us; in short, "reducing a new situation to elements so familiar that they can be accepted as a matter of course and put an end to our curiosity" (P. W. Bridgman, The Logic of Modern Physics, p. 50).
In this sense primitive man constructs a theory by explaining the thunderstorm 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 permit the prediction of their behavior in the future and to be, as far as possible, internal to the phenomenon itself. Already ancient Greece offers examples of theories of this kind, such as that of the proper places of heavy and light bodies, the atomistic theory of Democritus, the various theories on the nature of light, but above all those of the cycles and epicycles to explain the apparent motion of the stars. These latter theories show how, from antiquity onward, attempts were made to reduce the explanation of phenomena to geometrical and mechanical elements. Nevertheless, when one speaks of physical theories, one means to refer to the modern theories that arose from Galileo and Newton onward. In the construction of modern science, physical theories have a well-determined place and purpose. Modern science begins from the observation and measurement of the facts and elements of the physical phenomenon; these observations and measurements are linked to one another by logical and causal relations, the laws, which in the most favorable case assume the mathematical form of an equation that links the variables of experience to one another by means of functions. In turn, numerous empirical laws are linked together in a rational system that permits the deduction, from a few initial propositions, of the laws and facts of concrete experience; that is, the aim is to achieve with regard to laws the same purpose of synthesis and explanation that law has with regard to direct observations and measurements.
One can therefore define a physical theory, or in general a scientific theory, as a system of propositions, possibly expressed in mathematical form, whose purpose is to synthesize and explain in the simplest, most complete and most exact way a set of experimental laws.
We must at once distinguish two categories of physical theories: 1) theories that are a logical deduction from experimentally established facts. Thus, for example, the theory of optical instruments, in particular Gauss's theory of centered systems, the elementary theory of lenses, are a logical deduction from the experimental laws of geometrical optics (rectilinear propagation, laws of reflection, refraction, independence of light rays, etc.). Rational mechanics, a pure logical deduction from the laws of Galileo-Newton dynamics, is another example. 2) Theories that are logical deductions from hypotheses not experimentally verified. Newton's theory of universal gravitation, for example, capable of accounting for Kepler's experimental laws, is founded on the hypothesis, not experimentally verified, that all bodies attract one another in direct proportion to their mass and in inverse proportion to the square of their distance (E. Perucca, Fisica sperimentale, I, Turin 1949, p. 3).
I. VALUE OF PHYSICAL THEORIES. - One of the central problems of modern epistemology (v.) is the problem of the nature and value of physical theories: with regard to physical theories of the first category, the question is whether they express objective, universal and constant relations among phenomena and real things, or whether they are solely expressions of practical and subjective value; with regard to physical theories of the second category, moreover, the question is what value the hypothetical elements, which cannot be checked experimentally, have with respect to reality.
The classical conception, which persisted almost unchallenged until the second half of the last century, with a few doubtful 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 as early as Greek antiquity, but which became prevalent after Descartes, an attempt was made to reduce every real explanation to mechanistic explanation, by means of quantitative and motional elements alone; and in recent centuries this reduction formed the ideal explanation, indeed the only truly satisfactory explanation, in the words of William Thomson (Lord Kelvin): "I am never content until I have constructed a mechanical model of the object I am studying; if I can make a mechanical 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 has led, as recent epistemologists often note (Duhem, Whitehead), 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 hidden reality, endowed with extension and movement alone. As examples of physical theories to which the classical conception attributed real value, one should cite the theories of fluids of the 18th century, the wave and corpuscular theories of light, Dalton's atomic theory, the kinetic theory of gases, Bohr's electronic theory of the atom, etc.
Mechanistic explanation easily degenerated, especially among the English physicists of the 19th century (Lord Kelvin, Lodge, Maxwell), into the imaginative explanation of mechanical models: unlike mechanism properly so called, the construction of models does not claim to discover the true structure of reality, but consists only in imagining a set of mechanical devices, balls, springs, gears, levers, pulleys, etc., arranged in such a way that the changes of the machine thus constructed are analogous to natural phenomena. Mechanical models therefore have a purely metaphorical sense and are suggested more by fantasy and a poetic spirit than by the scientific spirit. It is therefore natural that the most rigorous scientists should have felt the need to purge science of this spurious baggage, and thus one arrived at the conception that considers physical theories as a purely logical and formal explanation. Thus, for Poincaré, "the mathematical theories of physics do not have as their object to reveal to us the true nature of things; that would be an unreasonable claim. Their only purpose is to coordinate the physical laws that experience makes known to us, but which, without the aid of mathematics, we could not even state" (Science et hypothèse, p. 245). For Duhem, "a physical theory is not at all an explanation, but only a system of mathematical propositions, deduced from a small number of principles... which can be formulated in an arbitrary manner"; and, just as "the magnitudes to which the calculations refer do not claim at all to be physical realities," so too "the principles of the deduction do not present themselves at all as statements of true relations among these realities" (La théorie physique, pp. 26 and 27). The purpose of physical theories, according to this conception, is solely the search for an economy (Mach) or convenience (Poincaré) and, at most, tends to give us a natural classification of physical laws (Duhem). This conception, which owes its rise to Mach's empiricism and to the constitution of thermodynamics in a purely energetic form, has gained greater strength among contemporary physicists and epistemologists because of the ever-increasing difficulties encountered by many mechanistic theories; so that the most modern physical theories, such as the relativistic and quantum ones, are today generally presented under this aspect of a pure logical synthesis of experimental data. To cite a single example of a contemporary physicist, for Dallaporta physical theories "do not possess intrinsic reality. And this, it must be clearly specified, not insofar as they are considered as results of a first approximation, owing to the fact that science is still relatively little advanced; results that would then be completed and integrated by more perfected theories to which, one very distant day, we might finally attribute certainty. No. They do not possess reality by the very criteria according to which they are constructed, by the very purpose to which they tend, by the very fact that whoever builds them does not propose at all to arrive, through them, 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 for it physical theories not only do not tell us the why of things, but not even how they really are; it is possible, however, to behave as if things were as described by the theory.
The most extreme formulations of this way of seeing are found in scientific pragmatism (James, Dewey) and in absolute nominalism (Wienerkreis, neopositivism), according to which the only knowledge is concrete empirical knowledge expressed in singular propositions, while laws and physical theories are not at all knowledge of the physical world, but only allow us to act upon it, and in themselves considered in their abstract form they reduce to a pure verbal statement, an indeterminate formula, an important non-sense.
Agreement on the value of physical theories is far from being reached among contemporary physicists and epistemologists; nevertheless a clarification of the problem and a path to its solution can be reached through a careful analysis of the elements of physical theories and of the evolution they have undergone in the continuous development of science.
II. ELEMENTS OF PHYSICAL THEORIES
In every physical theory there are elements of a different nature which a critical analysis must carefully distinguish in order to arrive at an objective judgment on the value of physical theories. Indeed, in the first constituting of these, elements of different value and utility are almost inevitably incorporated; the constructive moment cannot be subjected to rigorous rules, which would retard and perhaps completely drown the fertile spontaneity of inventive genius. But at a second stage criticism must return to the theories already constructed, not with a destructive intent, but in order to analyze and sift the individual elements. From the preceding exposition it follows that in every theory there are mathematical elements and mechanical elements, elements drawn directly from experience and hypothetical elements which can be confirmed by experience only a posteriori.As for the mathematical elements, it must be noted that they never exhaust the meaning of the physical theory, since every physical theory contains, besides the formal mathematical expression, intrinsic elements that have an essential, ineliminable reference to empirical data and to elementary concepts and that give a different meaning to formally identical or similar mathematical expressions.
Even in mathematical physics the mathematical expression constitutes only the formal aspect under which the material element, which remains properly physical, is considered; one might say, that is, in Thomist language, that mathematical physics is a mixed science, materially physical and formally mathematical. Moreover, mathematization, even if it constitutes the ideal of a physical theory because it allows a higher degree of intelligibility to be attained, cannot be pursued in an exclusive manner and, especially if one takes the broader term "scientific theory," the existence is undeniable of theories that are not and perhaps never will be reducible to mathematical expressions, above all in the field of biology, psychology and the human sciences in general; it suffices to recall, for all of them, the theory of biological evolution.
As for the mechanical elements, these too offer particular advantages of explanation, since the more they approach the intelligibility of mathematics, the more they lend themselves to measurement and calculation. One therefore easily understands the effort of mechanism, since a physical theory that reduces phenomena to mere elements of quantity and motion attains the ideal of explanation. Yet these too cannot be considered as exclusive elements of a physical theory. Already from 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 often with mere abstract mathematical description, setting aside the discovery of hidden mechanisms as the ultimate explanation of physical phenomena; the further developments of relativistic and quantum mechanics have forced, perhaps definitively, the renunciation of making a mechanical model of every phenomenon. Today it is quite clear in scientific thought that making a mechanical model is not always possible, and is indeed, in certain cases, dangerous. Many of the criticisms raised by modern epistemologists against the real value of physical theories are valid precisely, but also only, against the conception dominant until the middle of the last century, which arbitrarily sought to reduce every real explanation to a mechanistic explanation. To make a theory today means to derive a group of formulas coherent with the essential principles of physics, such as that of the conservation of energy and of momentum, of invariance with respect to the Lorentz transformation formulas, etc., on the basis of which, given the initial data of the problem, that is, once a group of measurements has been carried out, the results in another experiment, that is, of other measurements, may be predicted. This, however, does not exclude that certain mechanical elements may be considered as real and effective, as, for example, the motion of the molecules of a gas according to the kinetic theory; indeed one must not even completely disregard the value of many mechanical models, which, while not providing an effective description of reality in univocal terms, are nevertheless not mere suggestive artifices useful for intuition, but also give a true analogical knowledge of reality and therefore have a certain degree of truth.
Of great importance for the judgment on the value of a physical theory is also the second distinction between the elements derived directly from experience or obtained by logical generalization of experience itself and the purely hypothetical elements. The value of the former, as objective expressions of real relations among phenomena and things, cannot be disregarded except on the basis of empiricist or idealist philosophical prejudices. Such, for example, is the position of Poincaré, who considers all the most universal principles, both of mathematics and of physics, as mere conventional hypotheses or disguised nominal definitions. In many cases, on the other hand, the principles, such as those of classical mechanics and thermodynamics, are generalizations, in part idealized or even approximate, but always founded on empirical observation and scientific induction, which in the observed constancy logically allow one to discern real relations existing among phenomena, that is, true laws of nature. Thus also the mathematical formulas, although abstract, give the right answer to concrete problems and have a value not only practical, but also cognitive with regard to reality and its essence.
When, however, it is a question of hypothetical elements, the judgment on their value is more complicated and difficult. It would be unjustified to exclude a priori the possibility of attributing real value to them; such an exclusion has been occasioned above all by the identification, already mentioned, of mechanistic explanation and real explanation. On the other hand, the a posteriori confirmation of experience is not logically sufficient to give certainty of their truth, by the logical principle according to which from the truth of the consequences it is not legitimate to infer the truth of the hypothesis. Indeed it is generally possible to construct an infinity of hypotheses from which the same consequences can be drawn. The indirect confirmation of experience therefore cannot make a hypothesis certain, except in particular cases in which it is not possible to establish an experimentum crucis; it nevertheless gives a greater probability to the hypothesis considered. Indeed in some cases the convergence of the most disparate experimental confirmations can be such as to constitute a reasonable ground for the certainty of the hypothesis considered. Always, however, when it is a question of the judgment on the value of a hypothesis, a work of criticism is required, aimed at distinguishing within the hypothesis itself independent elements, some of which may prove superfluous with regard to the consequences confirmed by experience, such that, even eliminated, they allow the same deductions to be carried out. These superfluous elements, evidently, receive no validation from favorable experience.
III. EVOLUTION OF PHYSICAL THEORIES
Another argument, which is adduced by many epistemologists against the real value of physical theories, is the continuous and rapid evolution to which even those that once seemed the 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 give rise to new theories that do not take long to suffer the same fate. Against such a presentation of the history of physics, all the most authoritative physicists have spoken out, having brought to light the continuity of science even in the construction of physical theories. Certainly, there is no lack of cases in which the progress of science has led to the absolute rejection of theories once in great favor; one need only think of the theories of phlogiston and caloric, of the corpuscular theory of light, so much in vogue in the 17th and 18th centuries, and then completely abandoned with the progress of chemistry, thermodynamics and optics. Generally, however, scientific progress does not lead to the complete rejection of previous theories, but rather to a correction and integration of them.
This can happen in the first place through the elimination of elements contained in the primitive theory, which on critical reflection prove superfluous with regard to the consequences confirmed by experience, and through the substitution of new elements suggested by new experiences, which do not accord with the primitive theory. A particularly significant example is offered by the wave theory of light: in Huygens' primitive conception light was constituted by longitudinal oscillations of a fluid medium, like sound waves. Subsequently the phenomenon of polarization induced physicists (Fresnel) to eliminate the longitudinal oscillations and replace them with oscillations transverse to the direction of the light ray, and therefore to conceive the ether as a rigid medium capable of transmitting very rapid mechanical oscillations. Even this conception encountered very serious obstacles, until the progress of electromagnetism induced the rejection of the hypothesis of mechanical vibrations, to replace them with electromagnetic oscillations (Maxwell). Huygens' fundamental hypothesis concerning the wave nature of light had remained through the successive transformations, but purified of the superfluous and harmful elements and integrated by new elements, which allow a more adequate explanation of real phenomena.
The theory of light offers the example of another kind of evolution to which physical theories may be subject. For over two centuries, two theories had fought each other as opposed and irreconcilable, the corpuscular theory, prevalent at first through the authority of Newton, and the wave theory, which had ended up overwhelming the former. But precisely when the real value of the latter seemed placed beyond discussion, new phenomena (the photoelectric phenomenon and then the Compton effect and others) forced physicists to revise their theories once again and placed them under the necessity of reconciling the two opposed theories together in a single physical theory, which would account for all the observed phenomena. The logical possibility of such a reconciliation, and therefore the new kind of evolution of physical theories, was brought to light by Bohr by means of the principle of complementarity. Another type of evolution of physical theories consists in a progressive refinement of theories toward an ever greater approximation to reality, whose ideal goal consists in a perfect and total adequation, perhaps never attainable through human knowledge. The principles of the preceding theory are then considered as a first approximation, a schematizing abstraction valid for coarser experiences, but insufficient for a finer experience, for which it is necessary to take into account functions of variables neglected in the first theory. An example of evolution in this sense is given us by classical mechanics transformed into relativistic and quantum mechanics, which consider the variation of the measurements of length, time and mass as a function of the velocity of the observer and the discontinuous structure of energy, which in a first approximation could be neglected without harm. The historical evolution of physical theories is unjustifiable or at least hardly comprehensible in a rationalistic and aprioristic epistemology of the Cartesian, Newtonian and Kantian type, which considers all principles as the expression of pure rationality independent of any experience. It shows instead the necessity of a continuous action and reaction between experience and reason, in a form of dialectical progress, not of the Hegelian type, which has recently been brought to light by distinguished epistemologists, such as Bachelard and Gonseth. This dialectical progress, by no means relativistic or skeptical, is fully justifiable in the empirico-rationalistic epistemology of Aristotle and St. Thomas. By means of it the necessary absolute values can be saved, while yet making room for a continuous evolution of physical theories.
IV. PHYSICAL THEORIES AND REALITY
In conclusion, the problem of the value of physical theories with respect to reality cannot be resolved in a uniform manner for all of them. Indeed, if many modern physical theories have a purely formal value and are abstract mathematical formulations that do not explain the cause of the phenomenon and the nature of reality, but only make it possible to predict the outcome of future experiences, nevertheless others provide real analogies with the internal structure of reality, and some even constitute a true ontological explanation of phenomena, which, although presenting itself at first as a simple probable hypothesis, acquires with successive experimental confirmations an ever greater probability, which can even be transformed into true certainty. As examples of theories to which it would be unreasonable to deny such a value, one may cite the astronomical theories of the structure, dimensions and forms of the solar and galactic system and the kinetic molecular theory of gases, which compelled Poincaré himself to consider the chemical atom no longer as a purely convenient fiction, but as a reality (Dernières pensées, Paris 1913, pp. 196 and 199). Moreover, even the most abstract formal theories of mathematical physics are not simple practical recipes, nor purely formal expressions devoid of content and physical meaning, but always constitute a knowledge, albeit incomplete and analogical, of the real relations prevailing among phenomena and among things and of the very essence of physical reality. They certainly do not give the ultimate why of things, since this why can be found only in something that completely transcends matter and physical knowledge, so as to fall within the domain of pure metaphysics; they do, however, ever better enable us to «know the real external world» (M. Planck, La conoscenza del mondo fisico, p. 226) and increasingly confirm «the conviction that with our theoretical constructions it is possible to reach reality» (A. Einstein-L. Infeld, op. cit. in bibl., p. 303).BIBL.: sources