Except where indicated in bracketed notes and minor changes in punctuation and syntax, the article is as published in Science & Society, vol. 44, no. 2, 155–76
Physical Systems, Structures, and Properties
The nature of physical properties and their relationship to the structure of the physical world is increasingly becoming the subject of attention among both physicists and philosophers of science. The decrease in the influence of logical positivism and the widespread criticism leveled against the operational definitions associated with it has led many natural scientists and philosophers of science to seek other approaches to the concept of physical properties and physical quantities. Simultaneously, the growing application of systems theory to a wide number of fields has made the exploration of the relationship between systems, structures, and properties a very timely subject. Dialectical materialism provides a very valuable methodological tool for the exploration of such relationships and provides a convincing alternative to approaches based on reductionism and phenomenological emergence.1
Like other fields, physics is divided into a number of subfields. Members of physics departments at universities with extensive research programs are usually grouped around one or another such subfield. Some of these fields are clearly associated with what can be called the structural hierarchy of matter, such as elementary-particle physics, nuclear physics, atomic physics, solid-state physics, and soon. Some fields are of a more specialized nature such as crystallography, optics, and continuum mechanics, while others are of a more general nature such as mechanics, electricity and magnetism, and thermal physics. These more general fields, however, are general in the sense that they deal with a wide range of levels of matter, and in this sense they can still be embraced by the concept of hierarchy.
I will first consider some general characteristics of physical systems and their associated structural hierarchy. I will then discuss the concept of physical properties, and finally, physical quantities.
1. Physical systems
a) Hierarchical relations
Let us initially focus our attention on some aspects of the hierarchical structure associated with a finite volume of gas, for example, neon.
We can assume that the neon is of uniform isotopic composition and that about 20 grams of it is contained in a closed vessel, which means that we are dealing with about 1023 atoms of neon. Suppose now we are asked to say something about the characteristics of the gas contained in the vessel. We know that the relationship among the pressure, volume, and temperature for a fixed mass of gas is given approximately by the ideal gas law
pV/T = C, (1)
where p is the pressure, V is the volume, T is the thermodynamic temperature measured on an absolute temperature scale and C is a constant. Here the volume is the volume of the vessel. It is assumed that the gas is distributed uniformly over the entire volume. The pressure p is assumed to have the same value at every point inside the vessel and is directed radially outward except at the walls. The temperature T is assumed to be the same everywhere inside the vessel. On this level, which we can call the level of macroscopic thermodynamics, the gas is regarded as a continuous fluid medium having no internal structure. On the level of the kinetic-molecular theory of gases, however, the neon is viewed as consisting of about 1023 rigid molecules, the molecules in this case being single atoms of neon, conveniently, but not necessarily taken to be of spherical shape. The atoms interact with one another only through surface contact upon collision. The result of each collision can be calculated by classical mechanics. When we consider neon from the standpoint of kinetic-molecular theory, we are dealing with a level that is intermediate between the level of macroscopic thermodynamics and the atomic level. In the latter we are concerned with the actual structure of the atom and we can no longer regard the atom as a rigid body having a well-defined surface.
Our three levels therefore constitute a hierarchical structure of systems and subsystems. On one level we have a gas with properties characterized by the pressure, temperature, volume, mass density, and chemical composition. On the molecular-kinetic level we have a gas consisting of about 1023 molecules of atomic neon distributed essentially uniformly over the volume with a Maxwell velocity distribution. The molecules interact with one another only through collisions which occur when they come within about 10-8 cm of one another. The precise nature of this interaction on “contact” (or collision) is not significant except that they are elastic, that is, the molecules undergo no internal changes as a result of the collision. On the atomic level each molecule is a subsystem of ten electrons and a nucleus organized in a characteristic spatial configuration calculable from quantum mechanics.
Recognition of this hierarchical character is essential to understand the behavior of the gas. It would be incorrect to consider the gas simply as a system consisting of electrons and neon nuclei. It is necessary that sets of 10 electrons be associated in a given relationship with one nucleus to form individual neon atoms. These atomic subsystems then have velocity and spatial distributions which again constitute a set of relationships among them. We thus have a multi-level system of elements and relations, with elements and relations on the atomic level forming different elements and on relations on the molecular-kinetic level.
In the reductionist approach, an attempt is made to understand the behavior of the system by going down level by level until one reaches a level of substructures which can account for the particular behavior under study. The properties and structures of still lower levels can be ignored as not contributing in an essential way to the given behavior of the system. Such an approach can be quite adequate for broad ranges of physical problems, but it is a mistake to absolutize the reductionist approach to a philosophical principle. For example, to explain the wavelengths of light emitted by a neon lamp one could reduce the gas to a system of neon atoms, since the wavelengths can be accounted for on the basis of the atomic structure of neon. The relationship among the voltage, current, gas pressure, and intensity of light emitted by a neon lamp, however, cannot be derived on this reductionist basis, since the properties of a number of levels have to be taken into account. Similarly, the theoretical explanation of hysteresis loss in a sample of iron in an alternating magnetic field involves, among other things, the hierarchical interconnection between the magnetic domains in the crystal structure of the iron and the magnetic properties of atomic iron.
b) The essential and the nonessential
To arrive at those properties of interest to us it is necessary to classify certain relationships as essential and others as nonessential.. For example, if we were interested in studying the properties of neon as a gas, it will usually turn out that the precise spatial relationship defining the volume containing the neon is not an essential determining factor. However, the fact that the gas is distributed uniformly over the volume would be an essential spatial relationship.
c) The particular and the general
Since we are dealing with neon gas, and not liquid neon, we will be restricting the relationship among pressure, volume, and temperature to a range in which neon will be maintained in the gaseous state. Within a given range of pressure, a given volume of neon will be in a gaseous state only if its temperature is higher than some well-defined value that depends on the pressure. Each gas has its own particular relationship between the pressure and this minimum temperature. Although this relationship is a particular one for neon, it is a condition for ensuring a general relationship which distinguishes the gaseous state from the liquid or solid state—namely, that the average distance between any two molecules be roughly one or more orders of magnitude greater than the effective diameter of the molecules. It should be stressed that the particularness of relationships does not depend on the existence of sharp boundary conditions for the system. This can be readily be seen in what follows when we consider the upper temperature boundary in the transition of a gas into a plasma.
d) The necessary and the contingent
Owing to the character of the velocity distribution of the gas molecules, there will always be some probability of a collision taking place with sufficient energy to completely strip the nucleus of its orbital electrons. We consider the neon to be a gas when the temperature is such that this probability is negligibly small. At sufficiently high temperature the average kinetic energy of gas molecules can exceed that needed to completely remove the orbital electrons and we will no longer be dealing with a gas, but with a plasma. While the lower temperature limit forms a relatively sharp boundary, the upper limit is therefore not well defined. At most we can say that the transition from gas to plasma begins when the ionization potential for the orbital electrons is of the order kT, where k is the Boltzmann constant and T is the temperature on an absolute temperature scale. We again have a particular relationship expressing the upper boundary as an order of magnitude.
The condition that the gas be in equilibrium requires that the directions of motion of any two atoms be randomly oriented with respect to each other. This random relationship leads to a necessary one, namely that all properties of a gas in equilibrium be isotropic, that is, unrelated to any direction in space. In fact, as is pointed out by Truesdell,2 the isotropic character of the properties of fluids is precisely that which distinguishes fluids from other forms of continuous media.
e) System and structure
The characteristics outlined above can be expressed in more general terms through the concepts of system and structure. In general, the fundamental concepts of a scientific theory cannot be presented as definitions, since a definition implies a certain completeness in content. What we will say about systems and structures should be considered as elaborations of the concepts. This is a way of drawing attention to the fact that the deeper content of these concepts are still being investigated and that their description can by no means be considered complete.
Blauberg, Sadovsky, and Yudin list the following features of a system:3 (1) a system is an integral complex of interconnected elements; (2) a system forms a special unity with its environment; (3) any investigated system is usually an element (or subsystem) of a higher-order system; and (4) elements of any system usually appear as systems of lower order. With these features a system constitutes an integrated whole of hierarchically interconnected relations and elements. The principle of wholeness and hierarchy asserts the primacy of the system as a whole over its elements as well as the fundamental hierarchical structure of the system.
By structure we understand the totality of essential and nonessential, general and particular, necessary and contingent relations among the elements of a system in a definite interval of time.4 The term structure is generally used to denote the stable aspect of a system. The stability is always relative, determined as it is by the time interval over which the system’s elements and relations show no significant qualitative change.
The delineation of a physical system is an important step in the process of acquisition of knowledge about the physical world. In reality, no form of matter exists in complete isolation from other forms. By means of the concept of system we isolate temporarily some of the levels of matter from the infinity of levels associated with the hierarchical structure of matter in order to be able to study the laws governing the changes that take place inside the system and the law-governed consequences of the interaction of the system with the physical world outside it. The system is not only limited in range of levels but also in space and time. Since existence in space and time are basic forms of existence of matter, the specification of physically real systems necessarily involves limitation of spatial extension and the interval of time embraced by it, although the spatial extension itself may vary over the time interval. Once the system is isolated in this way the restrictions on spatial and temporal extension may be dropped from the theoretical reflection of the system if these boundaries are not essential to the aspects of the system under study, as is the case, say, if one is interested only in intensive physical variables, that is, in physical properties that do not depend on the quantity of matter. An example of this is the following relation among pressure, density, and temperature of an ideal gas:
p/ρT = C1 (2)
where p and T are the pressure and thermodynamic temperature, ρ is the gas density, and Cl is a constant. The qualification in a definite time interval attached to the description of a system in the preceding paragraph serves two purposes. All real physical systems change, even though some aspects of periods of stability may extend in time for billions or tens of billions of years, as appears to be the case for relatively isolated protons, our solar system, and even galactic systems [since we now estimate that 13 billions years have elapsed since the big bang, the phrase “or tens of billions” should be deleted—note by author in 2008]. Therefore the specification of a definite time interval, however large, is a way of recognizing that the properties of all physical systems are historically conditioned and that properties considered to extend in time beyond periods that have been theoretically and experimentally substantiated are the result of only speculative extrapolation.
In the case of a system in which the elements and the relations among them and the relations between the system as a whole and the physical world outside are undergoing change, it is still possible to retain the same relative spatial and temporal isolation of the system in order to study the various processes that are taking place. The specification of the interval of time is still useful to indicate the transitory nature of the isolation of the system. Consider, for example, the system formed by the capture of a slow anti-proton by a proton (protonium). The time interval extends through the cascade process in which the principal quantum number (associated with the energy levels) decreases until the proton and anti-proton annihilate one another. It may be useful to extend the time interval sufficiently to include the formation and subsequent emission of the annihilation products (photons, pions, etc.) if the annihilation reaction itself is to be included as an object of study.
In practice we usually build up our knowledge of the levels of a system by an iterative process.5 We form an approximate picture of the system at one level and then proceed to analyze the system elements and the relations among them to improve the approximation with which we started. Further improvements in our approximation of the system lead to a more detailed investigation of the elements and the relations, which ultimately leads to the study of the elements as separate subsystems. Synthesis of this information leads to still further improvements in our knowledge of the higher levels, and so on.
In logic and mathematics, a system is usually considered to be a set of elements and the relations among them. The elements are simply postulated as theoretical objects without internal structure. We, however, have been using the term system to apply both to the objectively existing physical systems and to their theoretical reflection, the latter being an approximate and incomplete expression of the former. The dialectical-materialist view of the infiniteness of matter in content means that there are no ultimate elements, that is, no ultimate forms of matter. This does not mean, however, that we cannot provisionally ignore the deeper structures as part of our theoretical analysis for a given range of levels.6 In the theoretical representation of physical systems, the term element can have the character of material points, as in the case of macroscopic particle dynamics; the character of an extended material body, as in the case of the mechanics of rigid bodies; or the character of interpenetrating fields, as in the case of electromagnetic theory.
The situation in elementary-particle physics illustrates, however, the dangers of introducing a rigid separation between the categories of elements and relations. For example, some dialectical-materialists have suggested that the number of “ultimate” elementary particles can be finite, but nevertheless accept the Leninist concept of infiniteness of matter in content. They resolve this apparent contradiction by asserting that it is the relations that are infinite. Does this suggestion really resolve the contradiction?
In his book entitled Things, Properties, and Relations, Ujemov notes that the three categories indicated by the title are capable of undergoing a dialectical transformation into one another.7 Here Ujemov is using the term thing in its general philosophical sense as material and nonmaterial entities or “objects”. (The set of integers is an example of nonmaterial entities or objects.) To illustrate how a relation can be transformed into a thing, we can consider the case of polygons with various numbers of sides. The vertex of each polygon represents a relationship between adjacent sides. We can derive a theorem for regular polygons, for example, which gives the vertex angle A of a polygon of n sides of equal length:
A = 180° – 360°/n.
Thus the vertex angle is 60° for an equilateral triangle, 90° for a square, 108° for a regular pentagon, etc. In this way, the vertex, which started out as a relation, has been transformed into vertices as things about which we can formulate new relations.
In physics we have a similar situation with material objects and the relations that embrace them. A sound wave in air represents a relationship of regular variation in density of the air molecules. The wave front emanating from a plane flying at a supersonic speed behaves like a material object which can shatter a glass window. In other words, on the macroscopic level the wave acquires the character of a material object capable of producing a collective effect that the individual air molecule cannot produce. In the microworld we also have examples of the interchange of particles and fields. A field is a form of matter and yet it expresses its existence as a relationship of a particle-like material object to the space around it. Thus an electric field at any point in space is defined to be the force (in some definite direction) on a unit electric charge located at that position in space. A particular kind of combination of electric and magnetic field forms the particle known as the photon. A thing (the electromagnetic field becomes a relationship (as fields of force) and also a particle (as a photon).
The suggestion that one can reduce matter to a finite number of material objects in particle form with an infinity of relationships thus does not seem to be consistent with all of our experience in physics (as well as in other fields too). Our experience repeatedly points to the absence of a rigid separation between the categories of relations and things, as we have seen above.
The designation of boundaries between the levels of a system and the distinction among essential and nonessential relations have a relative character and are closely connected with the nature of the knowledge we are seeking. Thus if we were interested in using neon for a lamp we could not require that the orbital electrons be in stable orbits (that is, the neon atom cannot be required to remain in its ground state). If we were interested in more precise relationships between the pressure and the temperature for a given volume of gas and a more detailed calculation of the deviations from the ideal gas laws, we would have to be concerned with the quantum-mechanical parameters of the interactions between the atoms to take into account the long- and short-range forces that exist between the neon atoms. Since these forces are connected with the atomic structure of the neon, the boundary between the atomic and kinetic-molecular levels is no longer so clearly defined.
The relativity of the system structure, however, does not mean that this relativity ultimately has a subjective basis. The relative nature of system concepts has an objective material basis arising out of the system itself. For example, we can neglect long-range attractive forces between molecules because usually they affect the pressure calculation by only a small amount. If this amount becomes a significant factor in our use of the system, then these attractive forces have to be included among the essential relationships within the system. The relative strength of the attractive forces is the objective material basis of the relativity of the system structures in this case.
The external boundary of the system is also relative. It is usually chosen to include elements and relations essential to the behavior of the system and to exclude elements and relations that are not essential factors determining the properties of the system. Thus as long as the exchange of heat through the walls of the vessel is not an essential factor for the properties of the system, we can limit the system to the internal walls of the vessel. Suppose that in the context of a larger system, which includes the walls of the system and the surrounding environment, it turns out that the temperature of the walls was slowly rising and that the temperature of the gas inside the vessel was, as a result, also rising, but that it was rising slowly enough so that the entire gas could be regarded as remaining in equilibrium (that is, the temperature of the gas was rising uniformly throughout the volume). We could still consider the system to be internal to the walls of the vessel and replace the temperature effects of the walls by the added condition that the temperature of the gas was rising slowly, without going into the cause, so long as the processes in the walls and the external environment were not essential to the situation with which we were concerned. Here, too, we see the relative nature of the boundary as corresponding to objective material conditions.
As is the case of the system structure, the particular boundary we impose upon the system is determined by the nature of our interest in the system and the method of analysis that we have chosen. There is often a certain arbitrariness in the choice of the details of the system structure and the system boundary made by individual investigators. This choice is associated to a certain extent with the technique of analysis employed. All theoretical descriptions of the same objective physical system involve some degree of approximation. Differences in the approaches to theoretical analysis of the same phenomena can have a subjective as well as an objective character.
The objective differences arise in connection with the goals of the theoretical analysis. They may be connected with the practical uses for which the analysis is necessary or with the particular physical phenomena under study. For example, the liquid-drop model of the nucleus is particularly useful for a wide range of problems arising with nuclear fission. The fission itself is an objectively occurring process and the approximations involved in the use of a liquid-drop model of the nucleus lead to results that more closely correspond to actual fission processes than are obtainable, say, with the independent-particle model of the nucleus. Another source of objective differences can lie in differences in the overall theoretical framework into which a given analysis is to be incorporated. For example, in the case of steady-state alternating-current circuits, the electrical circuit elements and the current and voltage variables are not represented in the same way as in the case of electrical transient phenomena. In the former case it is common to use root-mean-square magnitudes and phase angles, while in the latter case the solutions are arrived at by means of differential equations involving instantaneous values, and the circuit elements are not described explicitly by means of phase angles.
By subjective differences we mean differences which do not clearly lie in the nature of the physical process itself, but rather in the approach to the theoretical understanding of the physical process. It is obvious that the choice of system boundaries depends on the theoretical approach used in the analysis. We can readily distinguish two kinds of subjective differences depending on whether the differences are essential or not. An essential subjective difference between two choices of system boundaries would mean that one or both theoretical approaches have an incorrect or incomplete comprehension of the objectively existing physical system inappropriate to a given level of accuracy or approximation. As an example of such subjective differences we can take the differences in system boundaries that would result from a geocentric model of planetary motion as compared to a heliocentric one if one sought to account for the motion of Venus relative to the earth. For a geocentric model the system would include Venus and the earth (and possibly the other planets), but not the sun. A heliocentric model would have to include at least the sun as well as Venus. The relative motion of the sun would not be of particular interest in a geocentric model if one were interested primarily in the motion of Venus relative to the earth. (On the other hand, the motion of the other planets could provide some insight in connection with the motion of Venus in a geocentric model because of similarities in the motions of the planets.) Nevertheless, the geocentric system must be considered incorrect or incomplete since this choice of system boundaries could be useful to reveal only regularities in the relative motion of planets with respect to the earth, but not their source, namely the gravitational attraction between Venus and the sun. Thus for an investigation of the sources of planetary motion the difference between the geocentric and heliocentric models is a subjective difference.
Nonessential subjective differences refer to differences of merely a formal character, not embracing differences in theoretical understanding, just as one may use various techniques for solving simultaneous equations in algebra. In such cases the underlying theoretical structure is the same or equivalent. An example would be the derivation of equations of motion of mechanical systems by means of Newton’s law or by means of Hamilton’s principle of least action, since Newton’s laws and Hamilton’s principle are derivable from one another.
2. Physical properties
All systems have properties. Each material system has its own concrete existence and the concept property is connected with the classification of the characteristics of a unique concrete material object in terms of generalized concepts. Thus a property is simply that which all things of a given class have in common.8 Properties of a system arise from both the elements comprising the system (including their subsystems) and the relations among them.
Let us consider the properties of a small piece of bare copper wire. We can immediately enumerate a large number of properties: cylindrical surface with radius very much smaller than the length; ductile material; melts at 1083°C. The particular piece of wire may be unique, buts its properties are expressed in terms of relationships and general categories common to other material objects. Thus a cylindrical shape is common to a wide range of objects. Shape expresses a spatial relationship among various parts of an object as well as a relationship to other objects. The shape of the wire can be measured, say, with a ruler and a micrometer. The property of being copper refers to the class of atoms of which the wire is composed. The copper can be identified in various ways, for example, by spectral analysis. The property of being a good conductor of electricity can be determined by precise measurement or simply by its effective use in an electrical circuit. The wire’s ductile nature is displayed by its ability to be drawn to a smaller radius tby externally applied forces. Thus we see that all the properties which make a piece of copper wire what it is and not something else are inseparable from the objective existence of this physical object, that is, they arise from the material system which we have characterized as a small piece of bare copper wire, but the properties of this material system manifest themselves only as a relationship to, or an interaction with, other material systems. The concept of physical property is thus seen to have a contradictory nature. Physical properties are what give a physical object its individual identity, distinguish it from other things, and therefore characterize and affirm its objective existence. In this sense the property is intrinsic to the system. On the other hand, a property can only manifest itself externally.
To understand better this dialectical contradiction we should recall the statement made earlier that the concept of property is connected with the classification of an object’s characteristics in terms of generalized concepts. Thus it is not the interrelationship between a given object and some other individual object that characterizes a property associated with the former, but the interrelationship with an entire class of other objects, that is, objects which themselves share common properties. The same property may express itself phenomenologically in different ways with different subclasses of these other objects. Consider, for example, one of the essential properties of electrons, namely, their negative electric charge. Now let us consider the way electrons interact with the class of other charged particles. The property of having a negative electric charge expresses itself as a repulsive force with the subclass of other negatively charged particles, such as pi-minus mesons, and as an attractive force with the subclass of positively charged particles, such as protons. (That the difference between repulsive and attractive forces is not a trivial difference can be seen from the absence of any repulsive gravitational force.) Thus a property of an object, while intrinsic to the object itself, does not arise independently of other objects and does not exist independently of the existence or potential existence of other objects. The situation is somewhat like the relationship between ideas and matter. Ideas are not material and therefore ideas and matter have mutually exclusive contradictory characters. Yet insofar as ideas are not pathological fantasies (like spots before one’s eyes), but reflect objective reality, the ideas do not arise and exist independently of the material world which constitutes their ultimate source. (We could even say the same about the “pathological spots,” or about mistaken ideas generally, but the argument would take us too far afield.)
This contradictory nature has caused great conceptual difficulty among scientists and philosophers. Mach, like Berkeley, abandoned the concept of material system and regarded the special words for objects as being only symbols for their manifestations as sensations or observable phenomena. These observations or sensations were then regarded as the only reality. The operationalist approach developed in the 1920s by P. W. Bridgman,9 which still dominates many physics textbooks, sees physical properties only in terms of results of measurements made in a clearly specified way. Kant saw the material system as something inaccessible to us (the thing-in-itself), and therefore what remained was the phenomena and the pre-existing rationality or abstract reason which allowed human understanding to make some sense out of the phenomena.
The interconnection between these contradictory sides of a property provides a basis for the acquisition of objective knowledge about physical systems. The properties of the material system manifesting themselves as phenomena open the way for the theoretical investigation of the system. The system itself is not reducible, however, to the totality of phenomena associated with it. It is more accurate to say that a material system or object is nothing more than the totality of its properties, which are expressed through the interconnections of the object with other things.
This dialectical-materialist approach to the contradictory nature of properties leads to far-reaching epistemological conclusions: “There is definitely no difference in principle between the phenomenon and the thing-in-itself, and there cannot be any such difference. The only difference is between what is known and what is not yet known.”10 One can therefore conclude that there can be no such thing as a completely isolated system. Were such an isolated material system to exist, then there would be no phenomena associated with it and the system would constitute an unknowable thing-in-itself. But a system that had no external manifestations would contradict the criterion of direct or indirect detectability required by the materialist viewpoint and therefore could not be a material system. The universal interconnectedness of the material world is thereby one of the most general properties of matter and is one of the most basic principles of the dialectical-materialist view.
Properties can be divided into two groups.l1The properties in the first group constitute the quality of the system or object. The quality is an essential property. With the vanishing of these properties the system or object changes into something else. The properties in the other group do not constitute such a “boundary” for the existence of the physical object or system and we can call them simply properties or even nonessential properties if we are to contrast them with the essential properties. Some examples will be useful here. An essential property of oxygen atoms is that the nucleus have a positive charge of 8e, where e is the charge of an electron. Any change of this charge will mean that the atom is no longer an oxygen atom. The atomic number of the nucleus (corresponding to the total number of protons and neutrons in the nucleus) is not an essential property, since we use the term oxygen to embrace any number of possible isotopes of oxygen. If we were to specify a specific isotope, such as 16O, then, of course, the atomic number of the nucleus would be an essential property. If we were to consider the properties of water as a liquid at atmospheric pressure, the precise temperature of the water need not be an essential property, but it must lie in the range between boiling and freezing. Thus a physical quality used to denote a property of a system need not be quantitatively invariant to be an essential property as long as the system remains qualitatively stable.
We can summarize this discussion of properties as follows: The complex of internal and external relations among the elements of a physical object or system give rise to the properties of the system. These properties manifest themselves directly or indirectly by means of the external interactions of the system as phenomena. The totality of the relatively stable, essential properties of a system is the quality of the system. The quality distinguishes one system from other systems.
3. Physical quantities
In the physical sciences it is common practice to use the term physical quantity for certain physical properties that can be readily associated with numerical values. In our discussions above we discussed both the quantitative and qualitative sides, yet in the early development of physics, particularly in mechanics, the emphasis was almost entirely on the quantitative side of physical properties since the qualitative side was regarded as unchanging. Hence the term physical quantities.12
Concepts of spatial dimensions (length, area, volume) and of weight developed long before they were needed for physics. The oldest written records are largely inventories of grain, oil, and other agricultural products, and the units of measurement were needed to record accumulated private wealth. In fact, some forms of land measure, e.g., the Chinese mu, are derived from the agricultural yield expected from the given tract of land. As the first investigations of the mechanical interaction of matter got underway, it was found that weight could be used to characterize the inertial properties of matter even though the qualitative relationship between weight and mass were not understood. The unit of weight then became the means for designating subsequently the mass or quantity of matter. Newton’s laws subsequently showed the need for distinguishing between mass and weight. The original term for mass was simply the quantity of matter. Similarly, momentum, which was defined as the product of quantity of matter and the velocity, was called quantity of motion (and still is in French). It was thus possible to establish a quantitative expression for momentum even though its qualitative associations had not yet been firmly established. In the case of the concept of energy, we see a similar process of a stress on the quantitative at the expense of the qualitative, the consequences of which are still evident in the persistent failure of physics textbooks to discuss the concept of energy in other than quantitative terms.
There is no concept of quality that exists without some quantitative association. Quantitative gradations are not always connected directly with numerical values. We can use our fingers, for example, to characterize the temperature of water as ice cold, cold, lukewarm, mildly hot, very hot. The point of reference here is generally our body temperature. Such a system of measurement is obviously unsatisfactory for scientific investigations, since small differences of temperature cannot be reliably established, as they could be, say, with an ordinary alcohol thermometer. In any case, temperature as a physical quality has no meaning without its quantitative side.
The concept of quantity, however, is, in its essential character, the opposite of quality. Thus, the real numbers, our means for indicating quantity, can be considered to be quality-less quantity, indifferent as they are to the quality of the object. In a sense, the number is the great equalizer, the destroyer of quality. In Newton’s laws the quantity of matter, that is, the numerical value of the mass, was of no qualitative significance. All masses, large or small, obeyed the same laws of motion.
We have already discussed one set of opposite characteristics associated with physical properties: they are immanent in the object but not independent of other objects. We now find that physical properties, when expressed as physical quantities, are associated with another set of inseparable opposites: quantity and quality.
The quantitative aspect of a physical quantity is united with the quality through the concept of measure and is expressed as units of measurement. The term dimension or dimensional unit is also used for this purpose. Meters, pounds, seconds, quarts, dynes, and radians per second are examples of such units.
Physical quantities are usually divided into two groups, fundamental and derived. The dimensional units of mass, length, time, and electric charge are generally taken as fundamental units and the units of the derived quantities are considered to be expressible in terms of them. Thus the energy unit joule can be expressed in terms of the fundamental units as follows:
1 joule = 1 (kilogram)(meter)2 / (second)2 (3)
The right-hand side of the equation is obtained from the definition of mechanical work: the product of force and distance, where the force is replaced by the product of mass and acceleration on the basis of Newton’s second law. The joule is a general unit for energy and is also used as the unit for mechanical work
Unless an equation is an identity, its two sides must be nontrivially different qualitatively. On the other hand, the expression of equality indicates that there is something on each side that is not only quantitatively equal, but also qualitatively equal. What is the nature of the qualitative equality when units of one kind are expressed in terms of units of another kind, or more generally, when we express physical laws in the form of equations? In general the question cannot be answered by a formal mathematical examination of each side of the equation. The answer must be found in the conceptual framework and logical structure of the physical laws forming the basis of the physical theory. This is the basis on which certain physical quantities have to be identified as fundamental.
The connection between fundamental physical quantities and the fundamental laws can be better understood by considering the units of energy appearing in Equation 3. Let us look more closely at what is involved when we express energy in terms of mechanical work. It was Helmholtz who established the universality of the law of conservation of energy and demonstrated its mathematical consistency, which resulted in its acceptance by the scientific community, even though he was not the first to enunciate the law. He was unable, however, to give a qualitative explanation of the concept of energy. Maxwell defined the energy of a body as its “capacity for doing work,” where work itself was defined as the overcoming of resistance,13 a direct connection with the application of a force to move a body some distance. The inadequacy of tying the concept of energy to mechanical work can be seen from the fact that chemical energy can be transformed into electrical energy even though no mechanical work is actually done. In fact energy is never transformed into mechanical work, but mechanical work can be performed during a process of transformation of matter from one form to another. When we express energy changes in units of mechanical work we are expressing the maximum amount of mechanical work that can be performed potentially during a process in which energy is transformed from one form to another. Thus an electric crane lifting a weight transforms electrical energy into potential energy and does work against the earths’ gravitational field in the process.
The units on the right-hand side of Equation 3 are also the same units one would obtain from the kinetic energy ˝ mv2. Prior to Helmholtz’s work the term vis viva (living force) was used for mv2. Helmholtz explained that he added the coefficient ˝ as a mathematical convenience, “whereby it becomes identical with the measure of mechanical work.”14 Historically, therefore, the right-hand side of Equation 3 clearly represents units of mechanical work. Nevertheless, the concept of energy should not be tied to mechanical work, but be regarded as a qualitative expression of the transformability of matter from one form to another and as a quantitative measure of the capacity of a physical system to undergo such transformation. This meaning is almost entirely lost in the mechanistic focus on the quantitative.15 Perhaps the unit of energy should even replace mass as a fundamental unit. The well known Einstein relation E = mc2,` which relates mass directly to energy is another argument in favor of this.
4. Operational definitions of physical quantities
Operational definitions of physical quantities were introduced by P. W. Bridgman within the framework of the logical-positivist philosophy. In this view, physical quantities such as charge, temperature, mass, length, and time are “defined as the objective results of certain prescribed operations that can be carried out in the laboratory.”16 In other words, “the definition of a physical quantity has been given when the procedures for measuring that quantity are specified. This is called the operational point of view because the definition is, at root, a set of laboratory operations leading to a number with a unit.”17
Our criticism of the operationalist concept of a physical quantity should immediately be apparent. Physical quantities, as physical properties, are objective attributes of matter that can manifest themselves in a number of ways. An operational definition selects one particular phenomenal form and identifies that as the property without acknowledging the objectively existing material source of the phenomenon of which the measurement is an expression. A materialist understanding of a physical quantity as a property of matter immediately stimulates a multi-sided investigation of the property in all of its manifestations in order to deepen our knowledge of it. As an expression of the need to standardize measurement procedures, operational definitions introduced nothing new. This need had already been recognized. The principal positive contribution of the operationalist approach was its insistence on establishing precise quantitative definitions for the physical magnitudes used for particular theoretical models. For example, we can determine the radius of a proton by a number of experimental techniques. However, the term radius is defined differently within the framework of each model. The radius is thus defined in a model-dependent context and is determined quantitatively by interpreting the experimental data on the basis of a particular model. An operational definition of radius would simply associate the experimentally determined radius with the model used for its calculation from the data. Most physicists, however, would recognize that the problem is really that we do not yet know enough about the proton to be able to give the concept of radius a relatively unambiguous meaning.
In the absence of a comprehensive theoretical understanding of a physical system or in the presence of extremely complex detail, the use of different models is necessary for practical applications and further scientific investigation. The various parameters entering such models have to be precisely defined. The use of the term operational definition to describe this use of models obscures rather than clarifies their connection with the objectively existing physical system because of the philosophical context in which it was introduced—one which denied the existence of an objective reality independent of our being.
The shortcomings of operational definitions are readily seen by an example outside of physics: the operational definition of intelligence as “that which is measured by an IQ test.” If, as is often suggested, there is no scientifically sound basis for classifying individuals according to a scale of intelligence, then the operational definition ties a meaningless precision to a nonexistent human quality.18 This would be equivalent to the use of a theoretical model that in no way corresponded to the objectively existing properties of the system the model is supposed to reproduce.
During the past fifty years many, if not most, physicists in the United States fell under the influence of Bridgman’s operationalist concept’s. After taking root in physics, operationalism spread rapidly to other fields. During the last twenty years, however, there has been a growing criticism of these concepts and today there is increasing recognition among physicists that the concept of physical properties cannot be reduced to the specification of procedures for their measurement.
As I have already indicated, writers on philosophical problems of science are giving more attention to the nature of physical properties and how they arise on the various levels of matter. From the discussion above, it should be clear that dialectical materialism provides a powerful methodological tool for the discussion of physical properties. It is unfortunate that very little literature has been written in English on dialectical-materialist methods in physical sciences and that, aside from specialized discussions on quantum mechanics, very little of the rich literature in other languages (mostly from the socialist countries) is available for the English-language reader. [Note added by author in 2008: “socialist countries” refers to the former Soviet Union and the Eastern European socialist countries.]
A number of topics closely related to the discussion of this article could not be included if only for reasons of space. Among them are the relationship of dialectical and formal-logical contradictions and the connection between the logical and historical in the emergence of physical properties. These areas, however, still need much attention.
*Much of this work was done at Humboldt-University in Berlin, German Democratic Republic, where I spent a sabbatical year. I am grateful to the University authorities for the support given me. I am particularly indebted to Dr.Analiese Giese, Dr. Ulrich Röseberg, and Dr. Fritz Gehlar for very helpful discussions.
of Physics and Astronomy
University of Minnesota
1. See, for example, Evelyn B. Pluhar, “Emergence and Reduction,” Stud. Hist. Phil. Sci., vol. 9 (1978), no. 4, pp. 279–89.
2. Clifford A. Truesdell, Six Lectures in Modern Natural Philosophy (Berlin, Heidelberg: Springer, 1966), p. 11.
3. I. V. Blauberg, V. N. Sadovsky, and E. G. Yudin, Systems Theory.,Moscow: Progress, 1977), pp. 127–32.
4. H. Hörz, H.-D. Pöltz, H. Parthey, U. Röseberg, and K.-F. Wessel, Philosophical Problems of Physical Science (Minneapolis: Marxist Educational Press, 1980), ch. 2.
5. Blauberg et al., Systems Theory, pp. 276–82
6. Horz et al., section 2.6.
7. A. I. Ujomov, Dinge, Eigenschaften and Relationen (Berlin: Akademie-Verlag, 1965), ch. 4. (In German): translation of A. I. Uyemov, Veschi, svoistva i otnosheniya (Moscow: Izd. Akad. Nauk SSSR, 1963)
8. A. I. Ujomov, p. 34.
9 . P. W. Bridgman, The Logic of Modern Physics (New York: Macmillan, 1927).
10. V. I. Lenin, Materialism and Empirio-Criticism, vol. 14 of Collected Works, (Moscow:Progress Publ., 1972), p. 103
11. Ujomov, p. 35.
12. In some languages, e.g. German and Russian, the term magnitude is used instead.
13. James Clerk Maxwell, Theory of Heat, 4th ed. (London: Longmans, Green & Co., 1875), pp. 87–90.
14. Cited by Engels, Dialectics of Nature (New York: International Publ., 1940), p. 74.
15. For a more detailed discussion, see Erwin Marquit, “Stability and Development in Physical Science,” in Alan R. Burger, Hyman R. Cohen, and David H. DeGrood, eds., Marxism, Science, and the Movement of History (Amsterdam: B. R. Gruner, 1980).
16. David Halliday, Introductory Nuclear Physics, 2nd ed. (New York: Wiley, 1955), p. 4.
17. David Halliday and Robert Resnick, Fundamentals of Physics, revised printing (New York, Wiley, 1974), p. 1.
18. For other criticisms of operationalism see Erwin Marquit, “Philosophy of Physics in General Physics Courses,” American Journal of Physics 46, no. 8 (Aug. 1978), pp. 784-–89 and Mario Bunge, Philosophy of Physics (Dordrecht, Holland, 1974), ch. 1.