Space and Time

the universal forms in which matter exists. Space and time do not exist outside of matter or independently of it.

Spatial characteristics include position relative to other bodies (the coordinates of bodies), the distances between bodies, and the angles between different directions of space. Individual objects are characterized by length and form, which are determined by the distances between the parts of the objects and by the orientation of the parts. The characteristics of time are the instants at which phenomena occur and the length (duration) of processes. The relations between these spatial and temporal quantities are called metric. There are also topological characteristics of space and time—the contiguity of different objects and the number of directions. Purely spatial relations are involved only when it is possible to abstract from the properties and motions of bodies and their parts. Purely temporal relations are involved only when it is possible to abstract from the manifold of coexistent objects.

In reality, however, spatial and temporal relations are interconnected. Their direct unity is manifested in the motion of matter; displacement, the simplest form of motion, is characterized by quantities that represent different relations of space and time (speed, acceleration) and that are studied by kinematics. Modern physics has established a deeper-lying unity of space and time that is expressed in the regular covariation of the spatiotemporal characteristics of systems as a function of their motion and in the dependence of these characteristics on the concentration of masses in the environment.

Frames of reference are used to measure spatial and temporal quantities.

As knowledge of matter and motion advances, the scientific concepts of space and time are examined more closely and altered. Therefore, the physical meaning and significance of newly discovered regularities of space and time can be understood only by establishing the relation of these regularities to the general principles underlying the interaction and motion of matter.

The concepts of space and time are a necessary component of the overall picture of the world and therefore fall within the purview of philosophy. The study of space and time is advancing and developing as natural science—especially physics —develops. Among the other natural sciences, astronomy— especially cosmology—has contributed significantly to progress in the study of space and time.

The development of physics, geometry, and astronomy in the 20th century has confirmed the correctness of the position of dialectical materialism regarding space and time. In turn, the dialectical materialist concept of space and time makes it possible to interpret correctly the modern physical theory of space and time and to reveal the unsatisfactoriness of both the subjectivist interpretation of the theory and attempts to “develop” the theory by separating space and time from matter.

Spatiotemporal relations obey not only general laws but also specific laws characteristic of the objects of a given class, inasmuch as the relations are determined by the structure and intrinsic interactions of a material object. Such characteristics as the dimensions and shape of an object, lifetime, rate of processes, and type of symmetry are therefore significant parameters of an object of a given type that also depend on the conditions under which the object exists. Spatial and temporal relations are particularly specific in complex developing objects, such as an organism or society. In this sense we may speak of the individual space and time of such objects, for example, biological or social time.

Basic concepts. The most important philosophic problems bearing on space and time are the questions of the essence of space and time, the relation of these forms of existence to matter, and the objectivity of spatiotemporal relations and laws.

Two basic concepts of space and time have existed throughout virtually the entire history of natural science and philosophy. One concept comes from Democritus, Epicurus, Lucretius, and other ancient atomists, who introduced the concept of empty space and considered it homogeneous (the same at all points) and infinite; Epicurus believed that empty space was not isotropic, that is, not the same in all directions. In ancient times the concept of time was extremely poorly developed and was considered a subjective perception of reality.

In the modern era this concept was developed by I. Newton in connection with his elaboration of the principles of dynamics. Newton cleansed the concept of anthropomorphism. He held that space and time are special elements that exist independently of matter and each other. Space in and of itself (absolute space) is an empty repository of bodies that is absolutely immobile, continuous, homogeneous, isotropic, permeable without affecting or being affected by matter, infinite, and three-dimensional. Newton made a distinction between absolute space and the dimension of bodies, the fundamental property of bodies by virtue of which they occupy definite positions in absolute space and coincide with these positions. If we speak of the simplest particles (atoms), then dimension, according to Newton, is the initial and primary property that does not require explanation. Absolute space is unmeasurable and unknowable because of the indistinguishability of its parts. The positions of bodies and the distances between bodies can be determined only with respect to other bodies. In other words, science and practice deal only with relative space.

Time, as Newton saw it, is something absolute and entirely independent—pure duration per se flowing uniformly from the past to the future. It is an empty repository of events, events that may or may not fill it; the course of events does not affect the flow of time. Time is universal, one-dimensional, continuous, infinite, and uniform (everywhere the same). Newton distinguished relative time from absolute time, which also is unmeasurable. Time is measured by means of clocks, that is, by means of periodic motions. Newton regarded space and time as independent of each other. The independence of space and time is manifested above all in the fact that the distance between two given points in space and the time interval between two events retain their values independently of each other in any frame of reference and that any relations may obtain between these quantities (the velocities of bodies).

Newton criticized R. Descartes’s idea of a filled space, that is, the identity of extended matter with space.

The concept of space and time elaborated by Newton prevailed in natural science in the 17th to 19th centuries since it conformed to the science of that period—Euclidean geometry, classical mechanics, and the classical theory of gravitation. The laws of Newtonian mechanics hold only in inertial frames of reference. Inertial frames of reference were singled out in this way because they move translationally, uniformly, and rectilinearly with respect to absolute space and time and because they best correspond to absolute space and time.

According to Newton’s theory of gravitation, actions are transmitted instantaneously from some particles of matter to others through the empty space separating the particles. The Newtonian concept of space and time thus fully conformed to the overall physical picture of the world current in that era, and in particular to the concept of matter as primordially extended and by nature invariant. The essential contradiction in Newton’s concept was that absolute space and time remained unknowable by experimental means. According to the relativity principle of classical mechanics, all inertial frames of reference are equivalent and it is impossible to determine whether a system is moving with respect to absolute space and time or is at rest.

This contradiction served as an argument for advocates of the opposing concept of space and time. This concept, whose initial premises date back to Aristotle, was elaborated by G. W. von Leibniz, who also relied on some of Descartes’s ideas. The distinguishing feature of Leibniz’ concept is the rejection of the concept of space and time as independent elements of being that exist together with and independently of matter. According to Leibniz, space is the order of the relative arrangement of a set of bodies that exist outside each other, and time is the order of succeeding events or states of the bodies. Leibniz subsequently incorporated in the concept of order the concept of relative magnitude. Leibniz’ theory holds that the concept of the dimension of an individual body, if considered without regard to other bodies, is meaningless. Space is a relation (order) applicable only to many bodies—a series of bodies. One may speak only of the relative dimension of a body compared with the dimensions of other bodies. The same is true of duration: the concept of duration is applicable to an individual phenomenon insofar as the phenomenon is considered a link in a single chain of events. The extent of any object, according to Leibniz, is not a primary property but is due to forces acting within the object; internal and external interactions also determine the duration of a state. As for the very nature of time as the order of succeeding phenomena, time reflects the causal relation of phenomena. Leibniz’ concept is logically connected with his philosophic system as a whole.

However, Leibniz’ concept of space and time did not play a significant role in natural science in the 17th, 18th, or 19th centuries because it could not answer the questions raised by science in that period. Above all, Leibniz’ views on space seemed to be inconsistent with the existence of a vacuum; the problem of the vacuum was seen in a new light only after the discovery of the physical field in the 19th century. In addition, his views clearly contradicted the universal belief in the uniqueness and universality of Euclidean geometry. Finally, Leibniz’ concept appeared to be irreconcilable with classical mechanics because it seemed that recognizing the pure relativity of motion does not provide an explanation for the preferential role of inertial frames of reference. Thus, the natural science of Leibniz’ day found itself at odds with Leibniz’ concept of space and time, which was constructed on a much broader philosophic foundation. It was only two centuries later that scientific facts demonstrating the limited nature of the then prevalent concepts of space and time began to accumulate.

Concepts of space and time in philosophy and natural science in the 18th and 19th centuries. Although materialist philosophers of the 18th and 19th centuries attempted to solve the problem of space and time primarily in the spirit of the concepts of Newton or Leibniz, they generally did not fully adopt either concept. Most materialist philosophers opposed Newtonian empty space. J. Toland was one of the first to point out that the concept of a void is linked to a view of matter as inert and inactive. D. Diderot held the same views. G. W. F. Hegel adhered more to Leibniz’ concept. In the concepts of subjective idealists and agnostics, the problems of space and time amounted primarily to the question of the relation of space and time to consciousness and perception. G. Berkeley rejected Newton’s absolute space and time but considered spatial and temporal relations subjectivistically, as the order of perceptions; he did not deal with objective geometric and mechanical laws. Berkeley’s viewpoint therefore did not play a significant role in the development of scientific concepts of space and time.

This was not the case with the views of I. Kant, who at first accepted Leibniz’ concept. The contradiction between this concept and the views of natural science then current led Kant to adopt Newton’s concept and to attempt to substantiate it philosophically. His main point was that space and time were a priori forms of human contemplation, that is, the substantiation of their absolutization. Kant’s views of space and time found many supporters in the late 18th century and in the first half of the 19th. Their inconsistency was proved only after the creation and adoption of non-Euclidean geometry, which essentially contradicted Newton’s understanding of space. In rejecting the Newtonian concept, N. I. Lobachevskii and G. F. B. Riemann asserted that the geometric properties of space, being the most general physical properties, are determined by the general nature of the forces forming bodies.

The dialectical materialist view of space and time was formulated by F. Engels. According to Engels, to exist in space is to exist in an arrangement of one alongside another, and to exist in time means to exist in a sequence of one after another. Engels emphasized that “the two forms of existence of matter are naturally nothing without matter, empty concepts, abstractions which exist only in our minds” (K. Marx and F. Engels, Soch., 2nd ed., vol. 20, p. 550).

The crisis of mechanistic natural science at the turn of the 20th century led to a revival of subjectivistic views of space and time. Criticizing Newton’s concept and correctly noting its weak aspects, E. Mach once again developed the view of space and time as the order of perceptions, emphasizing the experiential origin of the axioms of geometry. Mach interpreted experience subjectivistically, however, and he therefore considered Euclidean, Lobachevskian, and Riemannian geometries as different methods of describing the same spatial correlation. V. I. Lenin provided a critique of Mach’s subjectivistic views of space and time in his Materialism and Empiriocriticism.

Development of the concepts of space and time in the 20th century. The late 19th and early 20th centuries saw a profound change in scientific concepts of matter and a corresponding radical change in concepts of space and time. The concept of field as a form of the material connection between particles of matter and as a special form of matter entered the physical picture of the world. All bodies thus were seen to be systems of charged particles connected by a field that transfers actions from some particles to others at a finite speed—the speed of light. It was believed that a field was a state of the ether, an absolutely immobile medium filling absolute space. It was later established by H. A. Lorentz and others that when bodies move at very high speeds close to the speed of light, a change in the field takes place that leads to a change in the spatial and temporal properties of the bodies. Lorentz believed that bodies shortened in the direction of their motion and that the rate of physical processes transpiring in the bodies slowed, with spatial and temporal quantities varying in coordination.

At first it seemed that it would be possible to determine in this manner the absolute velocity of a body with respect to the ether and consequently with respect to absolute space. All experimentation refuted this view, however. It was established that in any inertial frame of reference all physical laws, including the laws of electromagnetic interactions and field interactions generally, were identical. A. Einstein’s special theory of relativity, which was based on two fundamental assumptions—the limiting nature of the speed of light and the equivalency of inertial frames of reference—was a new physical theory of space and time. It follows from this theory that spatial and temporal relations—the length of a body (and in general the distance between two mass points) and the duration and rate of the processes transpiring in the body—are not absolute quantities, as Newtonian mechanics asserted, but relative. A particle, such as a nucleon, can manifest itself as spherical with respect to a particle moving slowly in relation to it and as a disk flattened in the direction of motion with respect to a particle moving toward it at a very high velocity. Accordingly, the lifetime of a slow-moving charged π-meson is ∼10^-8 sec, whereas that of a fast-moving π-meson (moving at a velocity close to the speed of light) is many times greater. The relativity of the spatiotemporal properties of bodies has been fully confirmed by experiment.

It follows from the above that the concepts of absolute space and time cannot be supported. Space and time are general forms of the coordination of material phenomena and not elements of being that exist independently of matter. The theory of relativity excludes the concept of space and time that are empty and have intrinsic dimensions. The concept of empty space was subsequently rejected in quantum field theory, with its new concept of the vacuum. The subsequent development of the theory of relativity showed that spatiotemporal relations also depend on the concentrations of masses. When we move to a cosmic scale, the geometry of space-time is not Euclidean or planar, that is, independent of the dimensions of the region of space-time. The geometry of space-time varies from one region of outer space to another as a function of the mass density in these regions and their motion. On the metagalactic scale, the geometry of space varies with time because of the expansion of the metagalaxy. Thus, the development of physics and astronomy has demonstrated the inconsistency of both Kant’s apriorism—the interpretation of space and time as a priori forms of human perception whose nature is invariant and independent of matter—and of Newton’s dogmatic concept of space and time.

The relation of space and time to matter is expressed not only in the dependence of the laws of space and time on general regularities that determine the interactions of material objects. It is also manifested in the presence of a characteristic rhythm in the existence of material objects and processes—average lifetimes and average spatial dimensions that are typical of each class of objects.

It follows from the above that extremely general physical regularities bearing on all objects and processes are inherent in space and time. This also pertains to problems connected with the topological properties of space and time. The problem of the boundary (contiguity) of individual objects and processes is directly connected with the question—raised even in antiquity —of the finite or infinite divisibility of space and time, their discreteness or continuousness. In ancient philosophy this question was answered purely speculatively. Zeno of Elea, for example, advanced hypotheses concerning the existence of “atoms” of time. In 17th-, 18th-, and 19th-century science the idea of the atomism of space and time lost its significance. Newton believed that space and time were in reality separated ad infinitum. This conclusion followed from his concept of empty space and time, the smallest elements of which are the geometric point and the instant of time. Leibniz believed that although space and time are divisible without limit, in reality they are not divided into points; in nature there are no objects and phenomena lacking dimension and duration. It follows from the concept of the unlimited divisibility of space and time that the boundaries of bodies and events are also absolute. The concept of the continuousness of space and time was further strengthened in the 19th century with the discovery of the field. In the classical interpretation, a field is an absolutely continuous entity

The problem of the real divisibility of space and time was raised in the 20th century by the discovery of the uncertainty principle in quantum mechanics. According to this principle, infinitely large momenta are needed to localize a microparticle with absolute precision; this is physically unfeasible. In addition, modern elementary-particle physics shows that when very strong effects are exerted on a particle the particle may not survive at all, and multiple particle production may even take place. In reality there exist no real physical conditions under which the exact value of field intensities could be measured at every point.

Thus, it has been established in modern physics that not only is the real division of space and time into points impossible but also that it is fundamentally impossible to carry out the process of real infinite division. Consequently, the geometric concepts of the point, curve, and surface are abstractions that reflect only approximately the spatial properties of material objects. In reality, objects are separated from each other not absolutely but only relatively. The same is also true of instants of time. This view of the “point nature” of events stems from what is called nonlocal field theory. The hypothesis of the quantization of space and time, that is, the existence of minimum length and duration, is being developed simultaneously with the idea of the nonlocality of interaction. Originally it was believed that the “quantum” of length was 10^-13 cm, on the order of the classical radius of the electron or the “length” of the strong interaction. However, phenomena associated with lengths of 10^-14 to 10^-15cm are being investigated by means of modern charged-particle accelerators, and the values of the quantum of length are decreasing (10^-17 cm, the “length” of the weak interaction, or even 10^-33cm).

The problem of the quantization of space and time is closely connected with the problems of the structure of elementary particles. Studies have appeared in which the applicability of the concepts of space and time to the submicroscopic world is denied altogether. However, the concepts of space and time should not be reduced to either metric or topological relations of known types.

The close interrelation of the spatiotemporal properties and nature of the interaction of objects is also seen when analyzing the symmetry of space and time. As early as 1918, E. Noether proved that the law of conservation of momentum corresponds to the uniformity of space, that the law of conservation of energy corresponds to the uniformity of time, and that the law of conservation of angular momentum corresponds to the isotropy of space. Thus, the types of symmetry of space and time as the general forms of coordination of objects and processes are interconnected with the most important laws of conservation. The symmetry of space with respect to mirror reflection has proved to be connected with an essential characteristic of microparticles—their parity.

The question of the direction of time is one of the important problems of space and time. In the Newtonian concept this property of time was considered to be self-evident and not in need of substantiation. For Leibniz the irreversibility of the flow of time was connected with the unambiguous direction of chains of causes and effects. Modern physics has concretized and developed this substantiation, connecting it with the modern understanding of causality. The directionality of time is apparently related to as integral a characteristic of material processes as development, which is fundamentally irreversible.

The question of the number of dimensions of space and time is among the problems of space and time that have been discussed since antiquity. In the Newtonian concept this number was considered to be primary. Aristotle, however, attempted to substantiate the three-dimensionality of space by the number of possible sections (divisions) of a body. Interest in this problem grew in the 20th century as topology developed. L. Brouwer established that the dimensionality of space is a topological invariant—a number that does not change on continuous and one-to-one mappings of space. The relation between the number of dimensions of space and the structure of the electromagnetic field has been demonstrated in a number of studies by H. Weyl, and the relation between the three-dimensionality of space and the spiral nature of elementary particles has also been demonstrated. All this has shown that the number of dimensions of space and time is inseparably connected with the material structure of the world around us.