Time is one of the undefined concepts in the paradigm of modern natural science. Any science is based on prerequisites like, in particular,

In deductive sciences the fundamental undefined concepts (which are used as evident ones, and, by an implicit convention, as the ones understood in the same way by different scientists) are the basis for logical framework construction.

When we ask "What is time?", we are expecting an answer in at least two meanings. The first one is: what is the origin of the World's dynamic variability? Where does the sequence of events come from? Why is any instant followed by another one? Why does everything that exists change? Why is a totally stable World impossible?

The second meaning of the term "time" is the quantitative measure of object variability. How can one relate a number to a variation? How can one compare changes in different objects? The experience of scientific cognition prompts us that if we are unable to measure the manifestations of variability, we take a risk of being unable to gain insight into what is called its "origin".

An attempt to explicate the time concept should lead to its splitting into at least two sub-concepts:

a pre-time as an understanding of variability existing in the World and

a parametric time as a way of its quantitative description by comparison with the variability of a reference object, commonly called "a clock". Mathematically the pre-time is usually represented by the order relation on the set of events (the sequence of events), while the parametric time is just a metric on the set of events ("length" of the events).

Modern science does not contain a viewpoint upon the nature of time which could be understood as the existence of certain mechanisms creating the novelty and being the origin of changes in the World. In pre-scientific (or non-scientific) cognition such a role is commonly played by the Demiurge under whose control there are both the creation of objects and changes of their fate.

Natural science uses most readily the time concept which has been formed in the physical sciences. Time is always one of the initial, basic concepts, underlying all the dynamic constructions. Moreover, the latter, in general, gain a physical sense just due to the time concept. Thus the structure of time as a physical object is postulated to be as simple as possible from the very beginning from the viewpoint of its elementary physical properties (Akchurin 1974).

In physics time is identified with the set of real numbers. Their mathematical architecture is very rich: their construction involves closely interwoven structures of order and topology and several algebraic structures. Evidently the mathematical properties of a straight line should conform to the real properties of the physical time. The structure of order creates the succession of time instant. The additive group of number addition forms the metric to measure physical time intervals. The number multiplication group enables us to choose arbitrary units for measuring time. The real-number line topology induces the physical time continuity. However, physics does not contain a necessity and sufficiency analysis of the real line axiomatics (containing one and a half or two tens of postulates) for describing the actual properties of time. A reason for that is the usual absence of an explicit non-mathematical concept of time in physics. (Attempts to give a physical interpretation of the concept of time can be found in papers by N. A. Kozyrev (1991), Yu. I. Kulakov (1982), and also articles by Yu. S. Vladimirov and V. V. Aristov in this volume.) The physical "time of an event is the reading of a clock at rest, situated at the same place and simultaneous with the event..." (Einstein 1905, p.10), i.e., the properties of physical time coincide with the properties of physical clocks.

A number of operational methods of the time interval measurements able to play the role of clocks have been suggested in physics. These methods are based solely on physical objects variability standards.

Natural scientists are not always pleased with the physical context of the concept of time measured by physical clocks and imagined as points of the real axis. Physics "specifies" time by excluding the formation, i.e., the property of time described using the concepts of past, present and future rather than the terms "before" and "after". In natural science where all the studied objects are frail, where the beginning and the end of each reality is so essentially inevitable, where the reversibility of phenomena is an exception rather than a rule, the "specified" image of time can drastically narrow the possibility of extrapolating the physical concept of time beyond the frames of special relativity. The interpretation of time as an intrinsic property of a physical system goes beyond the frames of the traditional physical description (Prigogine 1984). The question of whether the time of physics is the time of natural science, is so far unresolved, though repeatedly discussed (Bergson 1926; Vernadsky 1975; Meyen 1983; Prigogine 1984).

The natural scientists' dissatisfaction with the physical explication of the time phenomenon leads to attempts to introduce specific scientific concepts of time. In some fields of knowledge time becomes an essential rather than a background factor of the existence of natural objects. Above all those are certainly the objects of biology (Baer 1861; Vernadsky 1975). The specific biological time has appeared under the name of "organic" (Backman 1943) or "physiological" (Noüy 1936) time and continues to focus the scientists' attention (more detailed references can be found in the papers by A.M. Maurins, 1986). Only in the seventies about 25 books and 11 thousand journal articles, connected with the problems of time in biology, have been published (Study of Time, 1981).

The notion of specific time of geology (Neumayer and Pauli 1875; Vernadsky 1975) have become a working tool in geospheric studies (The Development of Time Studies in Geology, 1982; Simakov 1977; Onoprienko et al. 1984; Harland et al. 1982). As for psychological time, in the same period 35 books and more than a thousand of journal articles appeared (Study of Time, 1981), testifying the important role of the concept of time in the science of human psyche (see also a vast bibliography in the papers by Doob (1971), Golovakha and Kronik (1984)). Sometimes also geographic (Markov 1965, Rychkov 1984), economic and social (Study of Time, 1972, 1975, 1978, 1981) times are also mentioned.

In modern natural science, along with the studies of the scientific times, temporal characteristics of objects in different branches of rhythmology are frequently investigated, specifically, their variability with respect to astronomical cycles, synchronous with them or their multiples. However, there exist acyclic variability, irregular and unique temporal characteristics which also play a significant role in natural science. They are not covered by rhythmology but are studied within a wider investigation programme, namely, temporology ( Maurins 1986). The concepts of time acquire unequal senses in the intuition of scientists studying different fragments of the reality. Therefore as far as time is one of the undefined categories in the conceptual framework of science, temporology cannot be the field where a consistent discussion of the concepts of time would be possible.

Unlike many natural sciences, the field of human activity connected with the construction of computer "knowledge bases" and "artificial intelligence" inevitably requires an algorithmable construction of real time (Kondrashina et al. 1989).

A "true" age of a system can be measured only using the system's proper time scale rather than the astronomical one. To achieve that, a "proper scale" must be found and constructed.

Forecasting is one of the basic functions of science. The scientists' helplessness in forecasting the ecological consequences of human activities, seismic and climatic disasters on the Earth, the society's scientific, technological and social development aggravates the survival problems for the whole humanity. From A.M.Maurins point of view (1986), the most common factor exciting the humanity's interest to the problems of time, is a sharp acceleration of the social processes creating "a shock from a collision with the future" (Tofler 1972). Any scientific forecasting methodology implicitly contains the scientist's conception of time.

The forecasting problem can be formulated in a much more general scientific context. One could speak of searching the causes creating the very dynamics and evolution of the World's objects, i.e., the principles of event determination or causality.

Stressing the necessity of studying the problem of time, I. Prigogine (1984), referring to the fundamental work of J.Needham (1969), noted that even Chinese alchemists' supreme purpose was to be able to manipulate with time, namely, to make the biological time of their bodies obey their will. Knowledge of the origin of systems' temporal characteristics can make it possible to solve applied questions concerning time control and mastering, more precisely, to scientific ways of acceleration or deceleration of the systems' natural development. The proper development rates of natural objects vary significantly. The studies of time should explain the causes of the differences and reveal the possibilities to render influence on the proper time of the objects (the bounds of age, development rates, relative proceeding rates of different stages). If the temporal characteristics of a system cannot be affected, the very understanding of that could apparently be a significant scientific achievement.

In the seventies there appeared a hope that experimental studies of time might become part of normal physical studies. N.A.Kozyrev, led by his own conjecture on the substantionary nature of time, discovered the influence of irreversible processes, both on the Earth and in space, on the weight of nonrotating and rotating bodies and on some properties of matter, such as density, elasticity, viscosity, electric conductivity, etc. and on the conditions of living systems. N.A.Kozyrev connected the active factor of the irreversible processes with the active properties of time, with causality and with so far unknown physical energy sources (Kozyrev 1982, 1991; Yeganova 1984). At present a certain doubt still remains on whether all the traditional causes of the observed phenomena have been taken into account. The absence of observation of N.A.Kozyrev's effects in regular precision measurements and other experiments in the laboratories of the world also requires thorough explanation. For instance, Shaw's experiments (Piragas 1971), where the influence of the nonequilibrium process of heating on the value of the gravitational constant was investigated, demonstrated that the reading of a torsion balance was invariable up to 1.6 ´ 10-6, while Kozyrev's effects are of the order 10-4 - 10-5. However, an explanation of N.A.Kozyrev's experiments by more prosy conjectures than the active properties of time, was absent as well. The second part of this book contains a detailed discussion of the "active" properties of time according to N.A.Kozyrev.

The applied problems of time studies can be solved adequately only with the development of theoretical knowledge for which elaboration of the constructive notions of time is in my opinion of top necessity.

A task of the scientific approach in natural science can be formulated as the ability to forecast the variety and variability of natural objects.

In my opinion, the basic motivation in studying the time phenomenon is a hope to discover the ways of finding the laws of variability. One of the basic objects of science is to obtain these laws, otherwise it becomes impossible to fulfil the forecasting function of the cognition. Apparently it is impossible to find the laws of variability without having the correct causal and parametric descriptions of time.

A dynamic theory describing any fragment of the reality inevitably includes a number of components whose development forms, deliberately or, more frequently, implicitly, the stages in the process of creating a theory. (I.A.Akchurin (1974) is the one who clearly revealed the inevitability of solving some of the classes of methodological problems listed below.)

- The O component is a description of an idealized structure of the theory's elementary object.

- The S component lists the possible states of the objects. In other words, the S component is called the space of states of the studied system.

- The C component fixes the ways of object variability and corrects superfluous idealization connected with object selection, since there are no objects in the real world, there exist processes whose abstraction leads to the notion of objects. The C component inserts processes, variability, i.e., the "pre-time", to the theory.

Instead of rigorous definitions, I would like to give some examples of elementary objects and their variability.

In ecology of communities an elementary object is a population of organisms. The variability consists of births and deaths of individuals. The space of states can be described as a set of all possible vectors where n is the number of individuals of the i-th species - member of the community. The numbers are limited by the available resources of the environment.

- The T component of a theory consists in the introduction of clocks and parametric time into object description. The parametric time can be understood as an image of changing objects when the variability process is mapped into a linearly ordered set with a metric (generally a number set). The variability of a selected object is usually taken as a standard to be used in the measurements of other variabilities. A clock is just a natural object whose variability is a standard and an operational way of the above mapping.

Variability parametrization using physical clocks pierces through nearly all the human existence controlled by consciousness, including science, culture and everyday life... However, the changes occurring in the world, cannot be reduced to mechanical motions: there exist, for instance, chemical transformations of matter, the geological history of the Earth, the development and death of living organisms and whole communities, non-stationarity of the universe and social genesis... Would it be incorrect to recognize that the clocks which we pose in different frames of reference to describe the variability of natural objects, can be different? Can one assert in these conditions that some of the clocks, for instance, physical, are "good" while the others are "bad" ?

A. Poincaré stressed that "... a way of measuring time which would be more correct than another one, does not exist. The one adopted is just more convenient than the others. Comparing clocks, we cannot say whether one of them operates well or not, we can only say that one of them is preferred" (Poincaré 1898). In the nonphysical branches of natural science more and more frequently there appears the need to use a clock unsynchronized with the physical standards but more convenient and adequate than the latter when unphysical phenomena are to be described.

The L component of the theory is the formulation of the variability law which selects the real generalized motion of the objects in the space of states among all the possible motions (the term "generalized motion" is used as a synonym of object variability).

For many fields of natural science (in particular, for the already mentioned nuclear theory, embriogenesis and ecology) the variability law formulation is the aim of theory construction. This aim cannot be achieved if the classes of problems forming the O, C, S, and T components of the theory, are not solved in a consistent way. In natural science methodology the C and T components are elaborated less than the others. There is a close connection between the choice of these components and the way of obtaining the L component. According to A.A.Sharov (see the chapter in this book), the law of motion is a description of the variability of the studied object in terms of the variability of the standard clock, therefore the ability to discover the variability law can depend on the adequacy of the standard clock selection to the studied processes. The laws of motion affect the ways of measuring time in the domains where the T and L components agree with each other (Le temps et la pensee physique contemporaine 1968), for instance, "...simultaneity of two events or their sequential order, and the equality of two durations, must be defined in such a way that the formulations of the natural laws would be as simple as possible" (Poincaré 1893).

It seems that the difficulties in obtaining the equations of motion in many fields of science are connected with the disagreement of the physical methods of time measurement with the unphysical nature of the studied laws.

Finally, the I component of the theory is formed from the set of interpretation procedures. Firstly, that is the procedure of relating the mathematical constructions of the theory, which have, as a rule, a formal character, to the abstract notions of the reality; secondly, those are the rules of how these abstract subject notions are related to the quantities measured in the experiment.

The I component is a necessary ingredient of a theory. It is the interpretation procedure that turns a formal theoretical scheme into a science studying the reality. The possibility of developing the I component depends not only on the advantages of the theoretical scheme, and often not even as much so, but also on the "technology sum" achieved by the whole civilization.

A consistent solution of the theoretical and practical problems connected with the studies of time is impossible as long as time remains among the basic undefined concepts of science. In the modern scientific paradigm the time phenomenon is implicitly present in the explanations of practically all the manifestations of the reality. Apparently natural science lacks the entities and (or) elements of the conceptual basis to explain the existence of time. In my opinion, the main problem in the studies of time is to create an explicit construction of time which could yield a sufficiently rich language for discussing the intuitive notion of time inherent to the scientists investigating different sides of the reality. At present the main hing in the posed problem is to realize that the problem does exist.

The work aimed at creating such a construction of time that would meet all the requirements, is apparently unfinished. Summing up the viewpoints of the investigators of time, Prof. J. T. Fraser, founder of the International Society for the Studies of Time, was very optimistic: "But a universally acceptable framework that could accommodate the multitude of views about time, one which could serve as a guide for critical studies, does not exist. It may never be possible to consider physical, biological, psychological, historical, literary, and philosophical notions of time under the same heading. Yet, a survey of the literature of time does not leave one with the impression of complete incoherence, but rather with a kind of feeling that researchers often have while examining unreduced data. Surely there is a design to be found; surely there is universal truth to be discovered; there must be a pattern hidden somewhere among the multiplicity of facts, utterances, and fiction" (Fraser 1981, p.XIV ).

The views of time are closely connected with the concepts of motion, space, interaction, energy, entropy, etc. Thus a construction of time must be in agreement with these and many other constructions of general scientific concepts. A replacement of the time postulate in the conceptual ground of natural science would imply a significant revision of the whole conceptual framework of science. The experience shows that, despite the complexity of the problem, revisions of the conceptual grounds of separate branches of science occur rather frequently.

Evidently, different versions of the construction of time are possible. What are the plausibility criteria for those constructions? The problem approach to reviewing the developed models is suggested: to be adopted, a suggested model must describe certain properties of time, it must solve the prescribed set of problems and, as much as possible, it must give a key to the derivations of the laws of natural object variability or open a way to experimental studies of time.

An a priori selection of the verifying criteria certainly depends on the intuitive views concerning the content of the time phenomenon. I would like to suggest to the reader a set of the properties and problems of time formulated by the initiative group of Moscow Interdisciplinary Seminar on the Studies of Time in Natural Science (M.A.Arkadyev, A.D.Armand, D.A.Cherepanov, A.A.Kronik, A.P.Levich, G.E.Mikhailovsky, V.M.Sarychev, V.A.Volodin and A.A.Sharov).

- Is time universal or specific for different systems? If the latter is true, what is the sense of the assumed specific character of natural-scientific times, e.g., biological, geological, physical and others? What are the subordinations and connections of those specific times with each other?

- Is time discrete or continuous?

- Is time homogeneous or qualitatively alternate?

- Is it bounded or boundless?

- How can one describe the inhomogeneity of the proper times of different systems?

- Is time a reality or a convention?

- Is time a substance or a relation?

- Does time depend on matter? In other words, does the variability require a sort of external cause or is it a consequence of the inherent, independent activity of matter (Prigogine and Stengers 1986, p.362)?

- How do the natural systems "organize" or "produce" time?

-What is the origin of the appearance and the course of time? What is the cause of the World's variability? Why is the totally stable World impossible?

-Why is it that all the events throughout the World do not occur simultaneously (Whitrow 1961, p.352)? Where does the sequence of events come from? Why is any time instant followed by another one?

-Why is the present moment unique?

-Is an existence outside time possible?

- Why is everything that exists, perishable?

- What is the relation between time and causality?

- In what way is time included in the conceptual basis of natural science? Namely, in which way is time related to the other natural-scientific constructions such as space, motion, structure levels of matter, life, energy, mass, entropy, interaction, etc.?

- What are the relations between the coordinate time of the systems (the sequence "earlier - later") and the "proper" time (the sequence "past - present - future")?

- What determines the variety of the "proper" times of the systems and processes (the times of existence, relaxation, development...)?

It goes without saying that these lists can neither exhaust the existing properties nor the possible problems of time. An inquisitive reader can apply to the fundamental works of J.Whitrow (1961), Yu.B.Molchanov (1977, 1980), J.Fraser (1978) and V.P.Kazarian (1980). As for the problems themselves, they challenge the natural scientists: which construction of time is able to solve them?

REFERENCES