Laboratory-chair of modelling the natural references 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.

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 classical mechanics the elementary objects are material points with their positions and velocities in the physical space. For instance, the planets of the Solar system. The variability is determined by trajectories of the points. The space of states is the six-dimensional phase space, the product of the three-dimensional Euclidean space and the three-dimensional space of velocities.

In quantum mechanics the elementary objects are the probability amplitudes of the states of microobjects (for instance, the energy states of an atom). Variability in the space of states is determined by trajectories of vectors in the infinite-dimensional Hilbert space.

In nuclear theory the elementary objects are nucleons and some other elementary particles with their specific sets of quantum numbers. The variability consists in mutual transformations of particles and radiation. The space of states is confined to the combinations of quantum numbers for the transforming particles which satisfy the conservation laws.

In embriology the role of an elementary object is played by a living cell, while the variability is the process of cell fission. The space of states is described by archetype morphological indications in zoological taxonomies.

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 (n₁,n₂,...,n_w), where n_i 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.

Traditionally in natural science the clocks are based on physical processes, such as constructions with an elastic or gravitational pendulum, and on astronomic devices fixing the Earth's rotation around its own axis or around the Sun. Modern clocks use caesium or other sources of electromagnetic oscillations; from recent years the pulsar standard of hyperstable periods is widely discussed; radioactive decay can also be used. Here is A. A. Friedmann's (The world as space and time. 1966. P.50-53) description of the emergence of physical clocks: "Let us relate... a certain basic motion to each physical point and define a clock of the given point M as an instrument showing the length t of an arc covered by the material point in its basic motion along the trajectory... Let us call the quantity t the local physical time of the point M. Consider first the stellar time... Define the basic motion to be the motion of the end of an arrow of a specified length, directed from the center of the Earth to a selected star. The stellar time t_s will be measured by the length of the arc stroke by the above arrow end. The stellar time t_s will be the same in all the points of the space, it will be a universal time... Now let us consider another time, called for brevity the gravitational time... Let a material point fall in a constant gravitational field and let us take this motion to be the basic one; the clock shows the length of the path, t_G , passed by the point. This quantity is the one to be called the gravitational time. The stars move non-uniformly with respect to the gravitational time... Let us introduce also... the pendulum time. Let us build a large amount of equal clocks with a pendulum and define the basic motion to be that of the end of the second arrow of the clock at each point. Denote its path from a fixed initial position by t_p which will be called the pendulum time. Unlike the universal stellar and gravitational times, the pendulum time will be local and different at different latitudes".

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" ?

Such an estimate would be understandable if it concerned, e.g., Galilei, who tried to determine the law of motion of the physical pendulum, the temple chandelier, using his "physiological clock", the rhythm of his own heart.

A. Poincare 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" (A. Poincare. La Mesure du Temps// Revue de Metaphysique et de Morale. 1898. V.6. Pp.1-13). 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.

In embriology the development of different organisms is effectively described using the biological time unit equal to the interval between the same fission phase. The above unit depends on the temperature and the species, there-fore the laws of development revealed using the description in detlafs, remain undiscovered when the astronomical time is used. The populational time in ecology, ethnography and genetics is conveniently measured by the number of changed generations. The chronostratigraphic geological time scale is formed from a sequence of rocks with standard points selected in open-casts with the best preserved boundary layers. For biology-based stratigraphy the geological epoch durations can be measured by the vertical thickness of the layers where the corresponding species are met.

In a psychological time model the durations of time intervals between the events significant for an individual are measured by the number of connections between the events.

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).

In mechanics and field theory such a law usually has the form of the "equations of motion" which are postulated in the theory, for instance, Newton's equations for motions of macroscopic bodies with small velocity and weak fields, or the Schroedinger equations of non-relativistic quantum mechanics, or the Maxwell, Einstein, Dirac equations, etc. The law can be formulated in a form other than equations, such as, for instance, an extremum principle, like the minimum action principle (only those trajectories are real for which the temporal integral of the difference between the kinetic and potential energies is the least). The formulation of the variability law using the equations of motion is equivalent to that of the extremum principle. The "derivations" of the functionals used in the extremum principles often include considerations connected with the invariance properties of the space-time or field variables. If the action functional of the studied system is known, the dynamic equations, e.g., in quantum mechanics can be obtained using the Feynman path integral method. The least action principle turns out to be a specific case of the Feynman principle. An unusual method of variability law derivation, in particular, in the form of the Newton and Dirac equations, appears in the physical structure theory and binary geometrophysics. Formally the laws follow from the requirement that a certain specially constructed Gram determinant should be zero.

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. 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, 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" (Poincare 1898).

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 measure-ment 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 quan-tities measured in the experiment.

Thus the formalism of quantum mechanics uses the complex-valued wave functions and the operators acting upon them as the above formal objects. A transition to the concepts of the macroscopic reality is carried out by certain postulated rules: the absolute squared value of the wave function is the probability of finding the particle in the specified point of the space at a given time instant, while an eigenvalue of an operator is a numerical value of the corresponding physical quantity. Observation of the probability distributions requires, for instance, interference experiments with particles penetrating through barriers. The energy characteristics of an atom are determined via spectral line spacings in the experiments with radiation emission and absorption by the atoms.

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.

Democritis' conjecture on the atomic structure of matter required a millennium to become a verified theory. The enormous experience of the X-ray structure analysis has turned out to be necessary to transform the discrete heredity substance conjecture, the one put forward nearly a century before, into a consis-tent model involving a double spiral of the deoxyribonucleic acid.

The time phenomenon

The phenomenal treatment of time implies the existence of a natural phenomenon, or process, whose properties are responsible for the characteristics ascribed to time itself. See also the term "time reference". Alternative to the phenomenal treatment is the notion of time as a noumenon.

The time noumenon

The set of conceptions according to which time is considered as a construct of human thought and is thus a subject of gnosiology, as opposed to the viewpoint that time is a phenomenon and an ontological entity.

The nature of time

Mechanism of the origin of changes and novelties in the Universe. In the framework of the substantial concept of time, to understand the nature of time means to point at its natural reference, i.e., a process or phenomenon, a carrier in the material world, whose properties might be identified with or put into correspondence to the properties ascribed to the time phenomenon. (See the pages of the laboratory-chair "Modelling of natural references of time".)

A time reference

A natural process or phenomenon, a carrier in the material world, whose properties might be identified with or put into correspondence to the properties ascribed to the time phenomenon. (See the pages of the laboratory-chair "Modelling of natural references of time".)

A clock

A method of measuring the variability of systems. A clock is usually a natural object or process whose variability is assumed to be standard and uniform. A clock is thus a way of mapping the variability of an object under study onto a numerical scale introduced with the aid of the standard process. Examples of standard processes: the Earth's rotation around the Sun, the electromagnetic radiation of caesium atoms, the sequence of human heart beatings. See also the term "Substitutional, or metabolic time".

Time construction, or model

Replacement of time in the basic and undefinable concepts with other basic concepts. After such a replacement the properties of time itself may be formulated as theorems of a deductive theory rather than axioms created by a researcher's intuition. In such a theory it becomes possible to consistently discuss the properties of time. Since time necessarily enters into the very basics of the conceptual skeleton of science, creation of its construction means, in fact, restructuring of the whole basis of the logical fundamentals of natural science. Such restructuring is impossible without touching upon a wide circle of basic general scientific concepts, such as, for instance, space, motion, matter, interaction, energy, entropy, life... The creation of a time construction thus represents a vast interdisciplinary research programme. (See the pages of the laboratory-chair "Modelling of natural references of time".)

Generating flows

Hypothetical flows of elements from deep levels of the hierarchic structure of material objects. These element can be undetectable by the existing experimental technologies. The dynamical properties of the generating flows create the charges and interaction of matter. (A convenient way of visualization of the origin of charges from generating flows is the image of a source, or "spring", that "spouts" in the substantial "reservoir".) With respect to the generating flows, the systems of the World and the Universe itself turn out to be open. Each set of elements of a generating flow may be called a substance of the corresponding level of the system's hierarchic structure. The union of substances of a system may be considered as its space or medium. The motion of a system in its space consists in the substitution of generating flow elements on its hierarchic levels and is called substitutional motion. The generating flows are references of the substantial multicomponent time for natural systems (see also the term "substitutional time"). Number counts of generating flow elements being replaced in the system represents a basis for the introduction of substitutional, or metabolic clocks.

The identification of the course of time with substantial flows may meet the objection that the very notion of a flow already incorporates a prerequisite notion of time: a flow is usually, by definition, a change of the substance concentration or of a field with physical time. It is, however, possible to understand a flow in a more general manner. This understanding is fixed by the substitution construction of time: entry of elements into a certain standard system is considered as a flow of system elements, the entry events are called time instants, and the number of entries determines a measure of the time-flow. In other words, a change in the number of elements in a standard system is not parametrized by a certain external process (a "physical time"), but is parametrized by the element substitution process in the system itself. For a generating flow, the standard system is a universe which is open with respect to the entry of pre-elements from a deeper matter structure level. A change in the number of these pre-elements, i.e., the pre-element flow, determines the time of this universe.

The generating flow concept makes possible a constructive search for approaches to the existing problems of natural science. A connection between the time flow and non-equilibrium states, flow dissipation and irreversibility is trivial: the non-equilibrium nature of the system, i.e., the existence of a substantial flow through it, is nothing else but the course of time. What is nontrivial is that, for this triviality, a generating flow must exist ontologically. The questions on the "nature" of time, on the causes of its "course", on formation mechanisms are translated by the generating flow hypothesis into the question on the origin and status of the additional substantial feeding of our Universe. (See the pages of the laboratory-chair "Modelling of natural references of time".)

A substance

The notion of a substance is highly ambiguous both in natural science and in the methodology of science. Substance is often understood as the entities whose status of being is different from the status of the material particles, fermions, for instance: space, field, physical vacuum, or, historically, phlogiston, elastic light-carrying ether, entelecheia... In the context of the substitutional construction of time, I propose to call a substance a kind of matter which differs from the substrates represented by fermionic particles, atoms or molecules. This kind of matter is represented by generating flow elements, belonging to deep levels of matter structure which possibly cannot be identified by the existing experimental technologies. The dynamical properties of the substance create the charges and interactions of fermionic particles.

Substitutional, or metabolic time

The element replacement process in a system, on one or more levels of its hierarchic structure. The course of substitutional time may be identified with substitutional motion of the system. The properties of substitutional time can be enumerated as follows: multicomponent nature, course non-uniformity, system specificity, discreteness, possible non-additivity, the existence of the timeless events. (See the pages of the laboratory-chair "Modelling of natural references of time".)

Substitutional motion

The term "substitutio" (Latin) means "replacement". Substitutional motion of a system is the process of its elements replacement on one or several levels of its hierarchic structure. (A clear visualization of substitution motion is the image of a running line in advertisements, or the motion of a picture on the screen of a kinescope.) Thus substitutional motion in the system space (see the term "generating flows") is not implemented by "driving apart" the elements (points) of a medium but rather by their "entry" to the system or leaving it. Substitutional motion may be identified with the course of substitutional time. From the "element-centric" viewpoint, the replacement of medium elements (points) is considered as substitutional motion of the system in a medium "at rest". From the "system-centric" viewpoint, there occurs element substitution in a system "at rest", i.e., the course of its substitutional time. As a synonym to substitutional motion, one can also use the term "metabolic motion". (See the pages of the laboratory-chair "Modelling of natural references of time".)

Metabolic motion

"Metabole" is, according to Aristotle, change or motion in the widest sense (Aristotle, Collected works, v.3, Physics. Comment 9 to Chapter 11 of Book 4). Metabolic motion is a synonym to substitutional motion, i.e., the process of system element substitution on different levels of its hierarchic structure.

Substitutional, or metabolic clock

A substitutional clock is a natural object whose element substitution is taken as a uniform variability standard.

The proper time or the proper age of an organism can be defined from the counts of consumed oxygen molecules.

The proper age of an organism can be measured by the number of newly formed cells; by wound healing area; by growth of specified organs of the body, e.g., the size of eye crystalline lens is considered to be one of the best biological age markers for mammals; the number of separated cells of yeast, being their only stable age characteristic, unlike any chronological dating.

The scale of age stages of a plant: germination, juvenile, immature, young vegetative, young, mature, old, subsenile, senile stages) is treated as a specific form of ontogenetic time accounting, such that the intervals between the neighbouring age stages are taken to be equal. The same is the case for the scale using the instants of pea alternate leafs appearance.

In paleontology the analysis of large groups of organisms on the basis of measuring the number of taxons is quite common. One usually takes into account those characteristics which refer to a single stratigraphic division, namely, the overall number of taxons and the numbers of those appeared and died out. (See the pages of the laboratory-chair "Modelling of natural references of time".)

The multicomponent of substitutional time

As natural systems are hierarchical, the replacements of elements at various levels of their hierarchical structure set so much component substitutional of time of system, how many levels of a structure are essential for the description of system. I shall bring examples from area of biological systems:

The proper time t₁ of depth 1 for a cell is measured by the number of molecules replaced in that cell. In a similar manner the time of an organism is measured by the number of replaced cells. The time t₁ for a population is measured by the birth-death balance for the members of the population. For a community t₁ is the number of species changed in the succession. The biospheric time t1 is counted by associations of living organisms, replacing each other, disappearing and forming again.

An ecological community can be imagined as a unity of individuals belonging to all the species forming the community; the balance of changes of the total number of individuals determines the value of the time t₂ of depth 2 for the community. For an organism t₂ is determined by the molecular flow through the organism. The biospheric t₂ is the number of replaced species.

To find solutions of many ecological problems it is convenient to represent a community as a pool of a certain biogenic chemical element limiting the development of organisms (e.g., carbon, nitrogen or phosphorus). The sum of molecular number changes in the pool (in practice such quantities are estimated in terms of mass or concentration units) is the proper time of depth 3 for the community or 4.

The ideas that time is more than one-dimensional repeatedly emerged in natural science. "For life viewed from the geochemical standpoint, time is expressed in three different processes: firstly, the time of individual existence, secondly, the generation changing time, with the form of life unchanged, and, thirdly, the evolutionary time, i.e., that of changing forms along with generations" (V.I. Vernadsky. Philosophical ideas of naturelist. 1988, p.231). "The existence of many time scales is without doubt the most significant aspect of life.... For instance, there exist the physical time (in equations of motion), the catalytic time (necessary for describing fermentative reactions), the time of cellular fission, the ecological succession time and, finally, the evolutionary time..." (from G.Patti's letter addressed to C.H.Waddington. On the way to theoretical biology. V.1. Prolegomens, M. 1970, pp.177-178). G.E.Mikhailovsky (Biological time, its organization, hierarchy and presentation by complex values (PDF file, 110 Kb)) introduces the complex time of living organisms. Its real part is the ontogenetic time of an organism while the imaginary one is determined by the stage of the self-reproduction processes.

Non-uniformity of the course of substitutional time

"In the descriptions of the measurement process, so essentially simple, one can notice a significant reticence in many courses of mechanics and physics which have become classic. It was my task to establish more determinacy in the problem and, along with that, to show what a great arbitrariness is present in establishing a measurement. Namely, if a relation of order is established on a set K of the properties of a certain fragment of the reality, then those properties are called intensities. If the relation of "equal spacing" is defined for the intensities K₁, K₂ and K₃, i.e., K₁ is smaller than K₂ as much as K₂ is smaller than K₃, then these intensities are called measurable. For example, the volumes of geometric bodies are measurable intensities, while the quality of students' knowledge is an unmeasurable one. The mapping A: K → R of a class of properties K into a numerical set R is called arithmetization of the properties K. A monotonic arithmetization of intensities is called an estimate. Examples: estimation of students' knowledge using five- or hundred-grade scales; juxtaposition of the corresponding electromagnetic wavelengths to the colours of the solar light spectrum. Estimations of measurable intensities, satisfying the condition A(K₂) – A(K₁) = A(K₃) – A(K₂), are called measurements. Any two arithmetizations, if they are measurements, can different from each other only linearly, i.e., only zero points or measurement units can be different. Thus "any class of properties can be arithmetized; if these properties are made intensities (by our definition), then we can... estimate them by numbers; finally, if the intensities are made (again by our definition) measurable intensities, then we can... measure them; a measurement will contain certain arbitrariness, removed by establishing the zero point and the measurement unit" (Friedmann 1965, The world as space and time, p.15).

"A priori we can take any dynamic phenomenon and use its development to define the time scale. However, a uniform natural scale does not exist, since we cannot say what is meant by the word "uniform" with respect to time; we cannot catch the present minute and put it side by side with the next one. It is sometimes said that a uniform time scale is defined by periodic phenomena. However, allow me to ask a question: can anybody tell us that the two periods, following one another, are equal?" (E.A. Milne. Kinematic Relativity. Oxford. 1948. P.5)

In physics the role of a uniformity agreement is played by Newton's first law: the time intervals during which a body, moving without interaction with other bodies, covers equal distances, are called equal (W. Tompson, P.G. Tait. Natural philosophy. Cambrige. 1890).

The non-uniformity of metabolic time, as a consequence of the hierarchy and imperativity principles, is discovered only when several time scales are present. If a scale is unique, the course of time is uniform by the definition contained in the imperativity principle. For example: "The absolute, true, mathematical time as it is, by its very nature, without any relation to anything outside, flows uniformly and is also called duration. All the motions can accelerate or decelerate, while the flow of absolute time cannot change" (I.S. Newton. Philosophiae Naturalis Principia Mathematica. London. 1687).

Note that the physical processes aspiring to be used as time standards (the rotating Earth, the ephemeris time, the "second world time" taking into account the seasonal corrections to the rotation of the Earth, the tropic year, radiation of caesium atoms) represent the clocks of significantly different uniformities from the standpoint of the modern level of accuracy.

The choice of a clock is to a large extent a psychological problem: although very different natural processes can be suggested to play the role of standard clocks, the ones convenient for a man are preferred. I.e., those in agreement with the course of "time of the consciousness", which in turn is induced by the planetary conditions of human life. "As a matter of fact, the uniform motion concept already assumes the existence of time, while the expression "the stars are moving uniformly" means only that we call the stellar motion uniform. The uniformity of motion is an entirely relative concept: one can speak of one motion uniform with respect to the other, so that when we speak of a uniform motion, we mean motion uniform with respect to that of stars, or, though it sounds still more odiously, uniform with respect to the rotation of the Earth. Ascribing a specific, mystic sense to stellar time, one reveals the human unwillingness to understand the whole extent of the non-central, modest position of the planet where, as the fates decree, he has to live" (Friedmann 1965, p.13). The anthropomorphic selection of time scales is understandable but must not overshadow the possible application of time scales with different course uniformities in descripting various forms of generalized motion in various frames of reference.

A change of standard objects and the corresponding scale change connected with uniformity change is not just a replacement of measurement units or that of a zero point: that is necessarily a nonlinear transformation, since linear ones would preserve the scale uniformity, so that equal intervals would have remained equal. Most of "proper" time scales in natural science are non-uniform with respect to astronomical time, which sometimes allows one to discover certain laws escaping one's attention when the traditional physical time scales are used.

The scale connected with wound healing rate (L.P. Nouy. Biological Time. London. 1936) turns out to be non-uniform with re-spect to the chronological age: a five-year-old child's wound is healed ten times faster than that of a person of fifty. A nonlinear transformation of planetary time (G. Backman. Wachstum und Organishe Zeit. Leipzig. 1943) applied in a description of growth curves for a broad class of living organisms made it possible to discover the elementary durations, "life quanta"; their density is uniform in Backman's "organic time" and is much greater at the first stages of development from the viewpoint of the ordinary time scale (that is why it is so hard to catch them). E.Milne (1948) removed the postulate of congruence between time intervals shown by clocks of one type, namely, mechanical and atomic ones, and introduced the logarithmic scale to measure the cosmological time of the Universe. The time transformation eliminated the gravitational interaction from the fundamental equations of motion and greatly simplified the description of the non-stationary universe. Measurement of duration of stages of development of animals in "detlafs" (T.А. Detlaf. Hours for study of temporary laws of development animal // of a Design of time in natural sciences: on ways to understanding of a phenomenon of time. M.: The Moscow university. 1996. Сс. 135-151 (Gziped the PostScript-file, 214 Кб)) allows to compare times of development both at animal various kinds, and at the same kinds in various conditions of development.

The system-specific nature of substitutional time

The times determined by standards belonging to different system structure levels and, the more so, to different natural hierarchies, are specific rather than universal. Speaking of specific time, for instance, of physiological, ontogenetic or evolutionary times, we mean that the first one is measured by the number of absorbed oxygen molecules, the second one by the number of newly formed cells of a growing organism while the third one by the number of taxons in the reconstructed biosheric annals.

The geological, biological, geographic and other specific times are proper time pyramids constructed in the corresponding natural hierarchies.

The idea of universality of time originates from the fact that usually in a pyramid of time a sufficiently deep component is selected, corresponding to the physical time scales. Different natural systems often have a common material structure, for instance, the biological, geological, geographic, astronomical and other hierarchies include the molecular level and consequently all the previous (physical) levels. This implies the possibility to choose a unique time scale for systems of different nature. Thus the habitual universality (or absoluteness as I.Newton called it) of time is connected with the fact that only scales determined by deep levels of system structure are used. The deeper is the level which delegates the standard system, the vaster is the set of higher level systems for which that standard is applicable.

The universality of time, resulting from the use of "deep" standards, is to be paid for, and the price is the lost of information on system structure. The universality as though wipes off the structure of levels above the reference system level, therefore the characteristics of the general processes occurring at the higher levels, turn out to be insignificant. Thus, if an ecosystem is studied as a unity of molecules, of which all the biotic components and all the inanimate substance pools consist, we can say much about the substantial functioning basis of such systems. However, the molecular language is hardly applicable for formulating the ideas of trophic connections between species, of age, sexual and other structure of the population, of seasonal and other successions, on the behaviour of individuals and other non-molecular processes. In physics the role of a factor which "wipes up the structures", is frequently played by energy.

Using specific time scales, it is possible to explicate the properties of time determined by specific structures of systems, but the temporal properties of objects lying at lower levels of system structure become "indistinguishable". Thus the choice of a reference system level and, accordingly, of the universality and specificity degrees of the time scale determined by the chosen standard, depends on the aims of the study. Application of specific scales, nonlinear with respect to the usual time, may result in additional simplicity and adequacy of the study to the nature of the described phenomena, along with a hope to reveal the laws which escaped attention in other ways of description. Thus, for instance, application of the metabolic time scale, connected with the number of substrate molecules absorbed by cell populations in microalgae culture development, made it possible to discover the growth and consumption stages which had not shown themselves in any way when ordinary growth curves had been analysed. When the durations of development stages of animals was measured in "detlafs", it provided a way to compare development times both for different species and for the same species in different development conditions (e.g., at different temperatures). The problem of the existence of individual life duration bounds is very hard to analyse if the age is measured in ordinary chronological units. Unlike that, application of a proper time, for instance, in terms of the number of molecules of matter consumed by the organism, gives a hope to discover the natural bounds connected with a limiting total amount of oxygen, absorbed by an organism in its whole life, different for different species (provided the Rubner rule is valid).

Discreteness of substitutional time

Since time is determined by element replacements in systems, the course of time turns out to be discrete as far as the elements are discrete. However, the degree of discreteness of the time scale (as well as that of the system structure) depends on the choice of a reference level for time definition.

Let us call the quantity 1/N, where N is the number of elements of the reference object replaced between the appearance and disappearance of one object in the studied system, the degree of standard scale discreteness. A replacement of one organism (N = 1) in a population corresponds to replacements of N = 10 - 10¹³ of its cells or N ~ 10²³ of molecules contained in the organism. Thus a choice of deep scales for time measurements drastically lowers its degree of discreteness.

Non-additivity of substitutional time

In a proper time scale the additivity of a substrate implies the additivity of metabolic time. If, however, at a certain structure level the discreteness and additivity of a substrate are absent (that is the case for, e.g., the psychological phenomena or objects in landscape studies and biogeocoenology), then non-additivity appears in the properties of time. In that case the element replacement concept loses its definiteness and the general process description requires a special formalism (e.g., the Boolean-valued sets theory, in particular, fuzzy sets).

The timeless events in substitutional time

If a level i object has been chosen as a time standard, then measurement of time at level i – 1 requires an introduction of fractional intervals with respect to the standard system. However, an application of fractions to the lower level can turn out to be inadequate since their "uniformity" can fail to describe processes at deeper levels. Having in hand the metabolic time construction, it is not difficult to determine both the time intervals between the events and the durations of the events themselves. In such a description a type i event turns out to be a timeless ("instantaneous") phenomenon in scales of types i and higher (but not in scales of lower types than i ). For instance, if the electromagnetic time scale is chosen to be standard, all the preceding levels of system structure are excluded from the dynamical (and perhaps also causal) analysis.

Already in quantum mechanics there exist timeless events: emission and absorption of electromagnetic quanta by atoms, i.e., transitions to other energy states of atoms; wave packet reduction; changes in quantum numbers of one part of a quantum system resulting from a measurement process executed over the other, arbitrarily remote, part (the Einstein-Podolsky-Rosen paradox).

The paradigm of an open World, generated by substitutional time

A number of problems of natural science which admit temporal comprehension, require that the framework of the paradigm existing in modern science should be abandoned. Among such problems are:

The origin of formation, or the "course" of time.
The origin of mechanisms that create changes and novelties in the World.
The necessity to overcome the contradiction between the evident difference between the future and the past in the world of real processes and the time-reversibility of the basic equations of physics.
The absence of conventional methods of deriving (rather than guessing) the equations of "generalized motion" in different specific areas of science. (I would note that the equations of motion themselves describe the variability of an object under study with the aid of a certain standard variability, or clock, and therefore the choice of a clock adequate to the object under study decisively affects the form of the equations sought for.)
The necessity of both a unified description of specific times of natural science (physical, biological, psychological, geological, etc.) and returning a universal status to time.
The necessity of adequate measurement of self-age for the widest range of natural systems, and dreams about a "control" of their proper time.
The difficulties of scientific forecasting.

I would like to enumerate some features of the existing scientific paradigm, whose framework should be apparently abandoned for temporal comprehension of natural-scientific problems:

Time is studied by philosophy rather than natural science.
Time in science is an initial and undefinable concept.
Physical clocks on the basis of gravitational and electromagnetic processes are sufficient for measuring time.
The problems of time in natural science are the solved and unsolved problems of relativity theory.
Our Universe is an isolated system.
The conceptual armoury of science has no place for substances like phlogiston, light-carrying ether, entelecheia, etc.

The substitutional time construction, created by the generating flow concept, makes it possible to see the features of a new paradigm which will perhaps determine the ways of scientific research in the future:

One can speak of natural references of the concept of time. The time phenomenon can become a full-valued object of natural science.
The time of natural systems has a structure and can be a natural object of theoretical modelling.
For further development of the concepts of space, time, matter, motion and interaction in the conceptual basis of natural science, some new entities are apparently lacking, and their appearance is the most probable in the form of substantial approaches.
Standard processes, used for measuring the variability of objects under study, i.e., clocks can be of absolutely different nature. Different clocks can turn out to be non-uniform from each other's viewpoint, and the resulting descriptions of the laws of motion can be not reducible to each other by simple transformations.
A radical solution to the problem of time course and irreversibility apparently requires that the concept of isolated systems should be rejected, and there appears the concept of an open, nonlinear, self-organized World, perhaps becoming more and more complex.