DIOTIMA. Revue de recherche philosophique. / Espace cosmique et philosophie / Ed. par E.Moutsopoulos. V. 21, 1993. Paris: Librairie philosophique J.Vrin, 1993. Pp 123-125.
© O.S.Razumovsky

Models of Time in Physics and Cosmology

There exist two interconnected problems in philosophy: physics and cosmology. We have essence of time, and modelling of time. The latter is connected with the application of computers, which work in the regime of real time. At the same time in philosophy and cosmology there exist a number of problems where one tries to get rid of the time parameters. Jacoby, e.g., showed how it is possible to eliminate these parameters in the formula of an action of Hamilton. He geometrized the principle and expressed the quantity of an action through the total energy of a system, quantity of mass and the length of a path. As a result the principle determines the minimal action on the real mass, but not in the time interval as it was meant by Hamilton. In its turn the general theory of relativity demonstrated the dependence of space properties on mass distribution, which means energy distribution. In general a way to an understanding of the essence of space and time understanding of time is correlated with an ancient Indian one, according to which time is energy, (though it is not clear whether the meaning of this notion is the same in this philosophy and in modern physics). As far as the essence of time and time modelling in physics and cosmology is concerned, we do not consider models of physical and cosmological time to be isolated from time essence. On the contrary the latter manifests itself in these models absolutely clear. We should note that in the literature about time essence there are both natural-philosophical and methodological aspects. In physics a certain position is determined, according to which there are no observed characteristics without observer, and it is impossible to say anything reasonable about space, and build its theoretical models, without a coordinate system or a marking-off system as basic for an observer. A similar conclusion can be referred to the models of physical time by H.Harmuth. Here it is supposed that the existence of a “clock” causes physiological perception of time and determines the theoretical notion – an abstract time model. We proceed from the fact thay an observer himself as well an observed, by developing, changing from one state to another object and other objects for which changing from one state to another object and other objects for which changes of state are takeh as conventionally standard, can perform the role of a clock. Usually the change of time is understood this way, that is like a correlation of states of a standard object (clock) with changes of states of (and their duration) of an observed object.

In general, for changes of states of a clock, e.g. physical pendulum, some densities of are relatively constant. The observation of this fact gave us the ground to consider that clock time itself, as a standard, is homogeneous.

From this there appears an opportunity to make the abstraction of “homogeneity of time”. An observer fixed this homogeneity, as well as the absence of chaotic and non-rythmical deviations from a given density of states, and introduces by means of abstract thinking the notion of a “clock” as a standard of homogeneity of a process. He introduces also the abstraction of “time moment”. So an observer comes to the general notion of time through the notions of homogeneity of a process, and through observations of non-reversibility and the direction of changes of states (or events) in other systems, with the help of comparison. But it is impossible to say anything distinct and definite, or quantitatively precise about time as the conception of a change of systems, without determining some marking-off system, like a co-ordinate system, for time, and also without the notion of numerical differences, intervals in characteristics of states. Consequently it is impossible to make models of physical time. It is known that there exist different types of clocks: gnomon, sand-glass clock, water-clock, pendulum, hand-clocks with a numerical scale, etc. It is very probable that models of physical and cosmological time depend on a type of a clock. This follows from the fact of distinctions in their marking-off, and space in the co-ordination of systems. One can make a model of a real physical clock and realise it, using generalised space types of basic multimeasured spaces. (A radioisotopic clock, to our mind, appeared owing to this idea). This can give rise to different models of clocks. As a matter of fact, there should be developed not only the philosophy of time, physical chronology (cronography) but also physical and applied theory of clock as a theory of all possible types and kinds of standards of time measure.

Now we should note, taking in to account all that was said above, that a one-measured model of time is very strong abstraction. A two-measured model,e.g. when we speak about a plane of a pendulum swing, is closer to reality. In general models of time can be only geometrical-spatial or phase-spatial. Such an object as time in our model object does not exist directly in nature. Physical chronology should in principle admit multi-measured models of time. Among them a three-measured model is probably closest to physical reality. We should stress that the structure of a marking-off time in models of phisical time is directly connected with a physical nature of a clock. Most obviously this can be seen in sand-glass and water clocks. Here the final volume of a physical body just permits to determine a measure of time. It also prescribes the structure of a marking-off system. A measure of a given volume turns into a numerical unit of our time model, because we model time on a given volume. The given measure can be taken in principle arbitrarily, if we are not limited by generally accepted standard of time which come from astronomic observations of celestial objects. By a zero or infinitely large volume, it is impossible to measure time without an introduction of special lower and upper limits of such a physical model as a clock under study. The beginning of marking-off is connected here with a calibrated opening between vessels of the given clock. In the same way it is impossible to model time on a physical pendulum which has a zero or infinitely large length of thread. We should note that necessary limits of both types of clocks (sand-glass and pendulum) have an antropic character which is connected with human organization and physiology. Methodologically a clock with a circular dial is the most interesting, because there the beginning of marking-off and time measure are in fact arbitrary, inasmuch as they are limited by units and standard of time accepted by humanity. But the main idea of clock as a modeller of time, in our view, can be expressed by a simple thought: everything in the world is a clock, it is a clock itself and a total aggregate of an infinite amount of clocks. It seems that all this is correct when there is an observer. In cosmology, the problem of the description of the beginning and the evolution of the world is to find out initial conditions, knowing the present. But at the beginning of everything nobody observed our singular Universe, there was no other “clock” then the Universe itself. We should note that we must speak about parameters of states of the singular Universe using physical and cosmological language but not the language of chronology. That is why the cosmological problem of the initial conditions of the Universe can be expressed only in two languages: physical and chronological. The second language can be used here.

Summing up our considerations, we come to the conclusion that there is no time, as physical essence, that changes for an observer. The world parameters are energy and impulses; space parameters are functions of the latter. The differences of the world (their changes) give us, by the process of cognition, the idea of time. The notion of time in science from this point of view is relic of protoscientific and metaphysical epochs in human history. Following “Occam’s Rasor” we should get rid of this relic, at least in natural science and philosophy, because they study the initial essence of the world. In applied sciences, especially in computer mathematics, informatics, etc the idea of ancient Indian philosophy, that time is energy, is made more precise by the following affirmation: time can be understood as a measure of the energy change or states of any objects of the Universe and the Universe itself.