Relation of uncertainty for time

We introduce two time: deterministic Newton time-stream t and stochastic timeepoch τ . The relation of uncertainty for time-epoch of physical events ∆τ∆D ≥ c1, (∗) where c1 = const, is proved. The function D(t) = −c1 d dt ln fτ (t), characterizes velocity of disorganization of the event-phenomena; fτ (t) is density of probability of time-epoch τ . The relation (*) is verified not by means of experiment that is traditional for physics, but with the help of the reference to datas of historical science. In the World of events M we select such property as the time order. The time order contacts with such concept as a stream of time. Events are developed (unwrapped) before the observer consistently, in time. It means that for measurement of time the special measuring tool of the duration of the phenomenon in time and named a watch is used. With the help of watch to each event the concrete number named (time) moment of event or his(its) epoch is attributed. The time order allows to compare epoch of any events. However the time stream due to which the phenomena consisting of events are developed (unwrapped) consistently, event behind event, is given to the person as noted philosopher Kant, a priori, from birth. It is consequence of such fact that the person has topologically trivial 4-dimensional body [1, 2]. In other words, time as a stream is only subjective perception (recognition) of the phenomena of the World of the events inherent to the person. Therefore it is necessary to assume, that time can show itself in our human world, the world of human subjective representations about the World of events, absolutely differently than the time order. As a matter of fact it means, that time can find out itself as something that can violate time ordering in deployment of events! Hence events of which the phenomenon consists, can receive epoches with violation of the time order. Whether means it, what time can have properties similar to a random variable? Anyway it is necessary to try to apply principles of probability theory to the description of time. We shall accept further that the choice of the epoches (moments) of time which are attributed to events of the phenomenon with the help of some fixed watch can be casual. Let’s forget for simplicity about such concept as a place of event. In this case events in the World of events can be distinguished only with the help of the time order and formally it means that the World of events M is the linear ordered continuum like real straight line IR. Let’s assume that we choose watch t which allow each event x to attribute the moment of time appropriate to him, i.e. epoch τ . We shall accept that each event gets random epoch. It is understood as the following. So far as event (atomic event or the elementary phenomenon in the sense of A.D.Alexandrov) is some idealization, it should occupy only an instant τ in a time-stream t. It is accepted in the theory of a relativity. But actually it is stretched in a time-stream t and consequently its epoch τ is absolutely precisely unknown, though must lie on some concrete segment [τ, τ+∆τ ] of time t. Hence epoch τ of event x is a random variable τ :< X,S,P >→ IR, where X is probability space of events, S is σ-algebra on X, P is a probability measure on X. Identifying space of events X with the World of events M, and considering that M is real straight line IR, we receive time-epoch τ(t) as a random variable given in a time-stream t. 1 Event in probability theory is a measurable subset of space X. In our terminology the concept of the phenomenon corresponds to concept of event in probability theory. In turn the events which consist of the phenomenon are elements of set X which in probability theory correspond to elementary events. In terminology of Minkowski events are points of the World of events M. But it is obvious that this is simplification accepted in this theory. So, we shall accept that property of time which is shown in ”choice” of the moment of time which corresponds to event is a random variable which we shall name time-epoch. Let fτ (t) be a density of distribution of time-epoch τ satisfying two conditions