The well - known philosophical formula: Space and time are universal forms of existence of matter forces us to introduce several of representation of our knowledge about space-time relations, which we will conditionally call levels of ontologization of our understanding of these relations. These can be considered as ontological sections in the process of cognition of the essence of spatiotemporal relations and the formation of their conceptual certainty. A simple example is used to model the process of formation of spatiotemporal certainty in the Leibniz aspect: the transition from the quantum level (micro-) to the level of classical mechanics (macro-). In this regard, we can talk about the two-phase existence of matter. In addition, an attempt was made to outline the solution of space-time problems after work: Contextuality of one particle, nonlocality of two particles, entanglement, Wheeler's experiments with delay of choice, FWT and so on ...[12]. The current situation of the search for the essence of space-time relations resembles the early history of the search for the essence of phlogiston, which was resolved by the statistical theory of Gibbs ensembles, the definition of thermodynamic concepts and, in particular, the concept of temperature as the average kinetic energy of the ensemble. It is quite possible that the spatiotemporal relations are also some averages from the eigenvalues of the quantum object operators.
The well - known philosophical formula: Space and time are universal forms of existence of matter forces us to introduce several of representation of our knowledge about space-time relations, which we will conditionally call levels of ontologization of our understanding of these relations. These can be considered as ontological sections in the process of cognition of the essence of spatiotemporal relations and the formation of their conceptual certainty. A simple example is used to model the process of formation of spatiotemporal certainty in the Leibniz aspect: the transition from the quantum level (micro-) to the level of classical mechanics (macro-). In this regard, we can talk about the two-phase existence of matter. In addition, an attempt was made to outline the solution of space-time problems after work: Contextuality of one particle, nonlocality of two particles, entanglement, Wheeler's experiments with delay of choice, FWT and so on ...[12]. The current situation of the search for the essence of space-time relations resembles the early history of the search for the essence of phlogiston, which was resolved by the statistical theory of Gibbs ensembles, the definition of thermodynamic concepts and, in particular, the concept of temperature as the average kinetic energy of the ensemble. It is quite possible that the spatiotemporal relations are also some averages from the eigenvalues of the quantum object operators.
The well - known philosophical formula: Space and time are universal forms of existence of matter forces us to introduce several of representation of our knowledge about space-time relations, which we will conditionally call levels of ontologization of our understanding of these relations. These can be considered as ontological sections in the process of cognition of the essence of spatiotemporal relations and the formation of their conceptual certainty. A simple example is used to model the process of formation of spatiotemporal certainty in the Leibniz aspect: the transition from the quantum level (micro) to the level of classical mechanics (macro). In this regard, we can talk about the two-phase existence of matter. In addition, an attempt was made to outline the solution of space-time problems after work: Contextuality of one particle, nonlocality of two particles, entanglement, Wheeler's experiments with delay of choice, FWT and so on ...[12]. The current situation of the search for the essence of space-time relations resembles the early history of the search for the essence of phlogiston, which was resolved by the statistical theory of Gibbs ensembles, the definition of thermodynamic concepts and, in particular, the concept of temperature as the average kinetic energy of the ensemble. It is quite possible that the spatiotemporal relations are also some averages from the eigenvalues of the quantum object operators.
The current situation of the search for the essence of space-time relations reminds the early history of the search for the essence of phlogiston, which was resolved by the statistical theory of Gibbs ensembles, the definition of thermodynamic concepts and, in particular, the concept of temperature as the average kinetic energy in the ensemble. Thermodynamics has found its justification in statistical physics but space-time relationships of the macrocosm it is possible that it will find its rationale in the inevitable processes of condensation and localization in the environment of prameter and averaging the probabilistic parameters of the microcosm in the description of these processes.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.
Abstract. This research article aims to deepen understanding of the uncertainty phenomenon and to develop the corresponding conceptual apparatus. To get this aim, comparative analysis of a row of studies of certainty and uncertainty, known from the history of scientific and philosophical thought, was completed. It was found that the classical-scientific concept of certainty grasps three essential features: 1) everything that really exists – the Universe or any of its parts – is in an actual state at every moment, having a set of properties with precise quantitative characteristics; 2) the primary, universal and only possible are the laws of motion, of being in general, which connect the past, present and future states of the existing in an exclusively necessary way; the conjunction 1) /\ 2) is equivalent to the statement that 3) the fate of the whole Universe, of everything in the Universe, is absolutely certain objectively. If we additionally assume the existence of the Laplace demon with the "intelligence sufficiently vast" to 4) exhaustively and accurately comprehend 1) and 2) and correctly operate with the knowledge gained, then for this superhuman subject the fate of anything will be quite obvious, in particular predictable. Given the explicated content of the classical-scientific concept of certainty, one can conclude that in the human world the content of the corresponding concept of uncertainty in the presence of 1) /\ 2) necessarily includes ¬4), that is, it is a conjunction1) /\ 2)/\ ¬4): let call this “uncertainty1”. A century ago, physical science discovered in the Universe a domain of chance, uncertainty, unpredictability, and probability, the existence of which does not depend on the knowledge and intelligence of a real person or even Laplace's demon: this is the "strange" quantum reality and, naturally, everything it significantly affects. The key here is the special quantum-mechanical concept of uncertainty. It is related to ¬1) directly, but more fully – it grasps in its content the conjunction ¬1) /\ 2) /\ ¬4, where ¬4 acquires an objective ground: let call it “uncertainty2”. The comprehension of uncertainty developed in newest synergetics includes negation of all the features inherent to classical certainty, including the primacy, universality, and uniqueness of the laws of nature, which absolutize necessity: in the general case, the conjunction ¬1) /\ ¬2) /\ ¬4 comes into effect here. Accordingly, it is reasonable to introduce a third special – synergetic – concept of uncertainty, let call it “uncertainty3”. It is argued that the situation of uncertainty, or the "perfect storm", in the contemporary world forms at least partly objectively, and not only due to a situational lack of information, someone's "insufficiently vast" intelligence, or conscious intention. To understand it, the classical-scientific concept of uncertainty1 is not sufficient; instead, it requires the involvement of contextually interpreted concepts of uncertainty2 and uncertainty3. The future is open and subject to only limited prediction, control, or management. For this purpose, it seems appropriate to use tools similar to nonlocal probability distribution functions in synergetics. Under conditions of instability, the complex global system, its elements and structure, innovations or changes are indeed created by numerous actors of completely different scales, values or interests. Even a spontaneous action of a minor group or an act of one person – a relatively small event, a random fluctuation – can cause some kind of “resonance” and a more or less large-scale bifurcation, a transition to one of many very different “branches” of further existence. Thus, further development of our world will depend not only on the greatest "structuring force" of today – the competition between the USA and China, but also on an effective "at an uncertain time and in an uncertain place" political, economic, military or some other fluctuation. A bifurcation it causes will probably lead to a more or less long-term stabilization of the world system with leadership either by the USA and, in general, the renewed West, or by China, part of the East and the South. However, these are only the clearest "branches" of future development: the emergence of some currently uncertain "black swan" cannot be ruled out.
The laws of classical mechanics and quantum theory do not distinguish between the past and the future. But a lot of phenomena tell us that the "arrow of time" points only in one direction. For example, in biology we discover evolutionary processes leading to diversification and increasing complexity; it is a typical feature of such evolutionary processes that "forward" in time is possible but "backward" in time is impossible. At what level can phenomena like these be described? There is another problem in connection with time: within usual quantum theory, space-coordinates and time are not symmetrical to each other, which is in contrast to the basic results of special theory of relativity. In usual quantum theory coordinates are operators and play the role of statistical quantities; time however does not behave statistically and remains a simple parameter when we go from classical to quantum mechanics. For this reason there is no uncertainty relation for the time and energy within usual quantum theory which would agree in its physical content with that for the coordinates and momenta. The purpose of this paper is to show, on the basis of new aspects, that both one-sidedness of time and its uncertainty are charateristics at the fundamental level of quantum theory. We have extended usual quantum theory on the basis of space-time arguments. In this connection a time-operator appeared and there is in general temporal asymmetry at the microscopic level. The picture might be important in the description of phenomena with an "arrow of time", i.e., processes which belong to the physics of becoming. Furthermore, we have derived an uncertainty relation for the energy and time which agrees in its physical content with the uncertainty relation for the momentum and the coordinate; this relation is different from that of usual quantum theory. Within the frame of this physical picture all the concepts (diversity, natural selection, mutation), which are presently used in connection with the evolution of biological systems, are already established at the quantum mechanical level and, therefore, our theoretical picture might also be the foundation for the explanation of the phenomena at the biological (macro-molecular) level.
By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws ofmore » motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle.« less