The Newtonian mechanics was the model of classical science. In the classical science all the natural laws had an absolutely deterministic and descriptive character and defined the course and development of every phenomenon. The knowledge of these laws assured the human – observer the ability to understand not only the present but also the past and the future. In a deterministic and timeless universe, the arrow of time is nothing but a human illusion. Only the vision of the universe from the perspective of eternity ensures the truth of physical theories. In the deterministic universe of the classical science, the order always creates disorder and never vice versa! The scientific dream of a united (applying on the microcosm as well as on the macrocosm) and objective (i.e. independent of the observer) description of the natural world, would become the nightmare of the contemporary physics in the beginning of the 20th century. The quantum description and interpretation of the microcosm, which is regarded as the fundamental level in which all the natural phenomena are raised and explained, requires a radical review of not only the classical description but also of the metaphysical preconditions of classical science. 

The classical ideal in physics was to be able to predict with certainty the future development of a physical system. Newton’s mechanics led to the triumph of the deterministic vision of the natural processes: if we know the initial conditions of a dynamical system, then the solution of the differential motion equations would allow us to know in certainty not only the past but also the future of that system. This, however, is not feasible for two reasons: a) it is not possible to have the initial conditions of the system in absolute accuracy and b) the analytical solution is not feasible for the great majority of the systems. As far as the first reason is concerned, we have to mention that after the discovery of the unstable systems, it became clear that very neighboring orbits (which, namely correspond to initial conditions and whose values may differ slightly) after a certain period of time are removed exponentially. In this notion, the orbit is actually an idealization, since it is never possible to know the initial conditions in “infinite” accuracy. 

According to Heisenberg’s uncertainty principle and Bohr’s principle of correspondence, the neutral and deterministic description of the microcosm is impossible: discontinuity and indeterminacy are inherent characteristics of microphysical phenomena and in order to describe them we have to integrate the observer within his own observations!  Ρrigozine believed that the laws of nature and those of physics are not given apriori, nor are they entailed logically. They evolve in the same way the various species evolve. Since things are becoming more multiple, bifurcations and aids occur and new laws appear. “How can you be talking about the laws of biology if there are no living systems?” This proves the creativity of life. Each level of organization produces something fundamentally new, something that is not found in the constituents or the “parts” of the previous level. For example, in a mixture of hydrogen and oxygen there is no water. The mixture gets a new identity, which, in practice, sacrifices the “parts”, hydrogen and oxygen. The only way to get the parts back is to ruin the water. In other words, it was not obvious in the equations of quantum mechanics that a “quantum arrow of time” emerges. Prigogine notes that in the theory of relativity as well, time is irreversible and space and time are alternating mutually. This theory led to the formulation of the theory of Big-Bang, which in practice gives an irreversible sense to the history of the universe. 

Prigogine’s first challenge concerns the phenomenon of irreversibility. The second challenge has to do with the sense of simplicity. Since Democritus and Aristotle’s era, scientists believed that beneath the complexity of our world there should be simple objects and simple forces. Initially, scientists thought that the atoms are the simple structural stones. Later on, when it was discovered that the atoms consist of smaller parts, simple particles such as the proton and the electron became the structural stones. After that, when the quantum mechanics led to the unexpected discovery of an impressive world of particles at the subatomic level, the physicists invented the grand unified theory and began to look for the unique, simple power – the “superpower” which is supposed to have given birth to that number of interactions of elementary particles. Prigοgine points out that: “the idea of simplicity dissolves. Whichever direction we chose, there is complexity.” Complexity is the key idea for the understanding of his theory. According to him, an organism is born, grows to its maturity and passes away, namely, it has a history… Both the classical Newtonian physics and the physics of the 20th century with quantum mechanics and the theory of relativity, are expressed by equations, which are symmetrical with respect to time, i.e. they are reversible and deterministic. In those theories there is no discrimination between the past and the future. 

Thermodynamics, from approximately the half of the 19th century had posed the problem of the irreversible processes and the arrow of time. But the fundamentally nonlinear character of natural processes and the different behavior of natural systems, when they are away from the equilibrium state, were not yet recognized. The discovery, in the 19th century, of the non reversible time – in evolution and entropy – did not change the belief of the physicists that in the most basic levels of matter, time is reversible, while the irreversibility we can see around us is a kind of an illusion, as Einstein once pointed out. As Prigogine mentions, “the study of systems away from the equilibrium state led me to the belief that this cannot be the right view. Irreversibility plays a constructive role. It creates a form. It creates human beings. How could our simple ignorance of the initial conditions be the reason for this? Our ignorance cannot be the reason we exist.” Prigogine goes on: “If we could raise the knowledge, i.e. create a computer powerful enough, in order to write equations for the motion of all reversible and probabilistic individual molecules that compose a system, then would our ignorance disappear, would the illusion of irreversibility remain vague, and would life, evolution, death and time itself disappear? This is weird.” 

This time paradox resulted in the development of physical theories during Newton’s era and thereafter. Particularly the time paradox refers to the fact that while the classical equations are reversible with respect to time, from numerous physical data the arrow of time seems to exist. So, the question raised by Prigogine is the following: Does the arrow of time arise simply as a result of a phenomenological approach to the natural processes or does it represent a fundamental element which we must incorporate in the descriptions of these processes? The claim of Prigogine is summarized: “All laws of physics must be compatible to the existence of the arrow of time”. This means that the laws have to be redrafted in order firstly to contain the arrow of time (i.e. not to be symmetrical with respect to time) and secondly, the various levels of description can lead to the same future state.