[Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe (...) within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless. (shrink)

The formulation of the second law of thermodynamics in the frame of general relativity is reconsidered in the case of an istotropic homogeneous universe. We show that there appears then a direct link between the cosmological state of the universe, as expressed in terms of conformal coordinates, and quantities such as energy density, pressure, and entropy associated with the description of nature. In the early universe there appears a kind of phase transition due to transfer of gravitational energy to matter (...) associated with the cosmological expansion if the universe starts with a non-Euclidian (space) state. As a result, we may envisage the possibility of a “cold big-bang model,” in which the universe would start at zero temperature and entropy. The temperature goes then through a maximum before entering the present area of cooling related to adiabatic expansion. (shrink)

In recent papers the authors have discussed the dynamical properties of “large Poincaré systems” (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. We show that this Poincaré “catastrophe” can be eliminated by a natural time ordering of the dynamical states. We obtain then a dynamical theory (...) which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that this time ordering can be performed in an “extended” Hilbert space. In general, we need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space. (shrink)

In this book, after discussing the fundamental problems of current science and other philosophic concepts, beginning with controversies between Heraclitus and Parmenides, Ilya Prigogine launches into a message of great hope: the future has not been determined. Contrary to globalisation and the apparent contemporary mass culture society, individual behaviour is beginning to increasingly become the key factor which governs the evolution of both the world and society as a whole. It is a message that challenges existing widespread views, implicitly (...) or explicitly, through mass communication, moreover the importance of the individual's actions implies a reflection of each person on the responsibilities that each one assumes when taking or acting upon a decision. This responsibility is associated with the freedom of thought as well as a critical analysis of fashions, customs, preconceived ideas, and ideologies, externally imposed: exactly contrary to the ideas of those who wish us to be "perfect consumers" in a world dominated only by monetary wealth. Challenging this drive towards the elimination of freedom of though in the individual is now imperative if we are to save man and his planet from catastrophe which seems to be ever imminent and (unfortunately) irreversible. This last book of Ilya Prigogine provides a small, disputable, but nonetheless valuable contribution towards that end. (shrink)

Chaos theory of the 1977 Nobel Prize laureate I. Prigogine allows to consider any religious system as a dissipative structure, the development of which corresponds to the leading characteristics of chaotic systems. It should be noted that dissipative structures are called systems whose activity creates chaos, which destroys the existing order and, at the same time, is the basis for the emergence of self-organization and higher-order order. Modern scientific studies have proved the universal nature of nonlinear systems, have shown (...) that isolated systems do not exist in the world at all - everything is interconnected. This fully applies to the development of religious systems. (shrink)

We investigate the applicability of Hegerfeldts arguments on Quantum nonlocality in Quantum Electrodynamics following the work of Prigogine, Pronko, Petrosky, Ordonez and Karpov. We demonstrate the appearance of nonlocal effects at the level of quantum states. We show, however that the expectation values of some observables spread causally. Therefore the measurement of the nonlocality is questionable. We investigate an approach to classical measurement and conclude that the classical measurement cannot detect the “acausal” effects of the non-locality.

Ilya Prigogine was not a systematic author: his ideas, covering a wide arch of areas, are dispersed in his many writings. In particular, his philosophical thought has to be reconstructed mainly on the basis of his works in collaboration with Isabelle Stengers: La Nouvelle Alliance ( 1979 ), Order out of Chaos ( 1984 ), and Entre le Temps et l’Éternité ( 1988 ). In this paper I undertake that reconstruction in order to argue that Prigogine’s position, when (...) read in the light of Putnam’s internalist realism, can be characterized as an ontological pluralism. The main aim of this work is to show the striking parallelism between the philosophical views of Prigogine and Stengers and those of Hilary Putnam in Reason , Truth and History ( 1981 ). This task will lead me to critically review Prigogine’s general scientific program: the attempt to establish the foundations of objective irreversibility. (shrink)

I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of some quite radical proposals of the Prigogine school is given. I argue that their conclusion regarding the conceptual bankruptcy of the classical conceptions of an exact microstate and unique phase space trajectory is not completely justified. The analogy they want to draw with quantum mechanics is not sufficiently close to support their (...) most radical conclusion. (shrink)

Prigogine afirma que, en presencia de alta inestabilidad (caos), los estados puntuales y las trayectorias lineales en el espacio de las fases se convierten en una falsa idealización. En el presente trabajo se sostiene que: (i) los argumentos de Prigogine en favor de tal tesis no son concluyentes, y (ii) hay buenas razones para retener la postulacion de estados puntuales y trayectorias lineales, en tanto conceptos teóricos legítimos en mecánica estadística.Prigogine asserts that the existence of radical instability (...) (chaos) makes the postulation of pointlike states and linelike trajectories in phase space a false idealization. In this paper we argue that (i) Prigogine’s arguments for this claim are not conclusive, and (ii) there are good reasons for retain the positing of pointlike states and linelike trajectories as a legitimate theoretical posit in statistical mechanics. (shrink)

Challenges the conventional view of the nature of time.

Nonclarity around the understandingof the concept of chaos has caused someconfusion in the contemporary natural science.For instance, not making a clear distinctionbetween the deterministic and quantum chaos hasmade it impossible to evaluate the approach ofIlya Prigogine in an appropriate way. It isshown that Jean Bricmont has missed the targetin his critique of I. Prigogine's ideas, as thelatter has concentrated his interest on systemsconsisting of infinite (arbitrarily large)number of particles in incessant mutualimpact, the former on systems that have afinite (...) (not necessarily large, althoughsometimes very large) number of particles,which move freely of any mutual impact orparticipate only in transient interaction. Thedifference may sometimes be quite crucial. Itis also suggested that if we consider theirreversibility as the basic element ofdescription of physical world, the world oftrajectories and wave functions cannot beresearched apart from this real irreversibility. (shrink)

Unexpected discoveries in nonequilibrium physics and nonlinear dynamics are changing our understanding of complex phenomena. Recent research has revealed fundamental new properties of matter in far-from-equilibrium conditions, and the prevalence of instability-where small changes in initial conditions may lead to amplified effects.

La science classique s'est trouvée associée à un désenchantement du monde. C'est la leçon que Jacques Monod entendait tirer des progrès de la biologie : "L'ancienne alliance est rompue. L'homme sait enfin qu'il est seul dans l'immensité indifférente de l'Univers d'où il a émergé par hasard." Notre science n'est plus ce savoir classique, nous pouvons déchiffrer le récit d'une "nouvelle alliance". Loin de l'exclure du monde qu'elle décrit, la science retrouve comme un problème l'appartenance de l'homme à ce monde. Les (...) théories scientifiques ne peuvent plus supposer la possibilité d'un savoir omniscient : nous lisons, jusque dans leurs principes, les traces d'une activité d'exploration au sein d'une nature en évolution. (shrink)