Prigogine and the basic entities of the world

The main originality that Prigogine portrays is the way in which he sees the introduction of probabilities in the dynamical description of an unstable system (with persistent interactions). In classical dynamics this is seen as a measure of our ignorance of the system. In fact, as Prigogine recognises, “the equations of chaotic systems are deterministic” (p. 32)[i], which means that, the unpredictable character of the behaviour of unstable (or even chaotic) systems is due to the finite precision with which we can describe the initial conditions. Therefore, the unpredictability is seen as a characteristic of the description and not of the system itself.

On the other hand, some unstable systems, for instance the ones in which Poincaré resonances appear, are unpredictable because the trajectories in these systems are impossible to calculate (thus, infinite precision in the description of the initial conditions would not help). Like Prigogine says, in the classical interpretation this is still viewed as deriving from a lack of information: “any dynamical system must follow a trajectory, solution of its equations, disregarding the fact that we can reach them or not.” (p. 41)

Opposing this interpretation, Prigogine questions our reasons for supposing that trajectories are elementary entities. Instead, he proposes that probability waves or distributions should be seen as the elementary entities from which trajectories arise:

“But this [the trajectory] ceases to be an elementary concept in the statistical description. In this case, to obtain a trajectory, we should concentrate the distribution of probabilities in a single point. … The trajectory becomes the result of a physical-mathematical construction.” (p. 118)

There are at least three reasons advanced for this change in perspective: the first is because, in unstable systems, the description based on trajectories is not as complete as the statistical description. The latter, Prigogine argues, gives more complete and accurate predictions, especially because it includes non-local interactions,[ii] which is impossible for the trajectory description to account for. The second reason has to do with the introduction of the arrow of time in the microscopic laws of physics, thus eliminating the inconsistency between our theories and observations (according to our mechanical theories there should be no privileged direction of time). The third reason is that it allows for a realist interpretation of quantum mechanics.

But Prigogine’s proposal has to deal at least with two serious difficulties. The first one is to give a physical meaning to the probability distributions. Usually probability distributions are seen as theoretical concepts, how can they create or destroy physical things like electrons or photons? The second is that Prigogine, when saying that the statistical level can make better predictions (regarding unstable systems) than the ones based on trajectories, is using incomplete trajectory descriptions. Although this is not a problem if we want to speak of the theories we use, it certainly becomes one if we want to speak of the way the world is.

Anyway this last objection only shows that classical interpretation of dynamics is still defensible; the plausibility of Prigogin’s proposal will more strongly depend on whether we can conceive (non-physical) probabilities, or (popperian) propensities, as elementary entities, and the way in which a particular possibility is selected or actualised. A problem whose solution is inextricably connected with the lines that frame the philosophical mind-body problem since at least Descartes.

[i] All the quotes and page references were translated/taken from the portuguese edition of La Fin des Certitudes.

[ii] And also because it includes a description of the phase state: “So, it contains an additional information, which is lost in the description of individual trajectories.” (p.37)