The End of Certainty:

Time, Chaos, and The New Laws of Nature

By Ilya Prigogine (Nobel Prize Laureate in Chemistry 1977)

Excerpts and Comments

By Rami E. Cremesti

“ I believe that we are at an important point in the history of science. We have come to the end of the road paved by Galileo and Newton, which presented us with an image of a time-reversible, deterministic universe. We now see the erosion of determinism and the emergence of a new formulation of the laws of physics“.

With these prophetic words, Ilya Prigogine, 1977 Nobel Prize laureate and head of The Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems at U.T Austin , opens his book The End of Certainty: Time, Chaos, and The New Laws of Nature  which was published in 1997.

The book begins by asserting the importance of the role of time in the newly emerging science. Albert Einstein often asserted that Time is an illusion. This is true but only within the confines of classical Newtonian dynamics, relativity and quantum physics which do not distinguish between past and future. Yet everywhere - in chemistry, geology, cosmology, biology and the human sciences- past and future play different roles. This is the time paradox, one of the central concerns of this book. However, Prigogine believes that the paradox has been solved by the two recent developments in physics: the spectacular growth of non-equilibrium physics and the dynamics of unstable systems beginning with the idea of chaos.

Over the past several decades, a new science has been born, the physics of non-equilibrium processes, and has led to concepts such as self-organization and dissipative structures.This new science is widely used to day in a large spectrum of disciplines, including cosmology, chemistry, biology (including evolution), ecology and the social sciences.These processes illustrate the constructive role of time. Figuratively speaking, matter at equilibrium, with no arrow of time is blind, but with the arrow of time it begins to see. Without this new coherence due to irreversible, non-equilibrium processes, life on earth would be impossible to envision.

Classical science emphasized order and stability. Now in contrast, we see fluctuations, instability, multiple choices, and limited predictability at all levels of observation. Classical and quantum physics can be extended to include instability and chaos. In classical physics, laws of nature express certitudes. Once instability is included, the meaning of the laws of nature changes radically, and they now express possibilities or probabilities. We are now able to include probabilities in the formulation of the basics laws of physics.

At the end of this century, it is often asked what the future of science may be. For some, such as Stephen W. Hawking in his Brief History of Time, we are close to the end, the moment when we shall be able to read the mind of God. In contrast, Prigogine believes that we are actually at the beginning of a new scientific era, the birth of a science that is no longer limited to idealized and simplified situations but reflects the complexity of the real world.

Is the universe ruled by deterministic laws ? What is the nature of time?. What could be the meaning of human freedom in a deterministic world of atoms?: Time-old questions that have occupied the human mind since the time of the Pre-Socratics 2500 years ago.Kant, Whitehead, Heiddeger and many other great thinkers felt that they had to make a tragic choice between an alienating science or an anti-scientific philosophy or theology. They attempted to find some kind of compromise, but they all failed... The history of Western philosophy is characterized by perpetual oscillations between viewing the world as an automaton and a theology in which God governs the universe.

Prigogine believes that the recent developments in the physics and mathematics associated with chaos and instability have opened up different avenues of investigation. We are beginning to see these problems, which deal with the very position of mankind in nature, in a new light, and can now avoid the contradictions and dilemmas of the past.

Prigogine emphasizes the constructive role of irreversibility, which is very striking in far-from-equilibrium situations. We are now learning that it is precisely through irreversible processes associated with the arrow of time that nature achieves its most delicate and complex structures. Life is possible only in a non-equilibrium universe. This is contrary to the classical view in which irreversibility is viewed as an illusion not as a basic law of nature. As the physicist Roman Smoluchowski put it, if we continued our observation for an immeasurably long time, all processes would apprear to be reversible.

The distinction between reversible and irreversible processes was introduced through the concept of entropy associated with the so-called Second Law of Thermodymanics. Entropy was defined by Rudolf Julius Clausius in 1865. According to this law, irreversible processes produce entropy. In contrast, reversible processes leave the entropy constant. We recall here Clausius's famous formulation: The energy of the universe is constant. The entropy of the universe is increasing. This increase in entropy is due to the irreversible processes that take place in the universe. Clausius's statement was the first formulation of an evolutionary view of the universe based on the existence of these processes. Arthur Stanley Eddington called entropy the arrow of time. Nevertheless, according to the fundamental laws of physics, there should be no irreversible processes. We therefore see that we have inherited two conflicting views of nature from the nineteenth century: the time-reversible view based on the classical laws of dynamics and the evolutionary view based on entropy. How can these views be reconciled ?

In the nineteenth century, Boltzmann introduced the Kinetic Theory of Gases, which is statistical. Poincare was so impressed by the success of theory that he wrote Perhaps the kinetic theory of gases will serve as a model ... physical laws will then take on a completely new form; they will take on a statistical character. These were prophetic words ... In an extraordinarily daring move, Boltzmann introduced probability as an empirical tool and paved way to the new physics... The physics of populations.

“The creativity of nature is connected to distance from equilibrium and is the result of irreversible processes” . Stresses applied to systems at or near equilibrium lead to fluctuations that are damped. In other words, the system gradually returns to equilibrium. However, a far from-equilibrium system may evolve spontaneously to a state of increased complexity. The ordering we observe is the outcome of irreversible processes, and could not be achieved at equilibrium. At equilibrium, the entropy of a system has a maximum value and the free energy is at its minimum. However, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production. As a consequence, there is no guarantee that fluctuations are damped. Near equilibrium, laws of nature are universal, but when they are far from equilibrium, they become mechanism dependent. We therefore begin to perceive the origin of the variety in nature we observe around us.

Once we have dissipative structures, we can speak of self-organization. Even if we know the initial values and boundary conditions, there are still many states available to the system among which it “chooses” as a result of fluctuations. Indeterminism as conceived by Whitehead, Bergson, and Popper now appears in physics. Bifurcations can be considered the source of diversification and innovation. These concepts are now applied to a wide group of problems in biology, sociology, and economics at interdisciplinary centers throughout the world. In Western Europe alone, there have been more than fifty centers for nonlinear processes founded over the past ten years.

“Darwin showed that we are one species of animal among many others”. This is a quote from the book, which shows that Prigogine is obviously an atheist.

There is still a gap between the most complex structures that we can produce in non-equilibrium situations in chemistry and the complexity we find in biological systems.

The maintenance of order in nature is maintained by self-organization.

Dissipative structures require an arrow of time.

The fathers of statistical physics: Maxwell, Boltzmann, Gibbs and Einstein.

We need both equilibrium and non-equilibrium physics to describe the world around us.

Epicurus’ dilemma today has been solved. We no longer find ourselves obliged to choose between a deterministic view of the universe as ruled by strict laws in which there is no room for creativity and one ruled by mere chance. Today, the situation has changed significantly in the sense that the more we know about our universe, the more difficult it becomes to believe in determinism (NOTE: Prigogine believes that theologies centered on God as the governor of the universe are just another form of determinism). Chance or probability is now a part of a new, extended rationality.

Prigogine’s view on cosmology (the more widely accepted Big Band Theory and The Steady State Theory) agrees with that of the Indian cosmologist Jayant Vishnu Narlikar, who wrote “Astrophysicists of today who hold the view that the ‘ultimate cosmological problem’ has been more or less solved may well be in for a few surprises before this century is out”.

“Many scientists have been willing to explain this singularity (the big bang) in terms of the “hand of God” or the triumph of the biblical story or creation.”

“Why is there something rather than nothing? The ultimate question beyond the range of positive knowledge. One answer to this question is a theory that defines the birth of our universe as a free lunch. Edward Tryon presented this idea in 1973. In his view, our universe can be described as having two forms of energy: one related to attractive gravitational forces, which is negative, and the other related to mass according to Einstein’s celebrated formula E = Mc². It is tempting to speculate that the total energy of the universe could be zero, as is the energy of an empty universe. The big bang would thus be associated with fluctuations in the vacuum conserving the energy. Prigogine suggests that what happened in the big bang was an irreversible phase transition from a preuniverse that he calls the “quantum vacuum”. Thus, the birth of our universe is no longer seen to be associated with a singularity (a point of infinite density of matter and energy) that defies the laws of physics, but rather with an instability that is analogous to a phase transition or a bifurcation. This theory though, still has a number of vexing problems.”

“In accepting that the future is not determined, we come to the end of certainty” says Prigogine. He does not believe, however, that this is an admission of defeat for the human mind. He asserts that the opposite is true.

He views the universe as a giant thermodynamical system far from equilibrium, where we find fluctuations, instabilities, and evolutionary patterns at all levels.

Some great quotes from the end of the book:

For Einstein, science was a means of avoiding the turmoil of everyday existence. He compared scientific activity to the “longing that irresistibly pulls the town-dweller away from his noisy, cramped quarters and toward the silent high mountains. Einstein’s view of the human condition was profoundly pessimistic.

Science began with the Promethean affirmation of the power or reason, but it seemed to end in alienation – a negation of everything that gives meaning to human life.

Einstein repeatedly stated that he had learned more from Fyodor Dostoyevsky than from any physicist. In a letter to Max Born in 1924, he wrote that if he were forced to abandon strict causality (classical physics and relativity), he “would rather be a cobbler, or even an employee in a gaming house, than a physicist”. In order to be of any value at all, physics has to satisfy his need to escape the tragedy of the human condition. “And yet and yet”, when Einstein was confronted by Godel with the extreme consequences of his quest, the denial of the very reality that physics endeavors to describe, Einstein recoiled. (Godel took Einstein’s Theory of Relativity and classical physics and showed that past and future are equivalent and that it is possible to travel back in time).

Prigogine has tried to follow a narrow path between two conceptions that both lead to alienation: a world ruled by deterministic laws, which leaves no place for novelty, and a world ruled by a dice-playing God, where everything is absurd, acausal, and incomprehensible.

Prigogine ends his book with the following words:

“As we follow along the narrow path, we discover that a large part of the concrete world around us has until now “slipped through the meshes of the scientific net”, to use Whitehead’s expression. We face new horizons at this privileged moment in the history of science”.