The fundamental question that has to be addressed is: Is time an objective feature of the physical universe? Or is it something purely subjective, an illusion of the mind, or merely a convenient way of describing things to which it has no real relationship? The latter position has been held, in one or other degree, by a number of different schools of thought, all of them closely related to the philosophy of subjective idealism. Mach, as we have seen, introduced this subjectivism into science. It was decisively answered towards the end of the 19th century by the pioneer of the science of thermodynamics, Ludwig Boltzmann.

Einstein, under the influence of Ernst Mach, treated time as something subjective, which depended on the observer, at least in the beginning before he realised the harmful consequences of this approach. In 1905, his paper on the special theory of relativity introduced the notion of a “local time” associated with each separate observer. The concept of time here contains an idea carried over from classical physics, namely that time is reversible. This is really quite an extraordinary notion, and one that flies in the face of all experience. Film directors often resort to a trick photography, in which the camera is put into reverse, whereupon the most peculiar events occur: milk flows from the glass back into the bottle, buses and cars run backwards, eggs return to their shells, and so on. Our reaction to all this is to laugh, which is what is intended. We laugh because we know that what we are seeing is not just impossible, but absurdly so. We know that the processes we are seeing cannot be reversed.

Boltzmann understood this, and the concept of irreversible time lies at the heart of his famous theory of the arrow of time. The laws of thermodynamics represented a major breakthrough in science, but were controversial. These laws could not be reconciled with the existing laws of physics at the end of the 19th century. The second law cannot be derived from the laws of mechanics or quantum mechanics, and, in effect, marks a sharp break with the theories of previous physical science. It says that entropy increases in the direction of the future, not the past. It denotes a change in state over time, which is irreversible. The notion of a tendency towards dissipation clashed with the accepted idea that the essential task of physics was to reduce the complexity of nature to simple laws of motion.

The idea of entropy, which is usually understood as a tendency of things towards greater disorganisation and decay with the passing of time, entirely bears out what people have always believed: that time exists objectively and that it is a one-way process. The two laws of thermodynamics imply the existence of the phenomenon known as entropy that is observed in all irreversible processes. Its definition is based on another property known as available energy. The entropy of an isolated system may remain constant or increase, but it cannot decrease. One of the results of this is the impossibility of a “perpetual motion machine”.

Einstein considered the idea of irreversible time to be an illusion that had no place in physics. In Max Planck’s words, the second law of thermodynamics expresses the idea that there exists in nature a quantity that changes always in the same sense in all natural processes. This does not depend on the observer, but is an objective process. But Planck’s view was in a small minority. The great majority of scientists, like Einstein, attributed it to subjective factors. Einstein’s position on this question shows up the central weakness of his standpoint in making objective processes depend upon a non-existent “observer”. This was undoubtedly the weakest element in his entire outlook, and, for that very reason, is the part that has proved most popular with his successors, who do not seem aware of the fact that Einstein himself changed his mind on this towards the end of his life.

In physics and mathematics the expression of time is reversible. A “time-reversal invariant” implies that the same laws of physics apply equally well in both situations. The second event is indistinguishable from the first and the flow of time does not have any preferred direction in the case of fundamental interactions. For example, a film of two billiard balls colliding, in a near-perfect elastic collision, can be run forward or backward, without giving any idea of the true time sequence of the event. The same was assumed to be true of interactions at the subatomic level, but evidence to the contrary was found in 1964 in weak nuclear interactions. For a long time it was believed that the fundamental laws of nature were “charge symmetrical”. For example, an antiproton and a positron behave like a proton and an electron. Experiments have now shown that the laws of nature are symmetrical if three basic things are combined – time, charge and parity. This is known as a “CPT mirror”.

In dynamics, the direction of a given trajectory was irrelevant. For example, a ball bouncing on the ground would return to its initial position. Any system can thus “go backwards in time”, if all the points involved in it are reversed. All the states it previously went through would simply be retraced. In classical dynamics, changes such as time reversal (t – > –t) and velocity reversal (v – > –v) are treated as mathematically equivalent. This kind of calculation works well for simple closed systems, where there are no interactions. In reality, however, every system is subject to many interactions. One of the most important problems in physics is the “three-body” problem, for example, the moon’s motion is influenced by the sun and the earth. In classical dynamics, a system changes according to a trajectory that is given once and for all, the starting point of which is never forgotten. Initial conditions determine the trajectory for all time. The trajectories of classical physics were simple and deterministic. But there are other trajectories that are not so easy to pin down, for example, a rigid pendulum, where an infinitesimal disturbance would be enough to set it rotating or oscillating.

The importance of Boltzmann’s work was that he dealt with the physics of processes rather than the physics of things. His greatest achievement was to show how the properties of atoms (mass, charge, structure) determine the visible properties of matter (viscosity, thermal conductivity, diffusion, etc.). His ideas were viciously attacked during his lifetime, but vindicated by the discoveries of atomic physics shortly before 1900, and the realisation that the random movements of microscopic particles suspended in a fluid (“Brownian motion”) could only be explained in terms of the statistical mechanics invented by Boltzmann.

The bell-shaped Gauss curve describes the random motion of molecules in a gas. An increased temperature leads to an increase in the average velocity of the molecules and the energy associated with their motion. Whereas Clausius and Maxwell approached this question from the standpoint of the trajectories of individual molecules, Boltzmann considered the population of molecules. His kinetic equations play an important role in the physics of gases. It was a major advance in the physics of processes. Boltzmann was a great pioneer, who was treated as a madman by the scientific establishment. He was finally driven to suicide in 1906, having previously been compelled to retreat from his attempt to establish the irreversible nature of time as an objective feature of nature.

Whereas in the theory of classical mechanics, the events in the film earlier described are perfectly possible, in practice, they are not. In the theory of dynamics, for example, we have an ideal world in which such things as friction and collision do not exist. In this ideal world, all the invariants involved in a given motion are fixed at the start. Nothing could happen to alter its course. By these means, we arrive at a completely static view of the universe, where everything is reduced to smooth, linear equations. Despite the revolutionary advances made possible by relativity theory, Einstein, at heart, remained wedded to the idea of a static, harmonious universe – just like Newton.

The equations of motion of Newtonian or for that matter quantum mechanics have no built-in irreversibility. It is possible to run a movie film forward or backwards. But this is not true of nature in general. The second law of thermodynamics predicts an irreversible tendency towards disorder. It states that randomness always increases in time. Until recently, it was thought that the fundamental laws of nature are symmetrical in time. Time is asymmetrical and moves only in one direction, from past to future. We see fossils, footprints and photographs and hear recordings of things from the past, but never from the future. It is easy to mix eggs to make an omelette or put milk and sugar into a cup of coffee, but not to reverse these processes. The water in the bath transfers its heat to the surrounding air, but not vice versa.

The second law of thermodynamics is the “arrow of time”. The subjectivists objected that irreversible processes like chemical affinity, heat conduction, viscosity, etc., would depend on the “observer”. In reality, they are objective processes that take place in nature, and this is clear to everyone in relation to life and death. A pendulum (at least in an ideal state) can swing back to its initial position. But everyone knows that the life of an individual moves in only one direction, from the cradle to the grave. It is an irreversible process. Ilya Prigogine, one of the leading theorists of chaos theory, has devoted a lot of attention to the question of time. When he first began to study physics as a student in Brussels, Prigogine recalls that he was “astonished by the fact that science had so little to say about time, especially since his earlier education had centred mainly around history and archaeology.” In relation to the conflict between classical mechanics (dynamics) and thermodynamics, Prigogine and Stengers write:

“To a certain extent, there is an analogy between this conflict and the one that gave rise to dialectical materialism. We have described…a nature that might be called ‘historical’ – that is, capable of development and innovation. The idea of a history of nature as an integral part of materialism was asserted by Marx and, in greater detail, by Engels. Contemporary developments in physics, the discovery of the constructive role played by irreversibility, have thus raised within the natural sciences a question that has long been asked by materialists. For them, understanding nature meant understanding it as being capable of producing man and his societies.

“Moreover, at the time Engels wrote his Dialectics of Nature, the physical sciences seemed to have rejected the mechanistic world view and drawn close to the idea of an historical development of nature. Engels mentions three fundamental discoveries: energy and the laws governing its qualitative transformations, the cell as the basic constituent of life, and Darwin’s discovery of the evolution of species. In view of these great discoveries, Engels came to the conclusion that the mechanistic world view was dead.”

Against the subjective interpretation of time, the authors conclude: “Time flows in a single direction, from past to future. We cannot manipulate time, we cannot travel back to the past.”[45]

  1. Prigogine I. and Stengers, I. op. cit., pp. 10, 252-3 and 277.