Newton’s classical mechanics in their time represented an enormous step forward in science. For the first time, Newton’s laws of motion made possible precise quantitative predictions, which could be checked against the observed phenomena. However, precisely this precision leads to new problems when Laplace and others attempted to apply them to the universe as a whole. Laplace was convinced that Newton’s laws were absolutely and universally valid. This was doubly incorrect. First of all, Newton’s laws were not seen as approximations applicable in certain circumstances. Secondly Laplace did not consider the possibility that under different circumstances, in areas not yet studied in physics, these laws might need to be modified or extended. The mechanistic determinism of Laplace supposed that once the positions and velocities were known at any instant of time the future behaviour of the whole universe would be determined for all time. According to this theory, all the rich diversity of things can be reduced to an absolute set of quantitative laws based on a few variables.

Classical mechanics as expressed in Newton’s laws of motion deal with simple cause and effect, for example the isolated action of one body upon another. However, in practice, this is impossible, since no mechanical system is ever completely isolated. Outside influences inevitably destroy the isolated one-to-one character of the connection. Even if we could isolate the system, there will still be disturbances arisen from motions at the molecular level, and other disturbances at the even deeper level of quantum mechanics. As Bohm remarks:

Thus, there is no real case known of a set of perfect one-to-one causal relationships that could in principle make possible predictions of unlimited precision, without the need to take into account qualitatively new sets of causal factors existing outside the system of interest or at other levels.[14]

Does this mean that prediction is impossible? Not at all. When we aim a gun at a certain point, the individual bullet will not land precisely at the point predicted by Newton’s law of motion. However, a large number of shots fired will form a cluster in a small region near the point predicted. Thus, within a given range of error, which always exists, very precise predictions are possible. If we wanted to obtain unlimited precision in this instance, we would discover an ever increasing number of factors which influence the result – irregularities in the structure of the gun and bullet, tiny variations of temperature, pressure, humidity, air currents, and even the molecular motions of all these factors.

Some degree of approximation is necessary, which does not take into account the infinity of factors required for a perfectly precise prediction of a given result. This involves a necessary abstraction from reality, as in Newtonian mechanics. However, science continually proceeds, step by step, to discover ever deeper and more precise laws that enable us to gain a deeper understanding of the processes of nature, and thus make more accurate predictions. The abandonment of the old mechanical determinism of Newton and Laplace does not mean the abolition of causality, but a deeper understanding of the way in which causality actually works.

The first breaches in the wall of Newtonian science appeared in the second half of the 19th century, especially with Darwin’s theory of evolution and the work of the Austrian physicist Ludwig Boltzmann on a statistical interpretation of thermodynamic processes. Physicists endeavoured to describe many-particle systems like gases or fluids with statistical methods. Those statistics however, were seen as an auxiliary in situations where it was impossible for practical reasons to collect detailed information about all the properties of the system (for example all the positions and velocities of the particles of gas at a given moment in time).

The 19th century saw the development of statistics, first in the social sciences, then in physics, for example in the theory of gases, where randomness and determinacy can both be seen in the movement of molecules. On the one hand, individual molecules seem to move in an entirely random manner. On the other hand, very large numbers of the molecules that make up a gas are seen to behave in a way that obeys precise dynamical laws. How to explain this contradiction? If the movement of its constituent molecules is random and therefore cannot be predicted, surely the behaviour of a gas ought to be similarly unpredictable? Yet this is far from the case.

The answer to the problem is supplied by the law of the transformation of quantity into quality. Out of the apparently random movement of a large number of molecules, there arises a regularity and a pattern which can be expressed as a scientific law. Out of chaos arises order. This dialectical relation between freedom and necessity, between chaos and order, between randomness and determinacy was a closed book to the science of the 19th century, which regarded the laws governing random phenomena (statistics) to be entirely separate and apart from the precise equations of classical mechanics. Considering fluids Gleick writes:

Any liquid or gas is a collection of individual bits, so many that they may as well be infinite. If each piece moved independently, then the fluid would have infinitely many possibilities, infinitely many ‘degrees of freedom’ in the jargon, and the equations describing the motion would have to deal with infinitely many variables. But each particle does not move independently – its motion depends very much on the motion of its neighbours – and in a smooth flow, the degrees of freedom can be few.[15]

Classical mechanics worked very well for a long time, making important technological advances possible. Even down to the present time, it has a vast amount of applications. However, eventually it was found that certain areas could not adequately be dealt with by these methods. They had reached their limit. The neatly ordered, logical world of classical mechanics describes part of nature. But only part. In nature we see order, but also disorder. Alongside organisation and stability there are equally powerful forces tending in the opposite direction. Here we have to resort to dialectics, to determine the relation between necessity and chance, to show at what point the accumulation of tiny, apparently insignificant changes of quantity became transformed into sudden qualitative leaps.

Bohm proposed a radical re-thinking of quantum mechanics, and a new way of looking at the relation between whole and parts.

“In these studies…it became clear that even the one-body system has a basically non-mechanical feature, in the sense that it and its environment have to be understood as an undivided whole, in which the usual classical analysis into system plus environment, considered as separately external, is no longer applicable.” The relationship of the parts “depends crucially on the state of the whole, in a way that is not expressible in terms of properties of the parts alone. Indeed, the parts are organised in ways that flow out of the whole.”[16]

The dialectical law of transformation of quantity into quality expresses the idea that matter behaves differently at different levels. Thus, we have the molecular level, the laws of which are studied mainly in chemistry but partly in physics; we have the level of living matter, studied mainly in biology; the subatomic level, studied in quantum mechanics; and also another level still deeper than that of elementary particles, which is presently being explored in particle physics. Each of these levels has many subdivisions.

It has been shown that the laws governing the behaviour of matter at each level are not the same. This was already shown in the 19th century by the kinetic theory of gases. If we take a box of gas containing billions of molecules, moving in irregular paths and in constant collision with other molecules, it is clearly impossible to determine the precise motions of each individual molecule. In the first place, it is ruled out on purely mathematical grounds. However, even if it were possible to solve the mathematical problems involved, it would be impossible in practice to measure the initial position and velocity of each molecule which would be needed to make precise predictions concerning it. Even a slight change in the initial angle of motion of any molecule would alter its direction, in turn leading to a still bigger change in the next collision, and so on, leading to huge errors in any prediction concerning the movement of an individual molecule.

If we try to apply the same kind of reasoning to the behaviour of gases at the macroscopic (“normal”) level, one would assume that it is also impossible to predict their behaviour. But this is not the case; the behaviour of gases at a large-scale level can be perfectly predicted. As Bohm points out:

“It is clear that one is justified in speaking of a macroscopic level possessing a set of relatively autonomous qualities and satisfying a set of relatively autonomous relations which effectively constitute a set of macroscopic causal laws. For example, if we consider a mass of water, we know by direct large-scale experience that it acts in its own characteristic way as a liquid. By this we mean that it shows all the macroscopic qualities that we associate with liquidity. For example, it flows, it ‘wets’ things, it tends to maintain a certain volume, etc. In its motion it satisfies a set of basic hydrodynamic equations which are expressed in terms of the large-scale properties alone, such as pressure, temperature, local density, local stream velocity, etc. Thus, if one wishes to understand the properties of the mass of water, one does not treat it as an aggregate of molecules, but rather as an entity existing at the macroscopic level, following laws appropriate to that level.”

This is not to say that the molecular constitution has nothing to do with the behaviour of water. On the contrary. The relation between the molecules determines, for example, whether it manifests itself as a liquid, a solid or vapour. But, as Bohm points out, there is a relative autonomy, which means that matter behaves differently at different levels; there exists

“a certain stability of the characteristic modes of macroscopic behaviour, which tend to maintain themselves not only more or less independently of what the individual molecules are doing, but also of the various disturbances to which the system may be subjected from outside.”[17]

  1. Bohm, D. op. cit., p. 20.

  2. Gleick, J. Chaos, Making a New Science, p. 124.

  3. Bohm, D. op. cit., pp. x and xi.

  4. Bohm, D. op. cit., pp. 50-1.