The Bootstrap Hypothesis

So far, our exploration of the world view suggested by modern physics has repeatedly shown that the idea of ‘basic building blocks’ of matter is no longer tenable. In the past, this concept was extremely successful in explaining the physical world in terms of a few atoms; the structures of the atoms in terms of a few nuclei surrounded by electrons; and finally, the structures of the nuclei in terms of two nuclear ‘building blocks’, the proton and the neutron.

Thus atoms, nuclei and hadrons were, in turn, considered to be ‘elementary particles’. None of them, however, fulfilled that expectation. Each time, these particles turned out to be composite structures themselves, and physicists hoped that the next generation of constituents would finally reveal themselves as the ultimate components of matter.

On the other hand, the theories of atomic and subatomic physics made the existence of elementary particles increasingly unlikely. They revealed a basic interconnection of matter, showing that energy of motion can be transformed into mass, and suggesting that particles are processes rather than objects. All these developments strongly indicated that the simple mechanistic picture of basic building blocks had to be aban- doned, and yet many physicists are still reluctant to do so.

The age-old tradition of explaining complex structures by breaking them down into simpler constituents is so deeply ingrained in Western thought that the search for these basic components is still going on.

There is, however, a radically different school of thought in particle physics which starts from the idea that nature cannot be reduced to fundamental entities, such as elementary particles or fundamental fields. It has to be understood entirely through its self-consistency, with its components being consistent both with one another and with themselves.

This idea has arisen in the context of S-matrix theory and is known as the ‘bootstrap’ hypothesis.

Its originator and main advocate is Geoffrey Chew who, on the one hand, has developed the idea into a general ‘bootstrap’ philosophy of nature and, on the other, has used it (in collaboration with other physicists) to construct specific models of particles formulated in S-matrix language. Chew has described the bootstrap hypothesis in several articles’ which provide the basis for the following presentation.

The bootstrap philosophy constitutes the final rejection of the mechanistic world view in modern physics. Newton’s universe was constructed from a set of basic entities with certain fundamental properties, which had been created by God and thus were not amenable to further analysis.

In one way or another, this notion was implicit in all theories of natural science until the bootstrap hypothesis stated explicitly that the world cannot be understood as an assemblage of entities which cannot be analysed further. In the new world view, the universe is seen as a dynamic web of interrelated events. None of the properties of any part of this web is funda- mental; they all follow from the properties of the other parts, and the overall consistency of their mutual interrelations determines the structure of the entire web.

Thus, the bootstrap philosophy represents the culmination of a view of nature that arose in quantum theory with the realization of an essential and universal interrelationship, acquired its dynamic content in relativity theory, and was formulated in terms of reaction probabilities in S-matrix theory.

At the same time, this view of nature came ever closer to the Eastern world view and is now in harmony with Eastern thought, both in its general philosophy and in its specific picture of matter.

The bootstrap hypothesis not only denies the existence of fundamental constituents of matter, but accepts no funda- mental entities whatsoever-no fundamental laws, equations or principles-and thus abandons another idea which has been an essential part of natural science for hundreds of years. The notion of fundamental laws of nature was derived from the belief in a divine lawgiver which was deeply rooted in the

Judaeo-Christian tradition. In the words of Thomas Aquinas: There is a certain Eternal Law, to wit, Reason, existing in the mind of Cod and governing the whole universe.*

This notion of an eternal, divine law of nature greatly influenced Western philosophy and science. Descartes wrote about the ‘laws which Cod has put into nature’, and Newton believed that the highest aim of his scientific work was to give evidence of the ‘laws impressed upon nature by Cod’. To discover the ultimate fundamental laws of nature remained the aim of natural scientistsfor the three centuries following Newton. In modern physics, a very different attitude has now developed. Physicists have come to see that all their theories of natural phenomena, including the ‘laws’ they describe, are creations of the human mind; properties of our conceptual map of reality, rather than of reality itself.

This conceptual scheme is necessarily limited and approximate,* as are all the scientific theories and ‘laws of nature’ it contains. All natural phenomena are ultimately interconnected, and in order to explain any one of them we need to understand all the others, which is obviously impossible. What makes science so successful is the discovery that approximations are possible. If one is satisfied with an approximate ‘understanding’ of nature, one can describe selected groups of phenomena in this way, neglecting other phenomena which are less relevant.

Thus one can explain many phenomena in terms of a few, and consequently understand different aspects of nature in an approximate way without having to understand everything at once. This is the scientific method; all scientific theories and models are approximations to the true nature of things, but the error involved in the approximation is often small enough to make such an approach meaningful. In particle physics, for example, the gravitational interaction forces between particles are usually ignored, as they are many orders of magnitude weaker than those of the other interactions. Although the error caused by this omission is exceedingly small, it is clear that the gravitational interactions will have to be included in future, more accurate theories of particles.

Thus physicists construct a sequence of partial and approximate theories, each of them being more accurate than the previous one, but none of them representing a complete and final account of natural phenomena. Like these theories, all the ‘laws of nature’ they describe are mutable, destined to be replaced by more accurate laws when the theories are improved.

The incomplete character of a theory is usually reflected in its arbitrary parameters or ‘fundamental constants’, that is, in quantities whose numerical values are not explained by the theory, but have to be inserted into it after they have been determined empirically. Quantum theory cannot explain the value used for the mass of the electron, nor field theory the magnitude of the electron’s charge, or relativity theory that of the speed of light. In the classical view, these quantities were regarded as fundamental constants of nature which did not require any further explanation. In the modern view, their role of ‘fundamental constants’ is seen as temporary and reflecting the limitations of the present theories.

According to the bootstrap philosophy, they should be explained, one by one, in future theories as the accuracy and scope of these theories increase. Thus the ideal situation should be approached, but may never be reached, where the theory does not contain any unexplained ‘fundamental’ constants, and. where all its ‘laws’ follow from the requirement of overall self-consistency. It is important to realize, however, that even such an ideal theory must possess some unexplained features, although not necessarily in the form of numerical constants. As long as it is a scientific theory, it will require the acceptance, without explanation, of certain concepts which form the scientific language. To push the bootstrap idea further would lead beyond science:

In the broad sense, the bootstrap idea, although fascinating and useful, is unscientific . . . Science, as we know it, requires a language based on some unquestioned framework. Semantically, therefore, an attempt to explain all concepts can hardly be called ‘scientific’.3

The complete ‘bootstrap’ view of nature, in which all phenomena in the universe are uniquely determined by mutual self-consistency, comes very close to the Eastern world view. An indivisible universe, in which all things and events are interrelated, would hardly make sense unless it were self-consistent. In a way, the requirement of self-consistency, which forms the basis of the bootstrap hypothesis, and the unity and interrelation of all phenomena, which are so strongly emphasized in Eastern mysticism, are just different aspects of the same idea.

This close connection is most clearly expressed in Taoism. For the Taoist sages, all phenomena in the world were part of the cosmic Way-the Tao-and the laws followed by the Tao were not laid down by any divine lawgiver, but were inherent in its nature. Thus we read in the Tao Te Ching :

Man follows the laws of earth; Earth follows the laws of heaven; Heaven follows the laws of Tao; Tao follows the laws of its intrinsic nature.4