The quantum numbers, then, are used to arrange particles into families forming neat symmetric patterns, to specify the places of the individual particles within each pattern, and at the same time to classify the various particle interactions according to the conservation laws they exhibit. The two related concepts of symmetry and conservation are thus seen to be extremely useful for expressing the regularities in the particle world.

It is surprising that most of these regularities can be repre- sented in a very simple way if one assumes that all hadrons are made of a small number of elementary entities which have so far eluded direct observation. These entities have been given the fanciful name ‘quarks’ by Murray Cell-Mann who referred his fellow physicists to the line in James Joyce’s Finnegan’s Wake, ‘Three quarks for Muster Mark’, when he postulated their existence. Cell-Mann succeeded in accounting for a large number of hadron patterns, such as the octets and the decuplet discussed above, by assigning appropriate quantum numbers to his three quarks and their antiquarks, and then putting these building blocks together in various combinations to form baryons and mesons whose quantum numbers are obtained simply by adding those of their constituent quarks. In this sense, baryons can be said to ‘consist of’ three quarks, their antiparticles of the corresponding antiquarks, and mesons of a quark plus an antiquark.

The simplicity and efficiency of this model is striking, but it leads to severe difficulties if quarks are taken seriously as actual physical constituents of hadrons. So far, no hadrons have ever been broken up into their constituent quarks, in spite of bombarding them with the highest energies available, which means that quarks would have to be held together by extremely strong binding forces. According to our present understanding of particles and their interactions, these forces can only manifest themselves through the exchange of other particles, and consequently these other particles, too, would be present inside each hadron. If this were so, however, they would also contribute to the hadron’s properties and thus destroy the simple additive scheme of the quark model.

In other words, if quarks are held together by strong inter- action forces, these must involve other particles and the quarks must consequently show some kind of ‘structure’, just like all the other strongly interacting particles. For the quark model, however, it is essential to have pointlike, structureless quarks. Because of this fundamental difficulty, it has so far not been possible to formulate the quark model in a consistent dynamic way which accounts for the symmetries and for the binding forces.

On the experimental side, there has been a fierce but, so far, unsuccessful ‘hunt for the quark over the past decade. If single quarks exist, they should be quite conspicuous because Cell-Mann’s model requires them to possess some very unusual properties, like electric charges of l/3 and 2/3 of that of the electron, which do not appear anywhere in the particle world.

So far, no particles with these properties have been observed in spite of the most intensive search. This persistent failure to detect them experimentally, plus the serious theoretical objections to their existence, have made the reality of quarks extremely doubtful.

On the other hand, the quark model continues to be very successful in accounting for the regularities found in the particle world, although it is no longer used in its original simple form. In Cell-Mann’s original model, all hadrons could be built from three kinds of quarks and their antiquarks, but in the mean time physicists have had to postulate additional quarks to account for the great variety of hadron patterns.

Cell-Mann himself recently proposed that each quark can appear in three different varieties which he called-most appropriately in a lecture in Paris-‘red, white, and blue quarks’.

This increased the total number of quarks to nine, and since then three more quarks have been postulated,* which allowed one of the speakers at a recent physics conference to refer to them facetiously as ‘the twelve observed quarks’. The great number of regularities that can be successfully described in terms of these twelve quarks is truly impressive. There can be no doubt that hadrons exhibit ‘quark symmetries’, even though our present understanding of particles and inter- actions precludes the existence of physical quarks. At present, in the summer of 1974, the paradoxes surrounding the quark model are becoming increasingly sharp. A great deal of experi- mental data support the quark model; others contradict it violently. No one has ever seen a quark, and according ‘to our basic ideas about particle interactions quarks cannot exist.

Yet, hadrons very often behave exactly as if they consisted of pointlike elementary constituents. This situation is strongly reminiscent of the early days of atomic physics when equally striking paradoxes led the physicists to a major breakthrough in their understanding of atoms. The quark puzzle has all the traits of a new koan which, in turn, could lead to a major breakthrough in our understanding of subatomic particles.

The discovery of symmetric patterns in the particle world has led many physicists to believe that these patterns reflect the fundamental laws of nature. During the past fifteen years, a great deal of effort has been devoted to the search for an ultimate ‘fundamental symmetry’ that would incorporate all known particles and thus ‘explain’ the structure of matter.

This aim reflects a philosophical attitude which has been inherited from the ancient Greeks and cultivated throughout many centuries. Symmetry, together with geometry, played an important role in Greek science, philosophy and art, where it was identified with beauty, harmony and perfection.

Thus the Pythagoreans regarded symmetric number patterns as the essence of all things; Plato believed that the atoms of the 4 elements had the shapes of regular solids, and most Greek astronomers thought that the heavenly bodies moved in circles because the circle was the geometrical figure with the highest degree of symmetry.

The attitude of Eastern philosophy with regard to symmetry is in striking contrast to that of the ancient Greeks.

Mystical traditions in the Far East frequently use symmetric patterns as symbols or as meditation devices, but the concept of symmetry does not seem to play any major role in their philosophy. Like geometry, it is thought to be a construct of the mind, rather than a property of nature, and thus of no fundamental importance.

Accordingly, many Eastern art forms have a striking predilection for asymmetry and often avoid all regular or geometrical shapes. The Zen-inspired paintings of China and Japan, often executed in the so-called ‘one-corner’ style, or the irregular arrangements of flagstones in Japanese gardens clearly illustrate this aspect of Far-Eastern culture.

It would seem, then, that the search for fundamental symmetries in particle physics is part of our Hellenic heritage which is, somehow, inconsistent with the general world view that begins to emerge from modern science. The emphasis on symmetry, however, is not the only aspect of particle physics.

In contrast to the ‘static’ symmetry approach, there has always been a ‘dynamic’ school of thought which does not regard the particle patterns as fundamental features of nature, but attempts to understand them as a consequence of the dynamic nature and essential interrelation of the subatomic world. The remaining two chapters show how this school of thought has given rise, in the past decade, to a radically different view of symmetries and laws of nature which is in harmony with the world view of modern physics described so far and which is in perfect agreement with Eastern philosophy.