The Phenomenon of Waves

The subatomic world is one of rhythm, movement and continual change. It is not, however, arbitrary and chaotic, but follows very definite and clear patterns.

To begin with, all particles of a given kind are completely identical; they have xactly the same mass, electric charge, and other characteristic properties. Furthermore, all charged particles carry electric charges exactly equal (or opposite) to that of the electron, or charges of exactly twicethat amount.

The same is true of other quantities that are characteristic attributes of the particles; they do not take arbitrary values but are restricted to a limited number, which allows us to arrange the particles into a few distinct groups, or ‘families’. This leads to the question of how these definite patterns arise in the dynamic and ever-changing particle world,

The emergence of clear patterns in the structure of matter is not a new phenomenon, but was already observed in the world of atoms. Like subatomic particles, atoms of a given kind are completely identical and the different kinds of atoms, of chemical elements, have been arranged into several groups in the periodic table. This classification is now well understood; it is based on the number of protons and neutrons present in the atomic nuclei and on the distribution of the electrons in spherical orbits, or ‘shells’, around the nuclei.

The wave nature of the electrons restricts the mutual distance of their orbits and the amount of rotation an electron can have in a given orbit to a few definite values corresponding to specific vibrations of the electron waves.

Consequently, definite patterns arise in the atomic structure which are characterized by a set of integral ‘quantum numbers’ and reflect the vibration patterns of the electron waves in their atomic orbits. These vibrations determine the ‘quantum states’ of an atom and ascertain that any two atoms will be completely identical when they are both in their ‘ground state’ or in the same ‘excited state’.

The patterns in the particle world show great similarities to those in the world of atoms. Most particles, for example, spin about an axis like a top. Their spins are restricted to definite values which are integral multiples of some basic unit. Thus the baryons can only have spins of l/2, 3/2, 5/2, etc., whereas the mesons have spins of 0, 1, 2, etc. This is strongly reminiscent of the amounts of rotation electrons are known to display in their atomic orbits, which are also restricted to definite values specified by integral numbers.

The analogy to the atomic patterns is further enforced by the fact that all strongly interacting particles, or hadrons, seem to fall into sequences whose members have identical properties except for their masses and spins. The higher members of these sequences are the extremely short-lived particles called ‘resonances’ which have been discovered in great numbers over the past decade. The masses and spins of the resonances increase in a well-defined way within each sequence, which seem to extend indefinitely.

These regularities suggest an analogy to the excited states of atoms and have led physicists to see the higher members of a hadron sequence not as different particles, but merely as excited states of the member with the lowest mass. Like an atom, a hadron can thus exist in various short-lived excited states involving higher amounts of rotation (or spin) and energy (or mass).

The similarities between the quantum states of atoms and hadrons suggest that hadrons, too, are composite objects with internal structures that are capable of being ‘excited, that is, of absorbing energy to form a variety of patterns. At present, however, we do not understand how these patterns are formed.

In atomic physics, they can be explained in terms of the properties and mutual interactions of the atom’s constituents (the protons, neutrons and electrons), but in particle physics such an explanation has not yet been possible. The patterns found in the particle world have been determined and classified in a purely empirical way and cannot yet be derived from the details of the particles’ structure.

The essential difficulty particle physicists have to face lies in the fact that the classical notion of composite ‘objects’ consisting of a definite set of ‘constituent parts’ cannot be applied to subatomic particles. The only way to find out what the ‘constituents’ of these particles are is to break them up by banging them together in collision processes involving high energies.

When this is done, however, the resulting fragments are never ‘smaller pieces’ of the original particles. Two protons, for example, can break up into a great variety of fragments when they collide with high velocities, but there will never be ‘fractions of a proton’ among them. The fragments will always be entire hadrons which are formed out of the kinetic energies and masses of the colliding protons. The decomposition of a particle into its ‘constituents’ is thus far from being definite, depending, as it does, on the energy involved in the collision process. We are dealing here with a crucially relativistic situation where dynamic energy patterns are dissolved and rearranged, and the static concepts of composite objects and constituent parts cannot be applied to these patterns.

The ‘structure’ of a subatomic particle can only be understood in a dynamic sense; in terms of processes and interactions.

The way in which particles break up into fragments in collision processes is determined by certain rules, and as the fragments are again particles of the same kind, these rules can also be used to describe the regularities which can be observed in the particle world. In the ‘sixties, when most of the presently known particles were discovered and ‘families’ of particles began to appear, most physicists-quite naturally-concentrated their efforts on mapping out the emerging regularities, rather than tackling the arduous problem of finding the dynamic causes of the particle patterns. And in doing so, they were very successful.

The notion of symmetry played an important role in this research. By generalizing the common concept of symmetry and giving it a more abstract meaning, physicists were able to develop it into a powerful tool which proved extremely useful in the classification of particles. In everyday life, the most common case of symmetry is associated with mirror reflection; a figure is said to be symmetric when you can draw a line through it and thereby divide it into two parts which are exact mirror images of each other. Higher degrees of symmetry are exhibited by patterns which allow several lines of symmetry to be drawn, like the following pattern used in Buddhist symbolism.

Reflection, however, is not the only operation associated with symmetry. A figure is also said to be symmetric if it looks the

same after it has been rotated through a certain angle. The shape of the Chinese yin-yang diagram, for example, is based on such a rotational symmetry. In particle physics, symmetries are associated with many other operations besides reflections and rotations, and these can take place not only in ordinary space (and time), but also in abstract mathematical spaces. They are applied to particles, or groups of particles, and since the particles’ properties are inseparably linked to their mutual interactions, the symmetries also apply to the interactions, i.e. to the processes in which the particles are involved. The reason that these symmetry operations are so useful lies in the fact that they are closely related to ‘conservation laws’. Whenever a process in the particle world displays a certain symmetry, there is a measurable quantity which is ‘conserved’; a quantity, that is, which remains constant during the process. These quantities provide elements of constancy in the complex dance of subatomic matter and are thus ideal to describe the particle interactions. Some quantities are conserved in all interactions, others only in some of them, so that each process is associated with a set of conserved quantities. Thus the symmetries in the particles’ properties appear as conservation laws in their interactions. Physicists use tne two concepts interchangeably, referring sometimes to the symmetry of a process, sometimes to the

corresponding conservation law, whichever is more convenient in the particular case. There are four basic conservation laws which seem to be observed in all processes, three of them being connected with simple symmetry operations in ordinary space and time. All particle interactions are symmetric with respect to displace- ments in space-they will look exactly the same whether they take place in London or in New York. They are also symmetric with respect to displacements in time, which means they will occur in the same way on a Monday or on a Wednesday. The first of these symmetries is connected with the conservation of momentum, the second with the conservation of energy. This means that the total momentum of all particles involved in an interaction, and their total energy (including all their masses), will be exactly the same before and after the inter- action. The third basic symmetry is one with respect to orienta- tion in space. In a particle collision, for example, it does not make any difference whether the colliding particles approach each other along an axis oriented north-south or east-west. As a consequence of this symmetry, the total amount of rotation involved in a process (which includes the spins of the individual particles) is always conserved. Finally, there is the conservation of electric charge. It is connected with a more complicated symmetry operation, but in its formulation as a conservation law it is very simple: the total charge carried by all particles involved in an interaction remains constant. There are several more conservation laws which correspond to symmetry operations in abstract mathematical spaces, like the one connected with charge conservation. Some of them hold for all interactions, as far as we know, others only for some of them (e.g. for strong and electromagn.etic interactions, but not for weak interactions). The corresponding conserved quantities can be seen as ‘abstract charges’ carried by the particles. Since they always take integer values (, _+ 1, + 2, etc.), or ‘half-integer’ values (f l/2, f 3/2, + 5/2, etc.), they are called quantum numbers, in analogy to the quantum numbers in atomic physics. Each particle, then, is characterized by a set of quantum numbers which, in addition to its mass, specify its properties completely.

Hadrons, for example, carry definite values of ‘isospin’ and

‘hypercharge’, two quantum numbers which are conserved in all strong interactions. If the eight mesons listed in the table in the previous chapter are arranged according to the values of these two quantum numbers, they are seen to fall into a neat hexagonal pattern known as the ‘meson octet’. This arrange- ment exhibits a great deal of symmetry; for example, particles and antiparticles occupy opposite places in the hexagon, the two particles in the centre being their own antiparticles. The eight lightest baryons form exactly the same pattern which is called the baryon octet. This time, however, the antiparticles are not contained in the octet, but form an identical ‘anti-octet’. The remaining baryon in our particle table, the omega, belongs to a different pattern, called the ‘baryon decuplet’, together with nine resonances. All the particles in a given symmetry pattern have identical quantum numbers, except for isospin and hypercharge which give them their places in the pattern. For example, all mesons in the octet have zero spin (i.e. they do not spin at all); the baryons in the octet have a spin of l/2, and those in the decuplet have a spin of 3/2.

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 ob- jections 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 four 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.