To explain the symmetries in the particle world in terms of a dynamic model, that is, one describing the interactions between the particles, is one of the major challenges of present-day physics. The problem, ultimately, is how to take into account simultaneously quantum theory and relativity theory. The particle patterns seem to reflect the ‘quantum nature’ of the particles, since similar patterns occur in the world of atoms. In particle physics, however, they cannot be explained as wave patterns in the framework of quantum theory, because the energies involved are so high that relativity theory has to be applied. Only a ‘quantum-relativistic’ theory of particles, therefore, can be expected to account for the observed symmetries. Quantum field theory was the ‘first model of that kind. It gave an excellent description of the electromagnetic inter- actions between electrons and photons, but it is much less appropriate for the description of strongly interacting particles. As more and more of these particles were discovered, physicists soon realized that it was highly unsatisfactory to associate each of them with a fundamental field, and when the particle world revealed itself as an increasingly complex tissue of inter- connected processes, they had to look for other models to represent this dynamic and ever-changing reality. What was needed was a mathematical formalism which would be able to describe in a dynamic way &great variety of hadron oatterns: their continual transformation into one another, their mutual interaction through the exchange of other particles, the formation of ‘bound states’ of two or more hadrons, and their decay into various particle combinations. All these processes, which are often given the general name

‘particle reactions’, are essential features of the strong inter- actions and have to be accounted for in a quantum-relativistic model of hadrons. The framework which seems to be most appropriate for the description of hadrons and their interactions is called ‘S-matrix theory’. Its key concept, the ‘S matrix’, was originally proposed by Heisenberg in 1943 and has been developed, over the past two decades, into a complex mathematical structure which seems to be ideally suited to describe the strong interactions. The S matrix is a collection of probabilities for all possible reactions involving hadrons. It derives its name from the fact that one can imagine the whole assemblage of possible hadron reactions arranged in an infinite array of the kind mathe- maticians call a matrix. The letter S is a remainder of the original name ‘scattering matrix’ which refers to collision-or ‘scattering’-processes, the majority of particle reactions. In practice, of course, one is never interested in the entire collection of hadron processes, but always in a few specific reactions. Therefore, one never deals with the whole S matrix,

but only with those of its parts, or ‘elements’, which refer to the processes under consideration. These are represented sym- bolically by diagrams like the one above which pictures one of the simplest and most general particle reactions: two particles, A and B, undergo a collision to emerge as two different particles, C and D. More complicated processes involve a greater number of particles and are represented by diagrams like the following.

It must be emphasized that these S-matrix diagrams are very different from the Feynman diagrams of field theory. They do not picture the detailed mechanism of the reaction, but merely specify the initial and final particles. The standard process A+B+C+D, for example, might be pictured in field theory as the exchange of a virtual particle V, whereas in S-matrix

theory, one simply draws a circle without specifying what goes on inside it. Furthermore, the S-matrix diagrams are not space- time diagrams, but more general symbolic representations of particle reactions. These reactions are not assumed to take place at definite points in space and time, but are described in terms of the velocities (or, more precisely, in terms of the momenta) of the incoming and outgoing particles. This means, of course, that an S-matrix diagram contains much less information than a Feynman diagram. On the other hand, S-matrix theory avoids a difficulty which is characteristic of field theory. The combined effects of quantum and relativity theory make it impossible to localize an interaction between definite particles precisely. Due to the uncertainty principle, the uncertainty of a particle’s velocity will increase as its region of interaction is localized more sharply,* and consequently, the amount of its kinetic energy will be increasingly uncertain. Eventually, this energy will become large enough for new particles to be created, in accordance with relativity theory, and then one can no longer be certain of dealing with the original reaction. Therefore, in a theory which combines both quantum and relativity theories, it is not possible to specify the position of individual particles precisely. If this is done, as in field theory, one has to put up with mathematical incon- sistencies which are, indeed, the main problem in all quantum field theories. S-matrix theory bypasses this problem by

specifying the momenta of the particles and remaining suffi- ciently vague about the region in which the reaction occurs. The important new concept in S-matrix theory is the shift of emphasis from objects to events; its basic concern is not with the particles, but with their reactions. Such a shift from objects to events is required both by quantum theory and by relativity theory. On the one hand, quantum theory has made it clear that a subatomic particle can only be understood as a mani- festation of the interaction between various processes of measurement. It is not an isolated object but rather an occur- rence, or event, which interconnects other events in a particular way. In the words of Heisenberg: [In modern physicsl, one has now divided the world not into different groups of objects but into different groups of connections . . . What can be distinguished is the kind of connection which is primarily important in a certain phenomenon . . . The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole.’ Relativity theory, on the other hand, has forced us to conceive of particles in terms of space-time: as four-dimensional patterns, as processes rather than objects. The S-matrix approach com- bines both of these viewpoints. Using the four-dimensional mathematical formalism of relativity theory, it describes all properties of hadrons in terms of reactions (or, more precisely, in terms of reaction probabilities), and thus establishes an intimate link between particles and processes. Each reaction involves particles which link it to other reactions and thus build up a whole network of processes. A neutron, for example, may participate in two successive reactions involving different particles; the first, say, a proton and a z-, the second a Z- and a K+.The neutron thus inter- connects these two reactions and integrates them into a larger process (see diagram (a) opposite). Each of the initial and final particles in this process will be involved in other reactions; the proton, for example, may emerge from an interaction between a

K+ and a A (see diagram (b) above) ; the K+ in the original reac- tion may be linked to a K-and a n0; then- to three more pions. The original neutron is thus seen to be part of a whole net- work of interactions; of a ‘tissue of events’,-all described by the S matrix. The interconnections in such a network cannot be determined with certainty, but are associated with probabilities. Each reaction occurs with some probability, which depends on the available energy and on the characteristics of the reaction, and these probabilities are given by the various elements of the S matrix. This approach allows one to define the structure of a hadron in a thoroughly dynamic way. The neutron in our network, for example, can be seen as a ‘bound state’ of the proton and

the n- from which it arises, and also as a bound state of the C- and the K+ into which it disintegrates. Either of these hadron combinations, and many others, may form a neutron, and consequently they can be said to be components of the neutron’s ‘structure’. The structure of a hadron, therefore, is not understood as a definite arrangement of constituent parts, but is given by all sets of particles which may interact with one another to form the hadron under consideration. Thus a proton exists potentially as a neutron-pion pair, a kaon-lambda pair, and so on. The proton also has the potential of disintegrating into any of these particle combinations if enough energy is available. The tendencies of a hadron to exist in various mani- festations are expressed by the probabilities for the corres- ponding reactions, all of which may be regarded as aspects of the hadron’s internal structure.

By defining the structure of a hadron as its tendency to undergo various reactions, S-matrix theory gives the concept of structure an essentially dynamic connotation. At the same time, this notion of structure is in perfect agreement with the experimental facts. Whenever hadrons are broken up in high-energy collision experiments, they disintegrate into combinations of other hadrons; thus they can be said to ‘consist’ potentially of these hadron combinations. Each of the particles emerging from such a collision will, in turn, undergo various reactions, thus building up a whole network of events which can be photographed in the bubble chamber. The picture on

page 267 and the ones in Chapter 15 are examples of such net- works of reactions. Although it is a matter of chance which network will arise in a particular experiment, each network is nevertheless structured according to definite rules. These rules are the conservation laws mentioned before; only those reactions can occur in which a well-defined set of quantum numbers is conserved. To begin with, the total energy has to remain constant in every reaction. This means that a certain combina- tion of particles can emerge from a reaction only if the energy carried into the reaction is high enough to provide the required masses. Furthermore, the emerging group of .particles must collectively carry exactly the same quantum numbers that have been carried into the reaction by the initial particles. For example, a proton and a X-, carrying a total electric charge of zero, may be dissolved in a collision and rearranged to emerge as a neutron plus a n”, but they cannot emerge as a neutron and a z+, as this pair would carry a total charge of +1. The hadron reactions, then, represent a flow of energy in which particles are created and dissolved, but the energy can only flow through certain ‘channels’ characterized by the quantum numbers conserved in the strong interactions. In S-matrix theory, the concept of a reaction channel is more fundamental than that of a particle. It is defined as a set of

quantum numbers which can be carried by various hadron combinations and often also by a single hadron. Which com- bination of hadrons flows through a particular channel is a matter of probability but depends, first of all, on the available energy. The diagram opposite, for example, shows an inter- action between a proton and a n- in which a neutron is formed as an intermediate state. Thus, the reaction channel is made up first by two hadrons, then by a single hadron, and finally by the initial hadron pair. The same channel can be made up, if more energy is available, by a A-K0 pair, a Z–K+ pair, and by various other combinations. The notion of reaction channels is particularly appropriate to deal with resonances, those extremely short-lived hadron states which are characteristic of all strong interactions. They are such ephemeral phenomena that physicists were first reluctant to classify them as particles, and today the clarification of their properties still constitutes one of the major tasks in experimental high-energy physics. Resonances are formed in hadron collisions and disintegrate almost as soon as they come into being. They cannot be seen in the bubble chamber, but can be detected due to a very special behaviour of reaction probabilities. The probability for two colliding hadrons to undergo a reaction-to interact with one another-depends on the energy involved in the collision. If the amount of this energy is modified, the probability will also change; it may increase or decrease with increasing energy, depending on the details of the reaction. At certain values of energy, however, the reaction probability is observed to increase sharply; a reaction is much more likely to occur at these values than at any other energy. This sharp increase is associated with the formation of a short-lived intermediate hadron with a mass corresponding to the energy at which the increase is observed. The reason why these short-lived hadron states are called resonances is related to an analogy that can be drawn to the well-known resonance phenomenon encountered in con- nection with vibrations. In the case of sound, for example, the air in a cavity will in general respond only weakly to a sound wave coming from outside, but will begin to ‘resonate’, or vibrate very strongly, when the sound wave reaches-a certain frequency called the resonance frequency. The channel of a

hadron reaction can be compared to such a resonant cavity, since the energy of the colliding hadrons is related to the frequency of the corresponding probability wave. When this energy, or frequency, reaches a certain value the channel begins to resonate; the vibrations of the probability wave suddenly become very strong and thus cause a sharp increase in the reaction probability. Most reaction channels have several resonance energies, each of them corresponding to the mass of an ephemeral intermediate hadron state which is formed when the energy of the colliding particles reaches the resonance value. In the framework of S-matrix theory, the problem of whether one should call the resonances ‘particles’ or not does not exist. All particles are seen as intermediate states in a network of reactions, and the fact that the resonances live for a much shorter period than other hadrons does not make them funda- mentally different. In fact, the word ‘resonance’ is a very appro- priate term. It applies both to the phenomenon in the reaction channel and to the hadron which is formed during that phenomenon, thus showing the intimate link between particles and reactions. A resonance is a particle, but not an object. It is much better described as an event, an occurrence or a happening. This description of hadrons in particle physics recalls to mind the words of D. T. Suzuki quoted above:* ‘Buddhists have conceived an object as an event and not as a thing or substance.’ What Buddhists have realized through their mystical experience of nature has now been rediscovered through the experiments and mathematical theories of modern science. In order to describe all hadrons as intermediate states in a network of reactions, one has to be able to account for the forces through which they mutually interact. These are the strong-interation forces which deflect, or ‘scatter’, colliding hadrons, dissolve and rearrange them in different patterns, and bind groups of them together to form intermediate bound states. In S-matrix theory, as in field theory, the interaction

forces are associated with particles, but the concept of virtual particles is not used. Instead, the relation between forces and particles is based on a special property of the S matrix known as ‘crossing’. To illustrate this property, consider the following diagram picturing the interaction between a proton and a II -

If this diagram is rotated through 90°, and if we keep the convention adopted previously,* that arrows pointing down-

wards indicate antiparticles, the new diagram will represent a reaction between an antiproton (j3 and a proton (p) which emerge from it as a pair of pions, the n+ being the antiparticle of the n- in the original reaction. The ‘crossing’ property of the S matrix, now, refers to the fact that both these processes are described by the same S-matrix element. This means that the two diagrams represent merely two different aspects, or ‘channels’, of the same reaction.** Particle physicists are used to switching from one channel to the other in their calculations, and instead of rotating the diagrams they just read them upwards or across from the

**ln fact, the diagram can be rbtated further, and individual lines can be ‘crossed’ to obtain different processes which are still described by the same 5matrix element. Each element represents altogether six different processes, but only the two mentioned above are relevant for our discussion of interaction forces.

left, and talk about the ‘direct channel’ and the ‘cross channel’. Thus the reaction in our example is read as p+7t+p+n- in the direct channel, and as p+p-+z-+z+ in the cross channel.

The connection between forces and particles is established through the intermediate states in the two channels. In the direct channel of our exampl.e, the proton and the 7c- can form an intermediate neutron, whereas the cross channel can be made up by an intermediate neutral pion (x0). This pion

the intermediate state in the cross channel-is interpreted as the manifestation of the force which acts in the direct channel binding the proton and the rc- together to form the neutron. Thus both channels are needed to associate the forces with particles; what appears as a force in one channel is manifest as an intermediate particle in the other. Although it is relatively easy to switch from one channel to the other mathematically, it is extremely difficult-if at all possible-to have an intuitive picture of the situation. This is because ‘crossing’ is an essentially relativistic concept arising in the context of the four-dimensional formalism of relativity theory, and thus very difficult to visualize. A similar situation occurs in field theory where the interaction forces are pictured as the exchange of virtual particles. In fact, the diagram showing the intermediate pion in the cross channel is reminiscent of the Feynman diagrams picturing these particle exchanges,* and one might say, loosely speaking, that the proton and the Z- interact ‘through the exchange of a fl. Such words are often used by physicists, but they do not fully describe the situation. An adequate description can only be given in terms of direct and cross channels, that is, in abstract concepts which are almost impossible to visualize. In spite of the different formalism, the general notion of an interaction force in S-matrix theory is quite similar to that in field theory. In both theories, the forces manifest themselves as particles whose mass determines the range of the force,** and in both theories they are recognized as intrinsic properties of the interacting particles; they reflect the structure of the particles’ virtual clouds in field theory, and are generated by bound states of the interacting particles in S-matrix theory. The parallel to the Eastern view of forces discussed previously*** applies thus to both theories. This view of interaction forces, furthermore, implies the important conclusion that all known particles must have some internal structure, because only then can they interact with the observer and thus be detected. In

• It should be remembered, however, that S-matrix diagrams are not space-time diagrams but symbolic representations of particle reactions. The switching from one channel to the other takes place in an abstract mathematical space.

the words of Geoffrey Chew, one of the principal architects of S-matrix theory, ‘A truly elementary particle-completely devoid of internal structure-could not be subject to any forces that would allow us to detect its existence. The mere knowledge of a particle’s existence, that is to say, implies that the particle possesses internal structureY2 A particular advantage of the S-matrix formalism is the fact that it is able to describe the ‘exchange’ of a whole family of hadrons. As mentioned in the previous chapter, all hadrons seem to fall into sequences whose members have identical properties except for their masses and spins. A formalism proposed originally by Tullio Regge makes it possible to treat each of these sequences as a single hadron existing in various excited states. In recent years, it has been possible to incorporate the Regge formalism into the S-matrix framework where it has been used very successfully for the description of hadron reactions. This has been one of the most important develop- ments in S-matrix theory and can be seen as a first step towards a dynamic explanation of particle patterns. The framework of the S matrix, then, is able to describe the structure of hadrons, the forces through which they mutually interact, and some of the patterns they form, in a thoroughly dynamic way in which each hadron is understood as an integral part of an inseparable network of reactions. The main challenge, and so far unsolved problem, in S-matrix theory is to use this dynamic description to account for the symmetries which give rise to the hadron patterns and conservation laws discussed in the previous chapter. In such a theory, the hadron symmetries would be reflected in the mathematical structure of the S matrix in such a way that it contains only elements which correspond to reactions allowed by the conservation laws. These laws would then no longer have the status of empirical regularities but would be a consequence of the S-matrix structure, and thus a consequence of the dynamic nature of hadrons. At present, physicists are trying to achieve this ambitious aim by postulating several general principles which restrict the mathematical possibilities of constructing S-matrix elements and thus give the S matrix a definite structure. So far, three of

these general principles have been established. The first is suggested by relativity theory and by our macroscopic ex- perience of space and time. It says that the reaction probabilities (and thus the S-matrix elements) must be independent of dis- placements of the experimental apparatus in space and time, independent of its orientation in space, and independent of the state of motion of the observer. As discussed in the previous chapter, the independence of a particle reaction with regard to changes of orientation and displacements in space and time implies the conservation of the total amount of rotation, momentum and energy involved in the reaction. These ‘symmetries’ are essential for our scientific work. If the results of an experiment changed according to where and when it was performed, science in its present form would be impossible. The last requirement, finally-that the experimental results must not depend on the observer’s motion-is the principle of relativity which is the basis of relativity theory.* The second general principle is suggested by quantum theory. It asserts that the outcome of a particular reaction can only be predicted in terms of probabilities and, furthermore, that the sum of the probabilities for all possible outcomes- including the case of no interaction between the particles- must be equal to one. In other words, we can be certain that the particles will either interact with one another, or not. This seemingly trivial statement turns out to be, in fact, a very powerful principle, known under the name of ‘unitarity’, which severely restricts the possibilities of constructing S-matrix elements. The third and final principle is related to our notions of cause and effect and is known as the principle of causality. It states that energy and momentum are transferred over spatial distances only. by particles, and that this transfer occurs in such a way that a particle can be created in one reaction and destroyed in another only if the latter reaction occurs after the former. The mathematical formulation of the causality principle implies that the S matrix depends in a smooth way on the energies and momenta of the particles involved in a reaction, except for those values at which the creation of new

particles becomes possible. At those values, the mathematical structure of the S matrix changes abruptly; it encounters what mathematicians call a ‘singularity’. Each reaction channel contains several of these singularities, that is, there are several values of energy and momentum in each channel at which new particles can be created. The ‘resonance energies’ men- tioned before are examples of such values. The fact that the S matrix exhibits singularities is a con- sequence of the causality principle, but the location of the singularities is not determined by it. The values of energy and momentum at which particles can be created are different for different reaction channels and depend on the masses and other properties of the created particles. The locations of the singularities thus reflect the properties of these particles, and since all hadrons can be created in particle reactions, the singularities of the S matrix mirror all the patterns and sym- metries of hadrons. The central aim of S-matrix theory is, therefore, to derive the singularity structure of the S matrix from the general principles. Up to now, it has not been possible to construct a mathematical model which satisfies all three principles, and it may well be that they are sufficient to determine all the properties of the S matrix-and thus all the properties of hadrons-uniquely.* If this turns out to be the case, the philosophical implications of such a theory would be very profound. All three of the general principles are related to our methods of observation and measurement, that is, to the scientific framework. If they are sufficient to determine the structure of hadrons, this would mean that ‘the basic structures of the physical world are determined, ultimately, by the way in which we look at this world. Any fundamental change in our observational methods would imply a modification of the general principles which would lead to a different structure of the S matrix, and would thus imply a different structure of hadrons.

Such a theory of subatomic particles reflects the impossibility of separating the scientific observer from the observed pheno-

*This conjecture, known as the ‘bootstrap’ hypothesis, will be discussed in more detail in the subsequent chapter.

mena, which has already been discussed in connection with quantum theory,* in its most extreme form. It implies, ultimately, that the structures and phenomena we observe in nature are nothing but creations of our measuring and categorizing mind. That this is so is one of the fundamental tenets of Eastern philosophy. The Eastern mystics tell us again and again that all things and events we perceive are creations of the mind, arising from a particular state of consciousness and dissolving again if this state is transcended. Hinduism holds that all shapes and structures around us are created by a mind under the spell of maya, and it regards our tendency to attach deep significance to them as the basic human illusion. Buddhists call this illusion avidya, or ignorance, and see it as the state of a ‘defiled’ mind. In the words of Ashvaghosha, When the oneness of the totality of things is not recognised, then ignorance as well as particularisation arises, and all phases of the defiled mind are thus developed . . . All phenomena in the world are nothing but the illusory manifestation of the mind and have no reality on their own.3 This is also the recurring theme of the Buddhist Yogacara school which holds that all forms we perceive are ‘mind only’; projections, or ‘shadows’, of the mind: Out of mind spring innumerable things, conditioned by discrimination . . . These things people accept as an external world . . . What appears to be external does not exist in reality; it is indeed mind that is seen as multiplicity; the body, property, and above-all these, I say, are nothing but mind.4 In particle physics, the derivation of the hadron patterns from the general principles of S-matrix theory is a long and arduous task, and so far only a few small steps have been taken towards achieving it. Furthermore, the theory in its present form cannot be applied to the electromagnetic interactions that

give rise to the atomic structures and dominate the world of chemistry and biology. Nevertheless, the possibility that the hadron patterns will some day be derived from the general principles, and thus be seen to depend on our scientific framework, must be taken seriously. It is an exciting con- jecture that this may be a general feature of particle physics which will also appear in future theories of electromagnetic, weak, and gravitational interactions. If this turns out to be true, modern physics will have come a long way towards agreeing with the Eastern sages that the structures of the physical world are maya, or ‘mind only’. S-matrix theory comes very close to Eastern thought not only in its ultimate conclusion, but also in its general view of matter. It describes the world of subatomic particles as a dynamic network of events and emphasizes change and trans- formation rather than fundamental structures or entities. In the East, such an emphasis is particularly strong in Buddhist thought where all things are seen as dynamic, impermanent and illusory. Thus S. Radhakrishnan writes: How do we come to think of things, rather than of pro- cesses in this absolute flux? By shutting our eyes to the successive events. It is an artificial attitude that makes sections in the stream of change, and calls them things . . . When we shall know the truth of things, we shall realise how absurd it is for us to worship isolated products of the incessant series of transformations as though they were eternal and real. Life is no thing or state of a thing, bu It a continuous movement or change.5 Both the modern physicist and the Eastern mystic thave realized that all phenomena in this world of change and transformation are dynamically interrelated. Hindus Buddhists see this interrelation as a cosmic law, the law of karma, but they are generally not concerned with any specific patterns in the universal network of events. Chinese philosophy, on the other hand, which also emphasizes movement and change, has developed the notion of dynamic patterns which are continually formed and dissolved again in the cosmic flow of the Tao. In the I Ching, or Book of Changes, these patterns have been elaborated into a system of archetypal symbols, the so-called hexagrams.

The basic ordering principle of the patterns in the /Ching* is the interplay of the polar opposites yin and yang. The yang , the yin by a broken line is represented by a solid line (I I-1, and the whole system of hexagrams is built up naturally from these two lines. By combining them in pairs, four configurations are obtained,

and by adding a third line to each of these, eight ‘trigrams’ are generated : In ancient China, the trigrams were considered to represent all possible cosmic and human situations. They were given names reflecting their basic characteristics-such as The Creative’, The Receptive’, ‘The Arousing’, etc.-and they were associated with many images taken from nature and from social life. They represented, for example, heaven, earth, thunder, water, etc., as well as a family consisting of father, mother, three sons and three daughters. They were, furthermore, associated with the cardinal points and with the seasons of the year, and were often arranged as follows:

In this arrangement, the eight trigrams are grouped around a circle in the ‘natural order’ in which they were generated, starting from the top (where the Chinese always place the south) and placing the first four trigrams on the left side of the circle, the second four on the right side. This arrangement shows a high degree of symmetry, opposite trigrams having yin and yang lines interchanged.

In order to increase the number of possible combinations further, the eight trigrams were combined in pairs by placing one above the other. In this way, sixty-four hexagrams were obtained, each consisting of six solid or broken lines. The hexagrams were arranged in several regular patterns, among which the two illustrated on the opposite page were the most common; a square of eight times eight hexagrams, and a circular sequence showing the same symmetry as the circular arrangement of the trigrams. The sixty-four hexagrams are the cosmic archetypes on which the use of the I Ching as an oracle book is based. For the interpretation of any hexagram, the various meanings

of its two trigrams have to be taken into account. For example, when the trigram The Arousing’ is situated above the trigram The Receptive’ the hexagram is interpreted as movement meeting with devotion and thus inspiring enthusiasm, which is the name given to it. the Arousing the Receptive Enthusiasm The hexagram for Progress, to give another example, represents ‘The Clinging’ above ‘The Receptive’ which is interpreted as the sun rising over the earth and thus as a symbol of rapid, easy progress. the Clinging ~~ the Receptive Progress In the I Ching, the trigrams and hexagrams represent the patterns of the Tao which are generated by the dynamic inter- play of the yin and the yang, and are reflected in all cosmic and human situations. These situations, therefore, are not seen as static, but rather as stages in a continuous flow and change. This is the basic idea of the Book of Changes which is expressed in its very title. All things and situations in the world are subject to change and transformation, and so are their images, the trigrams and hexagrams. They are in a state of continual transition; one changing into another, solid lines pushing outwards and breaking in two, broken lines pushing inwards and growing together. Because of its notion of dynamic patterns, generated by change and transformation, the I Ching is perhaps the closest analogy to S-matrix theory in Eastern thought. In both systems, the emphasis is on processes rather than objects. In S-matrix theory, these processes are the particle reactions that give rise to all the phenomena in the world of hadrons. In the I Ching, the basic processes are called ‘the changes’ and are seen as essential for an understanding of all natural phenomena:

The changes are what has enabled the holy sages to reach all depths and to grasp the seeds of all things6 These changes are not regarded as fundamental laws imposed on the physical world, but rather-in the words of Hellmut Wilhelm-as ‘an inner tendency according to which develop- ment takes place naturally and spontaneously’.7 The same can be said of the ‘changes’ in the particle world. They, too, reflect the inner tendencies of the particles which are expressed, in S-matrix theory, in terms of reaction probabilities. The changes in the world of hadrons give rise to structures and symmetric patterns which are represented symbolically by the reaction channels. Neither the structures nor the symmetries are regarded as fundamental features of the hadron world, but are seen as consequences of the particles’ dynamic nature, that is, of their tendencies for change and transformation. In the I Ching, too, the changes give rise to structures-the trigrams and hexagrams. Like the channels of particle reactions, these are symbolic representations of patterns of change. As the energy flows through the reaction channels, the ‘changes’ flow through the lines of the hexagrams: Alteration, movement without rest, Flowing through the six empty places, Rising and sinking without fixed law, It is only change that is at work here! In the Chinese view, all things and phenomena around us arise out of the patterns of change and are represented by the various lines of the trigrams and hexagrams. Thus the things in the physical world are not seen as static, independent objects, but merely as transitional stages in the cosmic process which is the Tao: The Tao has changes and movements. Therefore the lines are called changing lines. The lines have gradations, there- fore they represent things.9 As in the world of particles, the structures generated by the

changes can be arranged in various symmetric patterns, such as the octagonal pattern formed by the eight trigrams, in which opposite trigrams have yin and yang lines interchanged. This pattern is even vaguely similar to the meson octet dis- cussed in the previous chapter, in which particles and anti- particles occupy opposite places. The important point, how: ever, is not this accidental similarity, but the fact that both modern physics and ancient Chinese thought consider change and transformation as the primary aspect of nature, and see the structures and symmetries generated by the changes as secondary. As he explains in the introduction to his translation’ of the I Ching, Richard Wilhelm regards this idea as the funda- mental concept of the Book of Changes:

The eight trigrams . . . were held to be in a state of continual transition, one changing into another, just as transition from one phenomenon to another is continually taking place in the physical world. Here we have the fundamental concept of the Book of Changes. The eight trigrams are symbols standing for changing transitional states; they are images that are constantly undergoing change. Attention centers not on things in their state of being-as is chiefly the case in the Occident-but upon their movements in change. The eight trigrams therefore are not representa- tions of things as such but of their tendencies in move- ment.lO In modern physics, we have come to see the ‘things’ of the subatomic world in very much the same way, laying stress upon movement, change and transformation and regarding the particles as transient stages in an ongoing cosmic process.