The Phenomenon of Waves

The exploration of the subatomic world in the 20th century has revealed the intrinsically dynamic nature of matter.

It has shown that the constituents of atoms, the subatomic particles, are dynamic patterns which do not exist as isolated entities, but as integral parts of an inseparable network of interactions.

These interactions involve a ceaseless flow of energy manifesting itself as the exchange of particles; a dynamic interplay in which particles are created and destroyed without end in a continual variation of energy patterns.

The particle interactions give rise to the stable structures which build up the material world, which again do not remain static, but oscillate in rhythmic movements. The whole universe is thus engaged in endless motion and activity; in a continual cosmic dance of energy.

This dance involves an enormous variety of patterns but, surprisingly, they fall into a few distinct categories. The study of the subatomic particles and their interactions thus reveals a great deal of order.

All atoms, and consequently all forms of matter in our environment, are composed of only three massive particles: the proton, the neutron and the electron. A fourth particle, the photon, is massless and represents the unit of electromagnetic radiation.

The proton, the electron and the photon are all stable particles, which means they live for ever unless they become involved in a collision process where they can be annihilated. The neutron, on the other hand, can dis- integrate spontaneously.

This disintegration is called ‘beta decay’ and is the basic process of a certain type of radioactivity. It involves the transformation of the neutron into a proton, accompanied by the creation of an electron and a new type of massless particle, called the neutrino.

Like the proton and the electron, the neutrino is also stable. It is commonly denoted by the Greek letter v (‘nu’), and the process of beta decay is symbolically written as n+p+e-+tr

The transformation of neutrons into protons in the atoms of a radioactive substance entails a transformation of these atoms into atoms of an entirely different kind. The electrons which are created in the process are emitted as a powerful radiation which is widely used in biology, medicine and industry.

The neutrinos, on the other hand, although emitted in equal number, are very difficult to detect because they have neither mass nor electric charge.

There is an antiparticle for every particle, with equal mass but opposite charge. The photon is its own antiparticle; the antiparticle of the electron is called the positron; then there is an antiproton, an antineutron, and an antineutrino.

The massless particle created in beta decay is not, in fact, the neutrino but the antineutrino (denoted by VI, so that the process is correctly written as

n+p+e-+v’

The particles mentioned so far represent only a fraction of the subatomic particles known today. All the others are unstable and decay after a very short time into other particles, some of which may decay again until a combination of stable particles remains. The study of unstable particles is very expensive as they have to be newly created in collision processes for each investigation, which involves huge particle accelerators, bubble chambers, and other extremely sophisticated devices for particle detection.

The table shows 13 different types of particles, many of which appear in different ‘charge states’. The pions, for example, can have positive charge (n+), negative charge (X-J, or be electrically neutral (16’). There are two kinds of neutrinos, one interacting only with electrons (v,), the other only with muons (~4. The antiparticles are listed as well, three of the particles (y, no, 7) being their own antiparticles.

Particles are arranged in the order of increasing mass: the photon and the neutrinos are massless; the electron is the lightest massive particle; the muons, pions, and kaons are a few hundred times heavier than the electron; the other particles are one to three thousand times heavier.

Most unstable particles live only for an extremely short time, compared with the human time scale; less than a millionth of a second. However, their lifetime has to be regarded in relation to their size which is also diminutive. When looked at in this way, it can be seen that many of them live for a relatively long period, and that one millionth of a second is, in fact, an enormous time span in the particle world. A human being can move across a distance a few times his or her size in a second. For a particle, the equivalent time span would therefore be the time it needs to travel over a distance a few times its own size; a unit of time which one could call a ‘particle second’.*

To cross a medium-sized atomic nucleus, a particle needs about ten of these ‘particle seconds’ if it travels at a speed close to the speed of light, as particles do in the collision experiments. Among the great number of unstable particles, there are about two dozen which can travel across at least several atoms before they decay. This is a distance of some 100,000 times their size and corresponds to a time of a few hundred ‘particle hours’. These particles are listed in the table overleaf, together with the stable particles already mentioned.

Most of the unstable particles in the table will; in fact, cover a whole centimetre, or even several centimetres, before they decay, and those which live longest, a millionth of a second, can travel several hundred metres before decaying; an enormous length compared with their size.

All the other particles known so far belong to a category called ‘resonances’ which will be discussed in more detail in the subsequent chapter. They live for a considerably shorter time, decaying after a few ‘particle seconds’, so that they can never travel farther than a few times their size. This means they cannot be seen in the bubble chamber; their existence can only be inferred indirectlv. The tracks seen in bubble chamber pictures can only be traced by particles listed in the table.

All these particles can be created and annihilated in collision processes; each one can also be exchanged as a virtual particle and thus contribute to the interaction between other particles.

This would seem to result in a vast number of different particle interactions, but fortunately, although we do not yet know why, all these interactions seem to fall into four categories with markedly different interaction strengths:

The strong interactions The electromagnetic interactions The weak interactions The gravitational interactions

Among them, the electromagnetic and gravitational interactions are the most familiar, because they are experienced in the large-scale world. The gravitational interaction acts between all particles, but is so weak it cannot be detected experimentally.

In the macroscopic world, however, the huge number of particles making up massive bodies combine their gravitational interaction to produce the force of gravity which is the dominating force in the universe at large. Electromagnetic interactions take place between all charged particles.

They are responsible for the chemical processes, and the formation of all atomic and molecular structures. The strong Interactions hold the protons and neutrons together in the atomic nucleus.

They constitute the nuclear force, by far the strongest of all forces in nature. Electrons, for example, are bound to the atomic nuclei by the electromagnetic force with energies of about ten units (called electron volts), whereas the nuclear force holds protons and neutrons together with energies of about ten million units!

The nucleons are not the only particles interacting through the strong interactions. In fact, the overwhelming majority are strongly interacting particles. Of all the particles known today, only five (and their antiparticles) do not participate in the strong interactions.

These are the photon and the four ‘leptons’ listed in the top part of the table. Thus all the particles fall into two broad groups: leptons and ‘hadrons’, or strongly interacting particles. The hadrons are further divided into ‘mesons’ and ‘baryons’ which differ in various ways, one of them being that all baryons have distinct antiparticles, whereas a meson can be its own antiparticle.

The leptons are involved in the fourth type of interactions, the weak interactions. These are so weak, and have such a short range, that they cannot hold anything together, whereas the other three give rise to binding forces-the strong inter- actions holding together the atomic nuclei, the electromagnetic interactions the atoms and molecules, and the gravitational interactions the planets, stars and galaxies. The weak interactions manifest themselves only in certain kinds of particle collisions and in particle decays, such as the beta decay mentioned earlier.

All interactions between hadrons are mediated by the exchange of other hadrons. It is these exchanges of massive particles that cause the strong interactions to have such a short range.* They extend only over a distance of a few particle sizes and can therefore never build up a macroscopic force.

Strong interactions are thus not experienced in the everyday world. The electromagnetic interactions, on the other hand, are mediated by the exchange of massless photons and thus their range is indefinitely long,* which is why the electric and magnetic forces are encountered in the large-scale world.

The gravitational interactions, too, are believed to be mediated by a massless particle, called the ‘graviton’, but- they are so weak that it has not yet been possible to observe the graviton, although there is no serious reason to doubt its existence. The weak interactions, finally, have an extremely short range -much shorter than that of the strong interactions-and are therefore assumed to be produced by the exchange of a very heavy particle, called the ‘W-meson’. This hypothetical particle is believed to play a role analogous to that of the photon in the electromagnetic interactions, except for its large mass. This analogy is, in fact, the basis of the most recent developments in field theory in which the formulation of a unified theory of electromagnetic and weak interactions is attempted.

In many of the collision processes of high-energy physics, the strong, electromagnetic and weak interactions combine to produce an intricate sequence of events. The initial colliding particles are often destroyed, and several new particles are created which either undergo further collisions or decay, sometimes in several steps, into the stable particles which finally remain. The picture opposite shows a bubble-chamber photograph* of such a sequence of creation and destruction.

It is an impressive illustration of the mutability of matter at the particle level, showing a cascade of energy in which various patterns, or particles, are formed and dissolved.

Opposite and above

An intricate sequence of particle collisions and decays: a negative pion (a-1, coming in from the left, collides with a proton-i.e. with the nucleus of a hydrogen atom-‘sitting’ in the bubble chamber; both particles are annihilated. and a neutron (n) plus two kaons (K- and K+) are created; the neutron flies off without leaving a track; the K- collides with another proton in the chamber, the two particles annihilating each other and creating a lambda (AI and a photon (7). Neither of these two neutral particles is visible, but the A decays after a very short time into a proton (p) and a K, both of which produce tracks. The short distance between the creation of the A and its decay can be made out very clearly in the photograph. The K+, finally, which was created in the initial collision, travels for a while before decaying into three pions. *Notice that only the charged particles produce tracks in the bubble chamber; these are bent by magnetic fields in a clockwise direction for positively charged particles, and anti-clockwise for negative particles.'

In these sequences, the creation of matter is particularly striking when a massless, but highly energetic photon, which cannot be seen in the bubble chamber, suddenly explodes into a pair of charged particles-an electron and a positron- sweeping out in divergent curves. Here is a beautiful example of a process involving two of these pair creations.

The higher the initial energy in these collision processes, the more particles can be created. The following photograph shows the creation of eight pions in a collision between an anti- proton and a proton, and the next one is an example of an extreme case; the creation of sixteen particles in a single collision between a pion and a proton.

All these collisions have been produced artificially in the laboratory by the use of huge machines in which the particles are accelerated to the required energies. In most natural phenomena here on Earth, the energies are not high enough for massive particles to be created. In outer space, however, the situation is entirely different. Subatomic particles occur in large numbers in the centre of the stars where collision pro- cesses similar to the ones studied in the accelerator laboratories take place naturally all the time. In some stars, these processes produce an extremely strong electromagnetic radiation-in the form of radio waves, light waves or X-rays-which is the astronomer’s primary source of information about the universe. Interstellar space, as well as the space between the galaxies, is thus filled with electromagnetic radiation of various fre- quencies, i.e. with photons of various energies. These, however, are not the only particles travelling through the cosmos. ‘Cosmic radiation’ contains not only photons but also massive particles of all kinds whose origin is still a mystery. Most of them are protons, some of which can have extremely high energies; much higher than those achieved in the most powerful particle accelerators. When these highly energetic ‘cosmic rays’ hit the atmosphere of the Earth, they collide with the nuclei of the atmosphere’s air molecules and produce a great variety of secondary particles which either decay or undergo further collisions, thus creating more particles which collide and decay again, and so on, until the last of them reach the Earth. In this way, a single proton plunging into the Earth’s atmosphere can give rise to a whole cascade of events in which its original kinetic energy is trans- formed’ into a shower of various particles, and is gradually absorbed as they penetrate the air undergoing multiple collisions. The same phenomenon that can be observed in the collision experiments of high-energy physics thus occurs naturally but more intensely all the time in the Earth’s atmo- sphere; a continual flow of energy going through a great variety of particle patterns in a rhythmic dance of creation and destruc- tion.Overleaf is a magnificent picture of this energy dance which was taken by accident when an unexpected cosmic-ray shower hit a bubble chamber at the European research centre CERN during an experiment

The processes of creation and destruction occurring in the world of particles are not only those which can be seen in the bubble chamber photographs. They also include the creation and destruction of virtual particles which are ex- changed in particle interactions and do not live long enough to be observed. Take, for example, the creation of two pions in a collision between a proton and an antiproton. A space-time diagram of this event would look like this (remember that the direction of time in these diagrams is from the bottom to the top!):

It shows the world lines of the proton (p) and the antiproton Q.3 which collide at one point in space and time, annihilating each other and creating the two pions (z+ and ~3. This diagram, however, does not give the full picture. The interaction between the proton and the antiproton can be pictured as the exchange of a virtual neutron, as the diagram below shows.

Similarly, the process shown in the following photograph where four pions are created in a proton-antiproton collision, can be pictured as a more complicated exchange process involving the creation and destruction of three virtual particles; two neutrons and one proton.

These examples illustrate how the lines in the bubble- chamber photographs give only a rough picture of the particle interactions. The actual processes involve much more com- plicated networks of particle exchanges. The situation becomes, in fact, infinitely more complex when we remember that each of the particles involved in the interactions emits and reabsorbs virtual particles incessantly. A proton, for example, will emit and reabsorb a neutral pion every now and then; at other times, it may emit a 71+ and turn into a neutron which will absorb the ;n+ after a short while and transform itself back into the proton. In the Feynman diagrams, the proton lines will in those cases have to be replaced by the following diagrams:

In these virtual processes, the initial particle may disappear completely for a short time, as in diagram (b). A negative pion, to take another example, may create a neutron (n) plus an antiproton (p) which then annihilate one another to re-establish the original pion:

It is important to realize that all these processes follow the laws of quantum theory, and thus are tendencies, or probabi- lities, rather than actualities. Every proton exists potentially, i.e. with a certain probability, as a proton plus a 710, as a neutron plus a z+, and in many other ways. The examples shown above are only the simplest virtual processes. Much more complicated patterns arise when the virtual particles create other virtual particles, thus generating a whole network of virtual inter- actions.* In his book The World of Elementary Particles, Kenneth Ford has constructed a complicated example of such a network involving the creation and destruction of eleven virtual particles, and he comments on it: ‘TThe diagram] pictures one such sequence of events, quite horrendous looking, but perfectly real. Every proton occasionally goes through exactly this dance of creation and destruction.”

‘It should be noted that the possibilities are not completely arbitrary, but are restricted by several general laws to be discussed in the subsequent chapter.

Ford is not the only physicist to have used phrases like ‘dance of creation and destruction’ and ‘energy dance’. The ideas of rhythm and dance naturally come into mind when

one tries to imagine the flow of energy going through the patterns that make up the particle world. Modern physics has shown us that movement and rhythm are essential properties of matter; that all matter, whether here on Earth or in outer space, is involved in a continual cosmic dance. The Eastern mystics have a dynamic view of the universe similar to that of modern physics, and consequently it is not surprising that they, too, have used the image of the dance to convey their intuition of nature. A beautiful example of such an image of rhythm and dance is given by Alexandra David- Neel in her Tibetan journey, where she describes how she met a Lama who referred to himself as a ‘master of sound’ and gave her the following account of his view of matter:

All things . . . are aggregations of atoms that dance and by their movements produce sounds. When the rhythm of the dance changes, the sound it produces also changes . . . Each atom perpetually sings its song, and the sound, at every moment, creates dense and subtle forms.2 The similarity of this view to that of modern physics becomes particularly striking when we remember that sound is a wave with a certain frequency which changes when the sound does, and that particles, the modern equivalent of the old concept of atoms, are also waves with frequencies proportional to their energies. According to field theory, each particle does indeed ‘perpetually sing its song’, producing rhythmic patterns of energy (the virtual particles) in ‘dense and subtle forms’. The metaphor of the cosmic dance has found its most pro- found and beautiful expression in Hinduism in the image of the dancing god Shiva. Among his many incarnations, Shiva, one of the oldest and most popular Indian gods,* appears as the King of Dancers. According to Hindu belief, all life is part of a great rhythmic process of creation and destruction, of death and rebirth, and Shiva’s dance symbolizes this eternal life-death rhythm which goes on in endless cycles. In the words of Ananda Coomaraswamy, In the night of B&man, Nature is inert, and cannot dance till Shiva wills it: He rises from His rapture, and dancing sends through inert matter pulsing waves of awakening sound, and lo! matter also dances, appearing as a glory round about Him. Dancing, He sustains its manifold phenomena. In the fullness of time, still dancing, He destroys all forms and names by fire and gives new rest. This is poetry, but none the less science.3 The Dance of Shiva symbolizes not only the cosmic cycles of creation and destruction, but also the daily rhythm of birth and death which is seen in Indian mysticism as the basis of all existence. At the same time, Shiva reminds us that the manifold forms in the world are maya-not fundamental, but illusory

and ever-changing-as he keeps creating and dissolving them in the ceaseless flow of his dance. As Heinrich Zimmer has put it: His gestures wild and full of grace, precipitate the cosmic illusion; his flying arms and legs and the swaying of his torso produce-indeed, they are-the continuous cre- ation-destruction of the universe, death exactly balancing birth, annihilation the end of every coming-forth.4 Indian artists of the tenth and twelfth centuries have repre- sented Shiva’s cosmic dance in magnificent bronze sculptures

of dancing figures with four arms whose superbly balanced and yet dynamic gestures express the rhythm and unity of Life. The various meanings of the dance are conveyed by the details of these figures in a complex pictorial allegory. The upper right hand of the god holds a drum to symbolize the primal sound of creation, the upper ieft bears a tongue of flame, the element of destruction. The balance of the two hands represents the dynamic balance of creation and destruction in the world, accentuated further by the Dancer’s calm and detached face in the centre of the two hands, in which the polarity of creation and destruction is dissolved and transcended. The second right hand is raised in the sign of ‘do not fear’, symbolizing main- tainance, protection and peace, while the remaining left hand points down to the uplifted foot which symbolizes release from the spell of maya. The god is pictured as dancing on the body of a demon, the symbol of man’s ignorance which has to be conquered before liberation can be attained. Shiva’s dance-in the words of Coomaraswamy- is ‘the clearest image of the activity of Cod which any art or religion can boast ~f’.~ As the god is a personification of Brahman, his activity is that of Brahman’s myriad manifestations in the world. The dance of Shiva is the dancing universe; the ceaseless flow of energy going through an infinite variety of patterns that melt into one another. Modern physics has shown that the rhythm of creation and destruction is not only manifest in the turn of the seasons and in the birth and death of all living creatures, but is also the very essence of inorganic matter. According to quantum field theory, all interactions between the constituents of matter take place through the emission and absorption of virtual particles. More than that, the dance of creation and destruction is the basis of the very existence of matter, since all material particles ‘self-interact’ by emitting and reabsorbing virtual particles. Modern physics has thus revealed that every sub- atomic particle not only performs an energy dance, but also is an energy dance; a pulsating process of creation and destruction. The patterns of this dance are an essential aspect of each particle’s nature and determine many of its properties. For example, the energy involved in the emission and absorption

of virtual particles is equivalent to a certain amount of mass which contributes to the mass of the self-interacting particle. Different particles develop different patterns in their dance, requiring different amounts of energy, and hence have different masses. Virtual particles, finally, are not only an essential part of all particle interactions and of most of the particles’ pro- perties, but are also created and destroyed by the vacuum. Thus, not only matter, but also the void, participates in the cosmic dance, creating and destroying energy patterns without end. For the modern physicists, then, Shiva’s dance is the dance of subatomic matter. As in Hindu mythology, it is a continual dance of creation and destruction involving the whole cosmos; the basis of all existence and of all natural phenomena. Hundreds of years ago, Indian artists created visual images of dancing Shivas in a beautiful series of bronzes. In our time, physicists have used the most advanced technology to portray the patterns of the cosmic dance. The bubble-chamber photographs of interacting particles, which bear testimony to the continual rhythm of creation and destruction in the universe, are visual images of the dance of Shiva equalling those of the Indian artists in beauty and profound significance. The metaphor of the cosmic dance thus unifies ancient mythology, religious art, and modern physics. It is indeed, as Coomaraswamy has said, ‘poetry, but none the less science’.