Relativity and Dirac

Relativity theory has had a profound influence on our picture of matter by forcing us to modify our concept of a particle in an essential way. In classical physics, the mass of an object had always been associated with an indestructible material substance, with some ‘stuff’ of which all things were thought to be made. Relativity theory showed that mass has nothing to do with any substance, but is a form of energy. Energy, however, is a dynamic quantity associated with activity, or with processes. The fact that the mass of a particle is equivalent to a certain amount of energy means that the particle can no longer be seen as a static object, but has to be conceived as a dynamic pattern, a process involving the energy which manifests itself as the particle’s mass.

This new view of particles was initiated by Dirac when he formulated a relativistic equation describing the behaviour of electrons. Dirac’s theory was not only extremely successful in accounting for the fine details of atomic structure, but also revealed a fundamental symmetry between matter and anti- matter.

It predicted the existence of an anti-electron with the same mass as the electron but with an opposite charge. This positively charged particle, now called the positron, was indeed discovered two years after Dirac had predicted it. The symmetry between matter and antimatter implies that for every particle there exists an antiparticle with equal mass and opposite charge. Pairs of particles and antiparticles can be created if enough energy is available and can be made to turn into pure energy in the reverse process of annihilation. These processes of particle creation and annihilation had been predicted from Dirac’s theory before they were actually discovered in nature, and since then they have been observed millions of times.

The creation of material particles from pure energy is certainly the most spectacular effect of relativity theory, and it can only be understood in terms of the view of particles out- lined above. Before relativistic particle physics, the constituents of matter had always been considered as being either elementary units which were indestructible and unchangeable, or as composite objects which could be broken up into their constituent parts; and the basic question was whether one could divide rnatter again and again, or whether one would finally arrive at some smallest indivisible units. After Dirac’s discovery, the whole question of the division of matter appeared in a new light. When two particles collide with high energies, they generally break into pieces, but these pieces are not smaller than the original particles.

They are again particles of the same kind and are created out of the energy of motion (‘kinetic energy’) involved in the collision process. The whole problem of dividing matter is thus resolved in an unexpected sense. The only way to divide subatomic particles further is to bang them together in collision processes involving high energies. This way, we can divide matter again and again, but we never obtain smaller pieces because we just create particles out of the energy involved in the process. The subatomic particles are thus destructible and indestructible at the same time. This state of affairs is bound to remain paradoxical as long as we adopt the static view of composite ‘objects’ consisting of ‘basic building blocks’. Only when the dynamic, relativistic view is adopted does the paradox disappear. The particles are then seen as dynamic patterns, or processes, which involve a certain amount of energy appearing to us as their mass. In a collision process, the energy of the two colliding particles is redistributed to form a new pattern, and if it has been increased by a sufficient amount of kinetic energy, this new pattern may involve additional particles.

High-energy collisions of subatomic particles are the principal method used by physicists to study the properties of these particles, and particle physics is therefore also called ‘high-energy physics’. The kinetic energies required for the collision experiments are achieved by means of huge particle accelerators: enormous circular machines with circumferences of several miles in which protons are accelerated to velocities near the speed of light and are then made to collide with other protons or with neutrons. It is impressive that machines of

*See photograph on pages 14-15, showing an aerial view of the accelerator at Fermilab, near Batavia, Illinois, which has a circumference of four miles (photograph taken in 1971 while the laboratory was still under construction).

that size are needed to study the world of the infinitely small. They are the supermicroscopes of our time. Most of the particles created in these collisions live for only an extremely short time-much less than a millionth of a second-after which they disintegrate again into protons, neutrons and electrons.

In spite of their exceedingly short lifetime, these particles can not only be detected and their properties measured but are actually made to leave tracks which can be photographed! These particle tracks are pro- duced in so-called bubble chambers in a manner similar to the way a jet plane makes a trail in the sky. The actual particles are many orders of magnitude smaller than the bubbles making up the tracks, but from the thickness and curvature of a track physicists can identify the particle that caused it. The picture overleaf shows such bubble chamber tracks.

The points from which several tracks emanate are points of particle collisions, and the curves are caused by magnetic fields which the experimenters use to identify the particles. The collisions of particles are our main experimental method to study their properties and interactions, and the beautiful lines, spirals and curves traced by the particles in bubble chambers are thus of paramount importance for modern physics.

The high-energy scattering experiments of the past decades have shown us the dynamic and ever-changing nature of the particle world in the most striking way. Matter has appeared in these experiments as completely mutable. All particles can be transmuted into other particles; they can be created from energy and can vanish into energy. In this world, classical concepts like ‘elementary particle’, ‘material substance’ or ‘isolated object’, have lost their meaning; the whole universe appears as a dynamic web of inseparable energy patterns.

So far, we have not yet found a complete theory to describe this world of subatomic particles, but we do have several theoretical models which describe certain aspects of it very well.

None of these models is free from mathematical difficulties, and they all contradict each other in certain ways, but all of them reflect the basic unity and the intrinsically dynamic character of matter. They show that the properties of a particle can only be understood in terms of its activity-of its interaction with the surrounding environment-and that the particle, therefore, cannot be seen as an isolated entity, but has to be understood as an integrated part of the whole.

Relativity theory has not only affected our conception of particles in a drastic way, but also our picture of the forces between these particles. In a relativistic description of particle interactions, the forces between the particles-that is their mutual attraction or repulsion-are pictured as the exchange of other particles.

This concept is very difficult to visualize. It is a consequence of the four dimensional space-time character of the subatomic world and neither our intuition nor our language can deal with this image very well. Yet it is crucial for an under- standing of subatomic phenomena. It links the forces between constituents of matter to the properties of other constituents of matter, and thus unifies the two concepts, force and matter, which had seemed to be so fundamentally different ever since the Greek atomists. Both force and matter are now seen to have their common origin in the dynamic patterns which we call particles.

The fact that particles interact through forces which manifest themselves as the exchange of other particles is yet another reason why the subatomic world cannot be decomposed into constituent parts. From the macroscopic level down to the

nuclear level, the forces which hold things together are relatively weak and it is a good approximation to say that things consist of constituent parts. Thus a grain of salt can be said to consist of salt molecules, the salt molecules of two kinds of atoms, those atoms to consist of nuclei and electrons, and the nuclei of protons and neutrons. At the particle level, however, it is no longer possible to see things that way.

In recent years, there has been an increasing amount of evidence that the protons and neutrons, too, are composite objects; but the forces holding them together are so strong or-what amounts to the same-the velocities acquired by the components are so high, that the relativistic picture has to be applied, where the forces are also particles.

Thus the distinction between the constituent particles and the particles making up the binding forces becomes blurred and the approximation of an object consisting of constituent parts breaks down.

The particle world cannot be decomposed into elementary components.

In modern physics, the universe is thus experienced as a dynamic, inseparable whole which always includes the observer in an essential way. In this experience, the traditional concepts of space and time, of isolated objects, and of cause and effect, lose their meaning.

Such an experience, however, is very similar to that of the Eastern mystics. The similarity becomes apparent in quantum and relativity theory, and becomes even stronger in the ‘quantum-relativistic’ models of subatomic physics where both these theories combine to produce the most striking parallels to Eastern mysticism.

Before spelling out these parallels in detail, I shall give a brief account of the schools of Eastern philosophy which are relevant to the comparison for the reader who is not familiar with them. They are the various schools in the religious philosophies of Hinduism, Buddhism and Taoism.

In the following five chapters, the historical background, characteristic features and philosophical concepts of these spiritual traditions will be described, the emphasis being on those aspects and concepts which will be important for the subsequent comparison with physics.