Quantum Physics

However,

The first of these developments was the discovery and investigation of electric and magnetic phenomena which could not be described appropriately by the mechanistic model and involved a new type of force.

The important step was made by Michael Faraday and Clerk Maxwell-the first, one of the greatest experimenters in the history of science, the second, a brilliant theorist. When Faraday produced an electric current in a coil of copper by moving a magnet near it, and thus converted the mechanical work of moving the magnet into electric energy, he brought science and tech- nology to a turning point.

His fundamental experiment gave birth, on the one hand, to the vast technology of electrical engineering; on the other hand, it formed the basis of his and Maxwell’s theoretical speculations which, eventually, resulted in a complete theory of electromagnetism. Faraday and Maxwell did not only study the effects of the electric and magnetic forces, but made the forces themselves the primary object of their investigation. They replaced the concept of a force by that of a force field, and in doing so they were the first to go beyond Newtonian physics.

Instead of interpreting the interaction between a positive and a negative charge simply by saying that the two charges attract each other like two masses in Newtonian mechanics, Faraday and Maxwell found it more appropriate to say that each charge creates a ‘disturbance’, or a ‘condition’, in the space around it so that the other charge, when it is present, feels a force. This condition in space which has the potential of producing a force is called a field. It is created by a single charge and it exists whether or not another charge is brought in to feel its effect.

This was a most profound change in man’s conception of physical reality.

In the Newtonian view, the forces were rigidly connected with the bodies they act upon.

Now the force concept was replaced by the much subtler concept of a field which had its own reality and could be studied without any reference to material bodies. The culmination of this theory, called electrodynamics, was the realization that light is nothing but a rapidly alternating electromagnetic field travelling through space in the form of waves.

Today we know that radio waves, light waves or X-rays, are all electromagnetic waves, oscillating electric and magnetic fields differing only in the frequency of their oscillation, and that visible light is only a tiny fraction of the electromagnetic spectrum.

In spite of these far-reaching changes, Newtonian mechanics at first held its position as the basis of all physics. Maxwell himself tried to explain his results in mechanical terms, interpreting the fields as states of mechanical stress in a very light space-filling medium, called ether, and the electromagnetic waves as elastic waves of this ether. This was only natural as waves are usually experienced as vibrations of something; water waves as vibrations of water, sound waves as vibrations of air.

Maxwell, however, used several mechanical interpretations of his theory at the same time and apparently took none of them really seriously. He must have realized intuitively, even if he did not say so explicitly, that the fundamental entities in his theory were the fields and not the mechanical models. It was Einstein who clearly recognized this fact fifty years later when he declared that no ether existed and that the electro- magnetic fields were physical entities in their own right which could travel through empty space and could not be explained mechanically. At the beginning of the twentieth century, then, physicists had two successful theories which applied to different pheno- mena : Newton’s mechanics and Maxwell’s electrodynamics. Thus the Newtonian model had ceased to be the basis of all physics.

MODERN PHYSICS

The first three decades of our century changed the whole situation in physics radically. Two separate developments- that of relativity theory and of atomic physics-shattered all the principal concepts of the Newtonian world view: the notion of absolute space and time, the elementary solid particles, the

strictly causal nature of physical phenomena, and the ideal of an objective description of nature. None of these concepts could be extended to the new domains into which physics was now penetrating. At the beginning of modern physics stands the extraordinary intellectual feat of one man: Albert Einstein. In two articles, both published in 1905, Einstein initiated two revolutionary trends of thought. One was his special theory of relativity, the other was a new way of looking at electromagnetic radiation which was to become characteristic of quantum theory, the theory of atomic phenomena. The complete quantum theory was worked out twenty years later by a whole team of physicists. Relativity theory, however, was constructed in its complete form almost entirely by Einstein himself. Einstein’s scientific papers stand at the beginning of the twentieth century as imposing intellectual monuments-the pyramids of modern civilization. Einstein strongly believed in nature’s inherent harmony and his deepest concern throughout his scientific life was to find a unified foundation of physics. He began to move towards this goal by constructing a common framework for electrodynamics and mechanics, the two separate theories of classical physics. This framework is known as the special theory of relativity. It unified and completed the structure of classical physics, but at the same time it involved drastic changes in the traditional concepts of space and time and undermined one of the foundations of the Newtonian world view. According to relativity theory, space is not three-dimensional and time is not a separate entity. Both are intimately connected and form a four-dimensional continuum, ‘space-time’. In relativity theory, therefore, we can never talk about space without talking about time and vice versa. Furthermore, there is no universal flow of time as in the Newtonian model. Different observers will order events differently in time if they move with different velocities relative to the observed events. In such a case, two events which are seen as occurring simultaneously by one observer may occur in different temporal sequences for other observers. All measurements involving space and time thus lose their absolute significance. In relativity theory, the Newtonian concept of an absolute space as the stage of

physical phenomena is abandoned and so is the concept of an absolute time. Both space and time become merely elements of the language a particular observer uses for his description of the phenomena. The concepts of space and time are so basic for the des- cription of natural phenomena that their modification entails a modification of the whole framework that we use to describe nature. The most important consequence of this modification is the realization that mass is nothing but a form of energy. Even an object at rest has energy stored in its mass, and the relation between the two is given by the famous equation E= mc2, c being the speed of light. This constant c, the speed of light, is of fundamental im- portance for the theory of relativity. Whenever we describe physical phenomena involving velocities which approach the speed of light, our description has to take relativity theory into account. This applies in particular to electromagnetic pheno- mena, of which light is just one example and which led Einstein to the formulation of his theory. In 1915, Einstein proposed his general theory of relativity in which the framework of the special theory is extended to include gravity, i.e. the mutual attraction of all massive bodies. Whereas the special theory has been confirmed by innumerable experi- ments, the general theory has not yet been confirmed con- clusively. However, it is so far the most accepted, consistent and elegant theory of gravity and is widely used in astrophysics and cosmology for the description of the universe at large. The force of gravity, according to Einstein’s theory, has the effect of ‘curving’ space and time. This means that ordinary Euclidean geometry is no longer valid in such a curved space, just as the two-dimensional geometry of a plane cannot be applied on the surface of a sphere. On a plane, we can draw, for example, a square by marking off one metre on a straight line, making a right angle and marking off another metre, then making another right angle and marking off another metre, and finally making a third right angle and marking off one metre again, after which we are back at the starting point and the square is completed. On a sphere, however, this procedure does not work because the rules of Euclidean geometry do not hold on curved surfaces. In the same way, we can define a

three-dimensional curved space to be one in which Euclidean geometry is no longer valid. Einstein’s theory, now, says that three-dimensional space is actually curved, and that the curva- ture is caused by the gravitational field of massive bodies

Wherever there is a massive object, e.g. a star or a planet, the space around it is curved and the degree of curvature depends on the mass of the object. And as space can never be separated from time in relativity theory, time as well is affected by the presence of matter, flowing at different rates in different parts of the universe. Einstein’s general theory of relativity thus completely abolishes the concepts of absolute space and time. Not only are all measurements involving space and time relative; the whole structure of space-time depends on the distribution of matter in the universe, and the concept of ‘empty space’ loses its meaning. The mechanistic world view of classical physics was based on the notion of solid bodies moving in empty space. This notion is still valid in the region that has been called the ‘zone of middle dimensions’, that is, in the realm of our daily experience where classical physics continues to be a useful theory. Both concepts-that of empty space and that of solid material bodies-are deeply ingrained in our habits of thought, so it is extremely difficult for us to imagine a physical reality where they do not apply. And yet, this is precisely what modern physics forces us to do when we go beyond the middle dimen- sions. ‘Empty space’ has lost its meaning in astrophysics and cosmology, the sciences of the universe at large, and the

concept of solid objects was shattered by atomic physics, the science of the infinitely small. At the turn of the century, several phenomena connected with the structure of atoms and inexplicable in terms of classical physics were discovered. The first indication that atoms had some structure came from the discovery of X-rays; a new radiation which rapidly found its now well known application in medicine. X-rays, however, are not the only radiation emitted by atoms. Soon after their discovery, other kinds of radiation were discovered which are emitted by the atoms of so-called radioactive substances. The phenomenon of radioactivity gave definite proof of the composite nature of atoms, showing that the atoms of radioactive substances not only emit various types of radiation, but also transform themselves into atoms of completely different substances. Besides being objects of intense study, these phenomena were also used, in most ingenious ways, as new tools to probe deeper into matter than had ever been possible before. Thus Max von Laue used X-rays to study the arrangements of atoms in crystals, and Ernest Rutherford realized that the so-called alpha particles emanating from radioactive substances were high-speed projectiles of subatomic size which could be used to explore the interior of the atom. They could be fired at atoms, and from the way they were deflected one could draw conclusions about the atoms’ structure. When Rutherford bombarded atoms with these alpha particles, he obtained sensational and totally unexpected results. Far from being the hard and solid particles they were believed to be since antiquity, the atoms turned out to consist of vast regions of space in which extremely small particles-the electrons-moved around the nucleus, bound to it by electric forces. It is not easy to get a feeling for the order of magnitude of atoms, so far is it removed from our macroscopic scale. The diameter of an atom is about one hundred millionth of a centi- metre. In order to visualize this diminutive size, imagine an orange blown up to the size of the Earth. The atoms of the orange will then have the size of cherries. Myriads of cherries, tightly packed into a globe of the size of the Earth-that’s a magnified picture of the atoms in an orange. An atom, therefore, is extremely small compared to macro-

scopic objects, but it is huge compared to the nucleus in its centre. In our picture of cherry-sized atoms, the nucleus of an atom will be so small that we will not be able to see it. If we blew up the atom to the size of a football, or even to room size, the nucleus would still be too small to be seen by the naked eye. To see the nucleus, we would have to blow up the atom to the size of the biggest dome in the world, the dome of St Peter’s Cathedral in Rome. In an atom of that size, the nucleus would have the size of a grain of salt! A grain of salt in the middle of the dome of St Peter’s, and specks of dust whirling around it in the vast space of the dome-this is how we can picture the nucleus and electrons of an atom. Soon after the emergence of this ‘planetary’ model of the atom, it was discovered that the number of electrons in the atoms of an element determine the element’s chemical pro- perties, and today we know that the whole periodic table of elements can be built up by successively adding protons and neutrons to the nucleus of the lightest atom-hydrogen*-and the corresponding number of electrons to its atomic ‘shell’. The interactions between the atoms give rise to the various chemical processes, so that all of chemistry can now in principle be understood on the basis of the laws of atomic physics. These laws, however, were not easy to recognize. They were discovered in the 1920s by an international group of physicists including Niels Bohr from Denmark, Louis De Broglie from France, Erwin Schrddinger and Wolfgang Pauli from Austria, Werner Heisenberg from Germany, and Paul Dirac from England. These men joined their forces across all national borders and shaped one of the most exciting periods in modern science, which brought man, for the first time, into contact with the strange and unexpected reality of the subatomic world. Every time the physicists asked nature a question in an atomic experiment, nature answered with a paradox, and the more they tried to clarify the situation, the sharper the paradoxes became. It took them a long time to accept the fact that these paradoxes belong to the intrinsic structure of atomic physics, and to realize that they arise whenever one attempts to describe atomic events in the traditional terms of physics.

Once this was perceived, the physicists began to learn to ask the right questions and to avoid contradictions. In the words of Heisenberg, ‘they somehow got into the spirit of the quantum theory’, and finally they found the precise and consistent mathematical formulation of this theory. The concepts of quantum theory were not easy to accept even after their mathematical formulation had been completed. Their effect on the physicists’ imaginations was truly shattering. Rutherford’s experiments had shown that atoms, instead of being hard and indestructible, consisted of vast regions of space in which extremely small particles moved, and now quantum theory made it clear that even these particles were nothing like the solid objects of classical physics. The subatomic units of matter are very abstract entities which have a dual aspect. Depending on how we look at them, they appear sometimes as particles, sometimes as waves; and this dual nature is also exhibited by light which can take the form of electromagnetic waves or of particles. This property of matter and of light is very strange. It seems impossible to accept that something can be, at the same time, a particle-i.e. an entity confined to a very small volume-and

a wave, which is spread out over a large region of space. This contradiction gave rise to most of the koan-like paradoxes which finally led to the formulation of quantum theory. The whole development started when Max Planck discovered that the energy of heat radiation is not emitted continuously, but appears in the form of ‘energy packets’. Einstein called these energy packets ‘quanta’ and recognized them as a fundamental aspect of nature. He was bold enough to postulate that light and every other form of electromagnetic radiation can appear not only as electromagnetic waves, but also in the form of these quanta. The light quanta, which gave quantum theory its name, have since been accepted as bona fide particles and are now called photons. They are particles of a special kind, however, massless and always travelling with the speed of light.

The apparent contradiction between the particle and the wave picture was solved in a completely unexpected way which called in question the very foundation of the mechanistic world view-the concept of the reality of matter. At the sub- atomic level, matter does not exist with certainty at definite places, but rather shows ‘tendencies to exist’, and atomic events do not occur with certainty at definite times and in definite ways, but rather show ‘tendencies to occur’. In the formalism of quantum theory, these tendencies are expressed as prob- abilities and are associated with mathematical quantities which take the form of waves. This is why particles can be waves at the same time. They are not ‘real’ three-dimensional waves like sound or water waves. They are ‘probability waves’, abstract mathematical quantities with all the characteristic properties of waves which are related to the probabilities of finding the particles at particular points in space and at parti- cular times. All the laws of atomic physics are expressed in terms of these probabilities. We can never predict an atomic event with certainty; we can only say how likely it is to happen. Quantum theory has thus demolished the classical concepts of solid objects and of strictly deterministic laws of nature. At the subatomic level, the solid material objects of classical physics dissolve into wave-like patterns of probabilities, and these patterns, ultimately, do not represent probabilities of things, but rather probabilities of interconnections. A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement. Quantum theory thus reveals a basic oneness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated ‘basic building blocks’, but rather appears as a complicated web of relations between the various parts of the whole. These re- lations always include the observer in an essential way. The human observer constitutes the final link in the chain of ob- servational processes, and the properties of any atomic object can only be understood in terms of the object’s interaction with the observer. This means that the classical ideal of an

objective description of nature is no longer valid. The Cartesian partition between the I and the world, between the observer and the observed, cannot be made when dealing with atomic matter. In atomic physics, we can never speak about nature without, at the same time, speaking about ourselves. The new atomic theory could immediately solve several puzzles which had arisen in connection with the structure of atoms and could not be explained by Rutherford’s planetary model. First of all, Rutherford’s experiments had shown that the atoms making up solid matter consist almost entirely of empty space, as far as the distribution of mass is concerned. But if all the objects around us, and we ourselves, consist mostly of empty space, why can’t we walk through closed doors? In other words, what is it that gives matter its solid aspect? A second puzzle was the extraordinary mechanical stability of atoms. In the air, for example, atoms collide millions of times every second and yet go back to their original form after each collision. No planetary system following the laws of classical mechanics would ever come out of these collisions unaltered. But an oxygen atom will always retain its characteristic con- figuration of electrons, no matter how often it collides with other atoms. This configuration, furthermore, is exactly the same in all atoms of a given kind. Two iron atoms, and con- sequently two pieces of pure iron, are completely identical, no matter where they come from or how they have been treated in the past. Quantum theory has shown that all these astonishing pro- perties of atoms arise from the wave nature of their electrons. To begin with, the solid aspect of matter is the consequence of a typical ‘quantum effect’ connected with the dual wave/particle aspect of matter, a feature of the subatomic world which has no macroscopic analogue. Whenever a particle is confined to a small region of space it reacts to this confinement by moving around, and the smaller the region of confinement is, the faster the particle moves around in it. In the atom, now, there are two competing forces. On the one hand, the electrons are bound to the nucleus by electric forces which try to keep them as close as possible. On the other hand, they respond to their confinement by whirling around, and the tighter they are

bound to the nucleus, the higher their velocity will be; in fact, the confinement of electrons in an atom results in enormous velocities of about 600 miles per second! These high velocities make the atom appear as a rigid sphere, just as a fast rotating propeller appears as a disc. It is very difficult to compress atoms any further and thus they give matter its familiar solid aspect. In the atom, then, the electrons settle in orbits in such a way that there is an optimal balance between the attraction of the nucleus and their reluctance to be confined. The atomic orbits, however, are very different from those of the planets in the solar system, the difference arising from the wave nature of the electrons. An atom cannot be pictured as a small planetary system. Rather than particles circling around the nucleus, we have to imagine probability waves arranged in different orbits. Whenever we make a measurement, we will find the electrons somewhere in these orbits, but we cannot say that they are ‘going around the nucleus’ in the sense of classical mechanics. In the orbits, the electron waves have to be arranged in such a way that ‘their ends meet’, i.e. that they form patterns known as ‘standing waves’. These patterns appear whenever waves are confined to a finite region, like the waves in a vibrating guitar string, or in the air inside a flute (see diagram overleaf). It is well known from these examples that standing waves can assume only a limited number of well-defined shapes. In the case of the electron waves inside an atom, this means that they can exist only in certain atomic orbits with definite diameters. The electron of a hydrogen atom, for example, can only exist in a certain first, second or third orbit, etc., and nowhere in between. Under normal conditions, it will always be in its lowest orbit, called the ‘ground state’ of the atom. From there, the electron can jump to higher orbits if it receives the necessary amount of energy, and then the atom is said to be in an ‘excited state’ from which it will go back to its ground state after a while, the electron giving off the surplus energy in the form of a quantum of electromagnetic radiation, or photon. The states of an atom, i.e. the shapes and mutual distances of its electron orbits, are exactly the same for all atoms with the same number of electrons. This is why any two oxygen atoms, for example,

will be completely identical. They may be in different excited states, perhaps due to collisions with other atoms in the air, but after a while they will invariably return to exactly the same ground state. The wave nature of the electrons accounts thus for the identity of atoms and for their great mechanical stability. A further characteristic feature of atomic states is the fact that they can be completely specified by a set of integral numbers, called ‘quantum numbers’, which indicate the loca- tion and shape of the electron orbits. The first quantum number is the number of the orbit and determines the energy an electron must have to be in that orbit; two more numbers specify the detailed shape of the electron wave in the orbit and are related to the speed and orientation of the electron’s

rotation.* The fact that these details are expressed by integral numbers means that the electron cannot change its rotation continuously, but can only jump from one value to another, just as it can only jump from one orbit to another. Again the higher values represent excited states of the atom, the ground state being the one where all the electrons are in the lowest possible orbits and have the smallest possible amounts of rotation. Tendencies to exist, particles reacting to confinement with motion, atoms switching suddenly from one ‘quantum state’ to another, and an essential interconnectedness of all pheno- mena-these are some of the unusual features of the atomic world. The basic force, on the other hand, which gives rise to all atomic phenomena is familiar and can be experienced in the macroscopic world. It is the force of electric attraction between the positively charged atomic nucleus and the negatively charged electrons. The interplay of this force with the electron waves gives rise to the tremendous variety of structures and phenomena in our environment. It is responsible for all chemical reactions, and for the formation of molecules, that is, of aggregates of several atoms bound to each other by mutual attraction. The interaction between electrons and atomic nuclei is thus the basis of all solids, liquids and gases, and also of all living organisms and of the biological processes associated with them. In this immensely rich world of atomic phenomena, the nuclei play the role of extremely small, stable centres which constitute the source of the electric force and form the skeletons of the great variety of molecular structures. To understand these structures, and most of the natural.pheno- mena around us, it is not necessary to know more about the nuclei than their charge and their mass. In order to understand the nature of matter, however, to know what matter is ultimately made of, one has to study the atomic nuclei which contain practically all of its mass. In the 193Os, after quantum theory had unravelled the world of atoms, it was therefore the main

*The ‘rotation’ of an electron in its orbit must not be understood in the classical sense; it is determined by the shape of the electron wave in terms of the probabilities for the particle’s existence in certain parts of the orbit.

task of physicists to understand the structure of nuclei, their constituents and the forces which hold them together so tightly. The first important step towards an understanding of nuclear structure was the discovery of the neutron as the second constituent of the nucleus, a particle which has roughly the same mass as the proton (the first nuclear constituent)-about two thousand times the mass of the electron-but does not carry an electric charge. This discovery not only explained how the nuclei of all chemical elements were built up from protons and neutrons, but also revealed that the nuclear force, which kept these particles so tightly bound within the nucleus, was a completely new phenomenon. It could not be of electro- magnetic origin since the neutrons were electrically neutral. Physicists soon realized that they were here confronted with a new force of nature which does not manifest itself anywhere outside the nucleus. An atomic nucleus is about one hundred thousand times smaller than the whole atom and yet it contains almost all of the atom’s mass. This means that matter inside the nucleus must be extremely dense compared to the forms of matter we are used to. Indeed, if the whole human body were com- pressed to nuclear density it would not take up more space than a pinhead. This high density, however, is not the only unusual property of nuclear matter. Being of the same quantum nature as electrons, the ‘nucleons’-as the protons and neutrons are often called-respond to their confinement with high velocities, and since they are squeezed into a much smaller volume their reaction is all the m-ore violent. They race about in the nucleus with velocities of about 40,000 miles per second! Nuclear matter is thus a form of matter entirely’different from anything we experience ‘up here’ in our macroscopic environ- ment. We can, perhaps, picture it best as tiny drops of an extremely dense liquid which is boiling and bubbling most fiercely. The essential new aspect of nuclear matter which accounts for all its unusual properties is the strong nuclear force, and the feature that makes this force so unique is its extremely short range. It acts only when the nucleons come very near to each other, that is, when their distance is about two to

three times their diameter. At such a distance, the nuclear force is strongly attractive, but when the distance becomes less the force becomes strongly repulsive so that the nucleons cannot approach each other any closer. In this way, the nuclear force keeps the nucleus in an extremely stable, though extremely dynamic equilibrium. The picture of matter which emerges from the study of atoms and nuclei shows that most of it is concentrated in tiny drops separated by huge distances. In the vast space between the massive and fiercely boiling nuclear drops move the electrons. These constitute only a tiny fraction of the total mass, but give matter its solid aspect and provide the links necessary to build up the molecular structures. They are also involved in the chemical reactions and are responsible for the chemical properties of matter. Nuclear reactions, on the other hand, generally do not occur naturally in this form of matter because the available energies are not high enough to disturb the nuclear equilibrium. This form of matter, however, with its multitude of shapes and textures and its complicated molecular architecture, can exist only under very special conditions, when the temperature is not too high, so that the molecules do not jiggle too much. When the thermal energy increases about a hundredfold, as it does in most stars, all atomic and molecular structures are destroyed. Most of the matter in the universe exists, in fact, in a state which is very different from the one just described. In the centre of the stars exist large accumulations of nuclear matter, and nuclear processes which occur only very rarely on earth predominate there. They are essential for the great variety of stellar phenomena observed in astronomy, most of which arise from a combination of nuclear and gravitational effects. For our planet, the nuclear processes in the centre of the Sun are of particular importance because they furnish the energy which sustains our terrestrial environment. It has been one of the great triumphs of modern physics to discover that the constant energy flow from the Sun, our vital link with the world of the very large, is a result of nuclear reactions, of phenomena in the world of the infinitely small. In the history of man’s penetration into this submicroscopic

world, a stage was reached in the early 1930s when scientists thought they had now finally discovered the ‘basic building blocks’ of matter. It was known that all matter consisted of atoms and that all atoms consisted of protons, neutrons and electrons. These so-called ‘elementary particles’ were seen as the ultimate indestructible units of matter: atoms in the Demo- critean sense. Although quantum theory implies, as mentioned previously, that we cannot decompose the world into in- dependently existing smallest units, this was not generally perceived at that time. The classical habits of thought were still so persistent that most physicists tried to understand matter in terms of its ‘basic building blocks’, and this trend of thought is, in fact, quite strong even today. Two further developments in modern physics have shown, however, that the notion of elementary particles as the primary units of matter has to be abandoned. One of these develop- ments was experimental, the other theoretical, and both began in the 1930s. On the experimental side, new particles were discovered as physicists refined their experimental techniques and developed ingenious new devices for particle detection. Thus the number of particles increased from three to six by 1935, then to eighteen by 1955, and today we know over two hundred ‘elementary’ particles. The two tables overleaf, taken from a recent publication,” show most of the particles known today. They illustrate convincingly that the adjective ‘elementary’ is no longer very attractive in such a situation. As more and more particles were discovered over the years, it became clear that not all of them could be called ‘elementary’, and today there is a widespread belief among physicists that none of them deserves this name. This belief is enforced by the theoretical developments which paralleled the discovery of an ever-increasing number of particles. Soon after the formulation of quantum theory, it became clear that a complete theory of nuclear phenomena must not only be a quantum theory, but must also incorporate relativity theory. This is because the particles confined to dimensions of the size of nuclei often move so fast that their speed comes close to the speed of light. This fact is crucial for the description of their behaviour, because every description of natural phenomena involving velocities close to the speed

of light has to take relativity theory into account. It has to be, as we say, a ‘relativist/c’ description. What we need, therefore, for a full understanding of the nuclear world is a theory which incorporates both quantum theory and relativity theory. Such a theory has not yet been found, and therefore we have as yet been unable to formulate a complete theory of the nucleus. Although we know quite a lot about nuclear structure and about the interactions between nuclear particles, we do not yet understand the nature and complicated form of the nuclear force on a fundamental level. There is no complete theory of the nuclear particle world comparable to quantum theory for the atomic world. We do have several ‘quantum- relativistic’ models which describe some aspects of the world of particles very well, but the fusion of quantum and relativity theory into a complete theory of the particle world is still the

central problem and great challenge of modern fundamental physics. 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 philo- sophies 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.