The Tao of Physics. Fritjof Capra

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 our 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 electromagnetic 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 phenomena: 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 describing the observed phenomena.

      The concepts of space and time are so basic for the description 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 importance 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 phenomena, 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 experiments, the general theory has not yet been confirmed conclusively. 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 curvature 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