The opening of the twentieth century heralded an unprecedented era of turnover and reevaluation of the classical theory that had governed Physics since pre- Newtonian times. Speaking on December 14, 1900, at the meeting of the German Physical Society, Max Planck stated that paradoxes pestering the classical theory of the emission and absorption of light by material bodies could be removed if one assumed that radiant energy can exist only in the form of discrete packages. Planck called these packages light quanta. Five years later, Albert Einstein successfully applied the idea of light quanta to explain the empirical laws of photoelectric effect; that is, the emission of electrons from metallic surfaces irradiated by violet and ultraviolet light. Still later, Arthur Compton performed his classical experiment, which showed that the scattering of X-rays by free electrons followed the same law as the collision between two elastic spheres. Thus, within a few years the novel idea of quantization of radiant energy firmly established itself in both theoretical and experimental physics.
In the year 1913, a Danish physicist, Niels Bohr, extended Planck's idea of quantization of radiant energy to the description of mechanical energy of electrons within an atom. Introducing specific "quantization rules" for the mechanical systems of atomic sizes, he achieved a logical interpretation of Ernest Rutherford's planetary model of an atom, which rested on a solid experimental basis but on the other side stood in sharp contradiction to all the fundamental concepts of classical physics. Bohr calculated the energies of various discrete quantum states of atomic electrons and interpreted the emission of light as the ejection of a light quantum with energy equal to the energy difference between the initial and final quantum states of an atomic electron. With his calculations he was able to explain in great detail the spectral lines of hydrogen and heavier elements, a problem which for decades had mystified the spectroscopists. Bohr's first paper on the quantum theory of the atom led to cataclysmic developments. Within a decade, due to the joint efforts of theoretical as well as experimental physicists of many lands, the optical, magnetic, and chemical properties of various atoms were understood in great detail. But as the years ran by, it became clearer and clearer that, successful as Bohr's theory was, it was still not a final theory since it could not explain some things that were known about atoms. For example, it failed completely to describe the transition process of an electron from one quantum state to another, and there was no way of calculating the intensities of various lines in optical spectra.
In 1925, a French physicist, Louis de Broglie, published a paper in which he gave a quite unexpected interpretation of Bohr quantum orbits. According to de Broglie, the motion of each electron is governed by some mysterious pilot waves, whose propagation velocity and length depend on the velocity of the electron in question. Assuming that the length of these pilot waves is inversely proportional to the electron's velocity, de Broglie could show that various quantum orbits in Bohr's model of the hydrogen atom were those that could accommodate an integral number of pilot waves. Thus, the model of an atom began to look like some kind of musical instrument with a basic tone (the innermost orbit with the lowest energy) and various overtones (outlying orbits with higher energy). One year after their publication, de Broglie's ideas were extended and brought into more exact mathematical form by the Austrian physicist Erwin Schrödinger, whose theory became known as Wave Mechanics. While explaining all the atomic phenomena for which Bohr's theory already worked, wave mechanics also explained those phenomena for which Bohr's theory failed (such as the intensities of spectral lines, etc.), and in addition predicted some new phenomena (such as diffraction of an electron beam) which had not even been dreamed of, either in classical physics or in Planck-Bohr quantum theory. In fact, wave mechanics provided a complete and perfectly self-consistent the ory of all atomic phenomena, and, as was shown in the late twenties, could explain also the phenomena of radioactive decay and artificial nuclear transformations.
Simultaneously with Schrödinger's paper on wave mechanics, there appeared a paper of a young German physicist, W. Heisenberg, who developed the treatment of quantum problems by using the so-called "non-commutative algebra," a mathematical discipline in which ax b is not necessarily equal to b xa. The simultaneous appearance of Schrödinger's and Heisenberg's papers in two different German magazines (Ann. der Phys. and Zeitsch. der Phys.) astonished the world of theoretical physics. These two papers looked as different as they could be, but led to exactly the same results concerning atomic structure and spectra. And it took more than a year until it was found that the two theories were physically identical except for being expressed in two entirely different mathematical forms. It was as if America was discovered by Columbus, sailing westward across the Atlantic Ocean, and by some equally daring Japanese, sailing eastward across the Pacific Ocean.
But there still remained one sharp thorn in the crown of the Quantum Theory, and it made itself felt pain- fully whenever one tried to quantize mechanical systems which, because of the very high velocities involved (close to the speed of light) required relativistic treatment. Many unsuccessful attempts had been made to unite the Theory of Relativity with the Theory of Quanta until finally, in 1929, a British physicist, P. A. M. Dirac, wrote his famous Relativistic Wave Equation. The solutions of this equation gave a perfect description of the motion of atomic electrons at velocities close to that of light, and gave automatically, as an unexpected bonus, the explanation of their linear and angular mechanical momenta and magnetic moments. Some formal difficulties connected with handling this equation led Dirac to suggest that along with ordinary negatively charged electrons there must also exist positively charged anti-electrons. His prediction was brilliantly verified a few years later when anti- electrons were found in the cosmic rays. The theory of anti-particles was extended to elementary particles other than electrons, and today we have anti-protons, anti-neutrons, anti-mesons, etc.
Thus, by 1930, only three decades after Planck's momentous announcement, the Quantum Theory took the final shape with which we are now familiar. Very little theoretical progress was made in the decades that followed these breathtaking developments. On the other hand, these later years have been quite fruitful in the field of experimental studies, especially in the investigation of the numerous newly discovered elementary particles. We are still waiting for a breakthrough in the solid wall of difficulties which prevent us from understanding the very existence of elementary particles, their masses, charges, magnetic moments, and inter- actions. There is hardly any doubt that when such a breakthrough is achieved, it will involve concepts that will be as different from those of today as today's concepts are different from those of classical physics.
In the following chapters an attempt will be made to describe the growth of the Quantum Theory of energy and matter through the first thirty years of its turbulent development, stressing the conceptual differences be- tween "good old" classical physics and the new look physics has assumed in the twentieth century.
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