P reliminary S urvey With the coming of the twentieth century, there came into being a new physics which was especially concerned with phenomena on the atomic and sub-atomic scale. It brought with it a new way of interpreting the phenomena of inanimate nature, which was destined in time to sweep away all the difficulties besetting the old classical mechanics. A preliminary glance over the vast territory of this new physics reveals three outstanding landmarks. First we notice an investigation which Prof. Planck of Berlin published in 1899. His aim was so to amend the classical mechanics that it should fit the observed facts of radiation, and show why the energy of bodies was not wholly transformed into radiation. We have already seen that this was likely to involve giving up either continuity or causality or the representation of phenomena as changes taking place in space and time. Actually his investigation seemed to show that continuity had to be given up, suggesting that in the last resort changes in the universe do not consist of continuous motions in space and time, but are in some way discontinuous. The classical mechanics had envisaged a world constructed of matter and radiation, the matter consisting of atoms and the radiation of waves. Planck's theory called for an atomicity of radiation similar to that which was so well established for matter.
P reliminary S urvey With the coming of the twentieth century, there came into being a new physics which was especially concerned with phenomena on the atomic and sub-atomic scale. It brought with it a new way of interpreting the phenomena of inanimate nature, which was destined in time to sweep away all the difficulties besetting the old classical mechanics. A preliminary glance over the vast territory of this new physics reveals three outstanding landmarks. First we notice an investigation which Prof. Planck of Berlin published in 1899. His aim was so to amend the classical mechanics that it should fit the observed facts of radiation, and show why the energy of bodies was not wholly transformed into radiation. We have already seen that this was likely to involve giving up either continuity or causality or the representation of phenomena as changes taking place in space and time. Actually his investigation seemed to show that continuity had to be given up, suggesting that in the last resort changes in the universe do not consist of continuous motions in space and time, but are in some way discontinuous. The classical mechanics had envisaged a world constructed of matter and radiation, the matter consisting of atoms and the radiation of waves. Planck's theory called for an atomicity of radiation similar to that which was so well established for matter.
Science has developed through a variety of investigations more or less over the time scale of human existence. On this scale, quantum mechanics is an extremely young field, existing essentially for only just over a century. Even our understanding of classical mechanics has existed for a comparatively long period—roughly having been formalized with Newton's equations published in his Principia Mathematica , in April 1686 (1687). Up until the very end of the nineteenth century, mechanics in the form of Newton's laws were comfortable, being understood and accepted by all who dealt with the motion of reasonable bodies. With the turn of the new century, however, mechanics would be shaken to its roots. The change began already on December 14, 1900, when Planck (1900) presented his new theory of black-body radiation to the German Physical Society, and this change would affect mechanics in physically small structures (and lead to quantum mechanics). Mechanics of large bodies would similarly be changed in 1905 with the arrival of Albert Einstein's (1905a) relativity theory. In this book, we will deal with only the first of these two great breakthroughs.
By the beginning of the twentieth century, classical physics had accumulated many contradictions that could only be resolved by changing the main concepts of space and time (Einstein’s theory of relativity, Chapter P1) and the laws of motion of particles on atomic scales (quantum mechanics). The first quantum concepts appeared at the very beginning of the century (Planck’s formula for thermal radiation and Einstein’s formula for photoeffect, Chapter P5), but quantum mechanics as a closed science was not constructed until the end of the 1920s.
The first Council in 1911 had made clear the need for a new physics, which would introduce a principle of discontinuity into the microscopic world. Ten years later, from the 1 st – 6 th April, 1921, the third Physics Council was to take place. The crucial advances made during this period can be summed up as follows: on the one hand, there was considerable progress on understanding the structure of the atom, notably thanks to Rutherford, and on the other, what might be called “the old theory of quanta” was updated, chiefly by Bohr, to take into account the emission of radiation by atoms. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...
Quantum mechanics deals with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents--electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons. Its concepts frequently conflict with common-sense notions derived from observations of the everyday world. Quantum mechanics has attracted some of the ablest scientists of the 20th century, and they have erected what is perhaps the finest intellectual edifice of the period. Quantum mechanics is concerned with phenomena that are so small-scale that they cannot be described in classical terms. The history of quantum mechanics may be divided into three main periods. The first began with Planck's theory of black-body radiation in 1900; it may be described as the period in which the validity of Planck's constant was demonstrated but its real meaning was not fully understood. The second period began with the quantum theory of atomic structure and spectra proposed by Niels Bohr in 1913. True quantum mechanics appeared in 1926, reaching fruition nearly simultaneously in a variety of forms--namely, the matrix theory of Max Born and Werner Heisenberg, the wave mechanics of Louis V. de Broglie and Erwin Schrodinger, and the transformation theory of P.A.M. Dirac and Pascual Jordan.
The principles of quantum mechanics are so contrary to ordinary intuition that they can best be motivated by taking a look at their prehistory. In this chapter we will consider the problems confronted by physicists in the first years of the twentieth century that ultimately led to modern quantum mechanics. Photons Physicists in the last decades of the nineteenth century were greatly concerned to understand the nature of black-body radiation — radiation that had come into thermal equilibrium with matter at a given temperature T . The energy ρ(ν, T ) d ν per volume at frequencies between ν and ν + d ν had been measured, chiefly at the University of Berlin, and it was known on thermodynamic grounds that ρ(ν, T ) is a universal function of frequency and temperature, but how could one calculate this function? A simple calculation was given in 1900 by John William Strutt (1842–1919), more usually known as Lord Rayleigh. It was familiar that one can think of the radiation field in a box as a Fourier sum over normal modes. For instance, for a cubical box of width L , whatever boundary condition is satisfied on one face of the box must be satisfied on the opposite face, so the phase of the radiation field must change by an integer multiple of 2π in a distance L .