Some preliminaries We have, until now, thought of atoms as tiny hard spheres that feel a force of attraction towards one another. We ignored the fact that an atom consists of a nucleus surrounded by one or more electrons. If we stopped at this, we would make little progress towards understanding the properties of solids, other than that the atoms may form crystals. We must therefore go on and take a look at the internal structure of the atom itself, and see how this changes when the atom is surrounded by other atoms in a crystal. We shall then find that we need a description that is somewhat removed from our everyday experience. There is a name for this description, quantum mechanics : mechanics, because it deals with the motion of objects, and quantum, because features of the motion, such as energy, are quantized , meaning that they can only have any one of a set of distinct values, and no other value in between. Imagine for example a car which is so constructed that it can travel only at speeds of 10, or 50, or 100 km per hour, and not at any other speed. Then we could say that the speed of the car is quantized. This idea of quantization is something alien to our usual way of thinking. After all, a car is able to go at any speed we like up to its maximum speed.
Some preliminaries We have, until now, thought of atoms as tiny hard spheres that feel a force of attraction towards one another. We ignored the fact that an atom consists of a nucleus surrounded by one or more electrons. If we stopped at this, we would make little progress towards understanding the properties of solids, other than that the atoms may form crystals. We must therefore go on and take a look at the internal structure of the atom itself, and see how this changes when the atom is surrounded by other atoms in a crystal. We shall then find that we need a description that is somewhat removed from our everyday experience. There is a name for this description, quantum mechanics : mechanics, because it deals with the motion of objects, and quantum, because features of the motion, such as energy, are quantized , meaning that they can only have any one of a set of distinct values, and no other value in between. Imagine for example a car which is so constructed that it can travel only at speeds of 10, or 50, or 100 km per hour, and not at any other speed. Then we could say that the speed of the car is quantized. This idea of quantization is something alien to our usual way of thinking. After all, a car is able to go at any speed we like up to its maximum speed.
Introduction It is believed that the basic physical building blocks forming the world we live in may be categorized into particles of matter and carriers of force between matter. All known elementary constituents of matter and transmitters of force are quantized. For example, energy, momentum, and angular momentum take on discrete quantized values. The electron is an example of an elementary particle of matter, and the photon is an example of a transmitter of force. Neutrons, protons, and atoms are composite particles made up of elementary particles of matter and transmitters of force. These composite particles are also quantized. Because classical mechanics is unable to explain quantization, we must learn quantum mechanics in order to understand the microscopic properties of atoms – which, for example, make up solids such as crystalline semiconductors. Historically, the laws of quantum mechanics have been established by experiment. The most important early experiments involved light. Long before it was realized that light waves are quantized into particles called photons, key experiments on the wave properties of light were performed. For example, it was established that the color of visible light is associated with different wavelengths of light. Table 2.1 shows the range of wavelengths corresponding to different colors. The connection between optical and electrical phenomena was established by Maxwell in 1864. This extended the concept of light to include the complete electromagnetic spectrum. A great deal of effort was, and continues to be, spent gathering information on the behavior of light.
At the atomic scale, the distinction between particles and waves breaks down. The realization, early in the twentieth century, that light consists of discrete packages, or “photons,” prompted the converse suggestion that particles could behave like waves. Confirmation of this idea came in 1927, from an experiment involving the scattering of electrons from a crystal. Today, “wave-particle duality” is central to quantum mechanics, and the wave properties of subatomic particles are widely used in microscopy and crystallography. Electron diffraction techniques are widely used to characterize atomic arrangements on solid surfaces and inside thin films, and to investigate the structures of molecules in gases. The dual nature of waves and particles is part of the “spookiness” of quantum mechanics, which cannot be explained in any classical way. It used to be that one could only imagine an experiment that would simultaneously demonstrate the particle and wave nature of electrons.
An atom consists of a nucleus, containing protons and neutrons, with various electrons swarming around the outskirts. The electrons are held in the vicinity of the nucleus as they are negatively charged and hence attracted by the positively charged protons. Although atoms are complicated objects, there are certain situations where they can be treated as simple lumps of matter. Their internal structure has no relevance to the details of what is happening. This sort of situation is exemplified by experiments in which atoms are deliberately smashed into one another at comparatively low energy and as such provide an ideal start in a study of the quantum physics of identical particles. When we are dealing with atoms, there is something more to being ‘identical’ than we can appreciate with larger-scale objects. Atoms of the same type are really identical, measurably identical if you like, which can make a considerable difference in some physically important situations.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. 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. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties 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. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
The Quantum theory deals with the microscopic structure of the Universe that describes the finer details of nature at the subatomic domain.To a physicist, quantum mechanics is one of the three great pillars supporting our intuition of evocative, bewildering and fascinating natural World as we continuously struggle with the inescapable strangeness of the subatomic domain as if something strange is always afoot.It is well accepted fact that quantum mechanics is a physical theory that describes the way things behave at subatomic level which is quite dazzling in its precision and explanatory power.A test of quantum electrodynamics, the oldest and best understood of the modern quantum theory that involves measuring the way an electron behaves in the vicinity of a magnetic force. Many of the technological and social changes that have revolutionized our lives have actually risen out of the fundamental theoretical research carried out with only motivation to understand the World in a better way than ever. For example, the invention of transistor actually came with the fundamental theoretical research on the Uncertainty Principle which states that the uncertainty of the position of a particle times the uncertainty of its velocity is always a constant. If we double the certainty of the position of the particle, we have to make half the certainty of its velocity and vice versa. Quantum theory is perhaps the prime example of the infinitely esoteric in the sense that it describes a World in which a particle really can be in several places at once and it moves from one place to another by exploring the entire Universe simultaneously-the theory of simultaneity. The diverse and complex Universe is actually made of a few tiny particles according to the rules of quantum theory which is so simple that can be summarized on the back of an envelope. The more we understand about the elemental nature of the Universe, the simpler it looks. We have already discovered that everything in the diverse and complex Universe is nothing but the different assemblies of atoms, and the wide variety of atoms are constructed using the three building blocks at the sub-atomic domain i.e. subatomic particles: protons, neutrons and electrons. We have also discovered that protons and neutrons ate made up of combination of three entities called quarks. And that is where things stop as far as recent discovery is concerned. But the recent progress in particle physics inspiring the quest for the ultimate unified theory of physics that can describe everything in the Universe in one go. The discovery of Boson particle certainty will revolutionaries the Newton's mass concept and gravity into whole new looks. To an optimistic point of view, we must hope the best out of the progress in physics.
What is it about quantum mechanics that continues to make its interpretation so difficult and controversial? It is now more than 70 years after its inception and at least half a century since the verification of its predictions of physical phenomena that range from the motion of electrons in solids to the basic structure and properties of the atomic nucleus. After reading the first half of this book one could be forgiven for believing that it has been just our unwillingness or inability to understand properly what Niels Bohr said from the beginning, and to update these ideas in the light of later experience. The aim of the present book is to do just this: to restate the Copenhagen interpretation and to show us how it has been developed to take modern results and ideas into account.