The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.
The photon in the interferometer This chapter introduces many of the ideas of quantum theory by exploring three specific “case studies” of quantum systems. Each is an example of a qubit , a generic name for the simplest type of quantum system. The concepts we develop will be incorporated into a rigorous mathematical framework in the next chapter. Our business here is to provide some intuition about why that mathematical framework is reasonable and appropriate for dealing with the quantum facts of life. Interferometers In Section 1.2 we discussed the two-slit interference experiment with a single photon. In that experiment, the partial waves of probability amplitude were spread throughout the entire region of space beyond the two slits. It is much easier to analyze the situation in an interferometer , an optical apparatus in which the light is restricted to a finite number of discrete beams . The beams may be guided from one point to another, split apart or recombined as needed, and when two beams are recombined into one, the result may show interference effects. At the end of the interferometer, one or more sensors can measure the intensity of various beams. (A beam is just a possible path for the light, so there is nothing paradoxical in talking about a beam of zero intensity.) Figure 2.1 shows the layout of a Mach–Zehnder interferometer , which is an example of this kind of apparatus.
Scope of this book Quantum mechanics is a difficult subject, and this book is intended to help the reader overcome the main difficulties in the way to understanding it. The first part of the book, Chs. 2–16, contains a systematic presentation of the basic principles of quantum theory, along with a number of examples which illustrate how these principles apply to particular quantum systems. The applications are, for the most part, limited to toy models whose simple structure allows one to see what is going on without using complicated mathematics or lengthy formulas. The principles themselves, however, are formulated in such a way that they can be applied to (almost) any nonrelativistic quantum system. In the second part of the book, Chs. 17–25, these principles are applied to quantum measurements and various quantum paradoxes, subjects which give rise to serious conceptual problems when they are not treated in a fully consistent manner. The final chapters are of a somewhat different character. Chapter 26 on decoherence and the classical limit of quantum theory is a very sketchy introduction to these important topics along with some indication as to how the basic principles presented in the first part of the book can be used for understanding them. Chapter 27 on quantum theory and reality belongs to the interface between physics and philosophy and indicates why quantum theory is compatible with a real world whose existence is not dependent on what scientists think and believe, or the experiments they choose to carry out. The Bibliography contains references for those interested in further reading or in tracing the origin of some of the ideas presented in earlier chapters.
In the last chapter we saw how the measurement problem in quantum theory arises when we try to treat the measurement apparatus as a quantum system. We need more apparatus to measure which state the first apparatus is in, and we have a measurement chain that seems to go on indefinitely. There is, however, one place where this apparently infinite sequence certainly seems to end and that is when the information reaches us. We know from experience that when we look at the photon detector we see that either it has recorded the passage of a photon or it hasn't. When we open the box and look at the cat either it is dead or it is alive; we never see it in the state of suspended animation that quantum physics alleges it should be in until its state is measured. It might follow, therefore, that human beings should be looked on as the ultimate measuring apparatus. If so, what aspect of human beings is it that gives them this apparently unique quality? It is this question and its implications that form the subject of the present chapter. Let us examine more closely what goes on when a human being observes the quantum state of a system. We return to the set-up described in the last chapter, where a 45° photon passes through a polarisation analyser that moves a pointer to one of two positions (H or V) depending on whether the photon is horizontally or vertically polarised. At least that is what would happen if the analyser and pointer behaved as a measuring apparatus. If however we treat them as part of the quantum system, the pointer is placed in a superposition of being at H and at V until its state is measured. We now add a human observer who looks at the pointer (it would be possible to imagine the observer using one of his other senses, for example hearing a particular sound caused by a change in the pointer’s position, but it is clearer if we think of a visual observation).
This chapter introduces core quantum mechanics concepts, focusing on Heisenberg's uncertainty principle and Schrödinger's equation, which describe quantum particles' wave–particle duality and probabilistic nature. The uncertainty principle and Schrödinger's equation are fundamental postulates validated by experiments, with the latter governing quantum behavior. The chapter explores wave functions, superposition, and entanglement, using light polarization to contrast classical and quantum interpretations, demonstrating that single photons exhibit probabilistic outcomes when interacting with polarizers. Additionally, it discusses polarizers and polarizing beam splitters, analyzing light propagation through these components using the law of Malus and comparing classical and quantum interpretations. The chapter concludes by highlighting the implications of these findings on photon polarization and measurement, providing a foundation for understanding quantum technologies.