This chapter shows how particles arise naturally as an effect of waves, known as “resonance,” and that the particle concept, properly understood, is not somehow incompatible with the existence of waves. The definitions of “fermion” and “boson” fields, often associated with “matter” and “energy” particles, are introduced. The solidness of objects in our experience is a direct consequence of fermion wave properties.

This chapter surveys modern progress in physics on the topic of “decoherence,” the physical process by which irreversible behavior can occur in wave systems. A substantial part of the chapter discusses a proposal by the author of this book for a spontaneous collapse theory that is connected to decoherence.

This chapter introduces the formal “second quantization” method for bosons in quantum field theory. It is shown that phonons (sound particles) and photons (light particles) are simple extensions of the physics of a spring-like oscillator. The connection of boson states to classical waves is shown in a discussion of “coherent states.”

This chapter presents some basic calculations that show counterintuitive or unexpected results. First, it is shown that the Planck spectrum of light, which played an important role in the history of quantum mechanics, doesn’t say anything about the existence of indivisible particles. Second, a brief discussion of “chaos theory” shows that jumpy and unpredictable behavior can occur in classical systems. Last, the concept of “entanglement” is introduced as a basic property of quantum systems.

This chapter discusses what we mean by particle detectors and “quantum jumps.” Modern results are presented that show that particle detection is not instantaneous, and that the photoelectric effect does not prove the existence of particles; it is a purely wavelike effect. The Born rule for random clicks of measurements in detectors is introduced and discussed, and quantum “uncertainty” is introduced.

This chapter begins a five-chapter mathematical introduction to quantum field theory, appropriate for upper-level undergraduate science or engineering students, or those with some mathematical training who would like to know what the “real” theory of quantum mechanics is. In this chapter, the basics of Dirac notation are presented. The last part of this chapter shows how the uncertainty principle of quantum mechanics is derived.

This chapter surveys several different mathematical methods for time-dependent change of quantum states using quantum field theory. The Bloch sphere method is introduced, which can be used to show the physics discussed in Chapter 3, that electronic transitions, or “jumps,” are not instantaneous.

This chapter begins a short, two-chapter section on calculations that specifically impact the philosophy of quantum mechanics. A quantitative discussion of the famous Einstein–Podalsky–Rosen (EPR) experiment is given, as well as a mathematical discussion of problems with the many-worlds hypothesis, the Bohmian pilot-wave hypothesis, and the “transactional” hypothesis for interpreting quantum mechanics.

This chapter starts out a short, two-chapter section on very basic mathematics of quantum mechanics, appropriate for those who have taken undergraduate science or engineering courses. The method of “unit analysis” is used as a way of getting at when quantum mechanics will play a role in the behavior of things.

Given the philosophical problems of the Copenhagen interpretation, several other approaches to interpreting quantum mechanics have been proposed over the years. This chapter surveys four of these approaches, namely the many-worlds hypothesis, Bohmian “pilot waves,” positivist approaches, and spontaneous collapse of the quantum wave function. Problems with each of these approaches are discussed.

After having shown in previous chapters that wave-particle duality is not a fundamental problem for quantum mechanics, this chapter introduces the really strange effect of quantum mechanics, namely “nonlocal correlations” that appear to act over long distances faster than the speed of light. The “Copenhagen” interpretation of quantum mechanics is introduced, which puts human knowledge in a special role, and some of the philosophical objections to it.

This chapter explains what we mean by “fields” and “waves” in physics, and argues that quantum waves are just as “real” as other waves we experience in daily life, such as water waves and sound waves.