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Chapter 1

Introduction

1.1 A new understanding of reality

There have been some major upheavals in the history of science, when humans were forced to rethink their deeply entrenched ideas of reality, with the result that a prevailing worldview had to make room for a new emerging worldview. Such upheavals — or paradigm shifts — include Copernicus’ heliocentric solar system, Newton’s discovery that the laws of gravity and motion are the same on the earth as on the distant stars, Maxwell’s insight into the nature of light as an electromagnetic wave, Darwin’s theory of evolution according to which humans and animals have a shared origin, and Einstein’s Relativity that brought together space, time and gravitation. Some of these discoveries provoked great consternation, since they conflicted with dominant philosophical and religious worldviews. Others were controversial within the scientific community, but with the growing success of the scientific method — according to which theories must be tested by experiment — controversies gradually yielded to consensus.

There is one significant discovery, not mentioned in the foregoing paragraph, which stands apart from all the others. The genesis of quantum theory represents the greatest intellectual leap that science has taken in the history of human civilization.

By the end of the nineteenth century, science had scored a decisive victory as a means of defining a reality that could be agreed upon by everyone regardless of their spiritual, religious or metaphysical traditions. Science had established the material universe with its component objects as an absolute reality that was independent of every subjective belief and perception. Reality was out there. Our scientific observations did not create reality, but only served to confirm the reality that was in existence whether we chose to notice it or not. A tree that fell in a forest made a sound regardless of whether anyone heard it.

A falling tree makes a sound even if no one hears it

Observation could not create reality. Nor could observation alter reality. And reality in the study of physics included every physical property of a material object. So, for a particle in motion, reality included its mass, its velocity (both magnitude and direction) and its position at every instant of time — which we call the trajectory of the particle. While an actual physical observation might interfere with what is being observed, it was believed that in principle one could make the instruments so sensitive that the measurement would provide an arbitrarily accurate map of every single detail of the concrete reality that was already out there. This was the triumph of nineteenth century physics. Then quantum theory came along and yanked the rug from under this long drawn out victory that science had won.

1.2A theory of particles and fields

But quantum theory does not deny reality. Far from it. Indeed, a century after the birth of this theory it is now accepted as the most accurate and most detailed description of reality that human intelligence has developed. Quantum theory does not claim that mass, energy, momentum, electric charge and other observable quantities are illusions. But it does assert that every measurement is necessarily an interaction between the object that is being studied and the subject that is doing the studying, and that in this interaction there is a limit to the information that can be obtained by the subject from the object. And this limit is not due to any imperfections in the experimental apparatus that is currently available, but is due to the very nature of reality.

Many of the rules of quantum theory run counter to what we might expect on the basis of intuition. For example, quantum theory says there is no such thing as a trajectory of a particle. Particles move from point to point in space without having an intervening path or trajectory, something that was unheard of in physics prior to the twentieth century. Trajectories are meaningful only for large objects such as baseballs, bullets and planets, all which contain billions of microscopic particles. But the individual microscopic particles themselves do not behave the same way as enormous aggregates of particles do. Indeed, the most accurate statement we can make about these particles is that they do not even exist until they are detected!

Microscopic particles have no color and even the idea of shape has little meaning in this realm. And because they have no trajectories, it becomes impossible to picture them in our minds. And so quantum theory is necessarily abstract. This abstraction arises from the very nature of the behavior of microscopic objects. And in the realm of physics the language of abstraction has a mathematical shape. The mathematical methods used in quantum theory constitute what is known as quantum mechanics. In this introductory book we will not study quantum mechanics in detail, though we shall touch upon some of the basic principles of quantum mechanics. The bibliography at the end of this book lists some excellent books for the reader who wishes to move on to a rigorous study of the subject.

Quantum physics has important applications such as the photoelectric cell, positron electron tomography, the electron microscope, superconducting magnets, etc. But in this book we shall focus on the theory, with at most a cursory mention of important applications.

Quantum theory can be described as a study of particles and fields.¹ Particles and fields were both studied by classical physics. In classical physics these two entities were studied distinctly. So we had one sort of physics that described particles, and another sort of physics that described fields. Newton’s Laws of motion describe particle motion, and Maxwell’s equations describe the electromagnetic field. But in quantum theory both these entities come together. A particle is a particle of a field, and a field is a field of a particle. This statement may sound meaningless, but it expresses a very basic concept of quantum theory. But before we attempt to unpack this concept, we shall perform a review of classical physics (Chs. 2, 3 and 4) to get a better understanding of particles and fields in their own right.

The word particle means a solid object that is sufficiently small so that its dimensions can be neglected, and our interest is only in the motion of the particle. A particle could be physically as small as an electron, but if we are considering the dynamics of the solar system as a whole, an entire planet can be considered as a particle, since the size of the planet is small compared to the radius of its orbit round the sun. Particles feature prominently in the mechanics based on Newton’s laws of motion.

The word field signifies a region of space that has an effect on certain particles that are present in that region. An apple that hangs from a tree experiences a force caused by the earth’s gravitational field. A charged particle such as an electron is affected by electric and magnetic fields. A positively charged proton creates an electric field that extends in all directions leading away from the proton. This field gets progressively weaker as one moves further away. If another charged particle — say an electron — were to be brought near the proton, it would experience a force of attraction towards the proton. So in this case the proton is like the earth which produces the field, and the electron is like the apple which experiences a force due to the field. (For the sake of accuracy we clarify that both the earth and the apple generate their own gravitational fields, and both the proton and the electron generate their own electric fields.)

1.3 Outline of the book

We will first do a quick review of the classical physics of particles which will give us a lead into the notion of particles in quantum theory. Chapter 2 will cover the fundamental classical mechanics of particle motion. It is impossible to understand modern physics without a basic knowledge of classical Newtonian physics. Chapter 3 will examine the significance of the atomic structure of matter. This chapter is entitled Statistical Mechanics to draw attention to this very important area of physics. Statistical mechanics played a historical role in the advent of quantum theory, as will be explained in Ch. 5, and today figures prominently in the rapidly growing branch of physics called quantum information theory. Chapter 4 will outline the classical physics of fields — specifically gravitational and electromagnetic — which will set up the background for understanding the notion of a field in quantum theory. The subsequent chapters will explain quantum theory in detail, beginning with its historical origin in Ch. 5. An important concept in modern quantum theory is entanglement, which cannot be appreciated without a knowledge of Relativity, and so Chs. 8 and 9 are devoted to explaining the concepts and the implications of Einstein’s Special Theory of Relativity. We keep the mathematics to a bare minimum throughout, because this book is meant to serve as an introduction that is accessible to readers who may not have a strong mathematical background.

Quantum mechanics is a thoroughly mathematical discipline, requiring algebra and calculus. But because our aim is to avoid mathematics as far as that is possible, we will not do much quantum mechanics in this book. Nevertheless, the foundational principles of quantum mechanics can be learnt without a great deal of mathematics, and so we will present these principles in the course of this book.

Numerical calculations are helpful for gaining a better understanding of physics, and so we have provided simple numerical exercises throughout the book. A knowledge of basic algebra is sufficient to work out these exercises. Answers to the exercises (where required) are provided in an appendix at the end of the book.

¹In older textbooks quantum theory was commonly described as a study of particles and waves. While there are good historical reasons for this description, in the calculations of quantum theory today we deal mostly with abstract fields and observable particles.