This introductory chapter outlines the differences between classical physics and quantum physics by positing three imaginary worlds. World 1 is governed by the laws of classical Newtonian mechanics, World 2 by classical field physics, and World 3 by quantum physics. The point is that classical physics deals with well-defined, continuously-existing physical quantities, including trajectories, while quantum physics is fundamentally about physical quantities defined in terms of probability functions.
This introductory chapter outlines the differences between classical physics and quantum physics by positing three imaginary worlds. World 1 is governed by the laws of classical Newtonian mechanics, World 2 by classical field physics, and World 3 by quantum physics. The point is that classical physics deals with well-defined, continuously-existing physical quantities, including trajectories, while quantum physics is fundamentally about physical quantities defined in terms of probability functions.
The behavior of classical macroscopic particles – from baseballs to planets – is governed by Newtonian mechanics as we have described in the first chapters of this book. The behavior of very small particles, on the other hand, is governed by an entirely different collection of equations and rules that go under the name of “quantum mechanics” and these particles are referred to as quantum particles. These rules have analogies to classical mechanics, but are fundamentally different and somewhat mysterious as we discussed in Chapter 8. The fundamental principles of quantum mechanics cannot be proven to be correct. They were developed based on the results of experimental observation, by analogy with classical mechanics, and through the consideration of logical implications of the formalisms used. There is no way to derive the fundamental elements of quantum mechanics, any more than one could predict from first principles that Newtonian forces should add as vectors. On the other hand, quantum mechanics is among the most rigorously tested theories in science, and the predictions of quantum mechanics have, so far, always been in agreement with experiment. In this chapter, we will present quantum mechanics as a series of postulates and examine their implications in application to simple one-dimensional systems. In the next chapter we will examine quantum effects in real systems including atoms, molecules, crystals, and artificially engineered nano-structures. Postulates of quantum mechanics QM Postulate 1: A quantum particle is described by a wave function Ψ( x , y , z , t ) which is a function of spatial coordinates and time. All physically determinable quantities can be derived from the wave function Ψ( x , y , z , t ) ; quantities which cannot be found from the wave function are not physically meaningful. Note that some things that one could ask about a quantum particle, for example the exact position and simultaneous exact momentum of a particle, are not derivable from the wave function and are therefore considered indeterminate (or uncertain ). These are things which cannot ever be known about a particle, and, as such, they are meaningless to contemplate.
What is quantum mechanics and what does it do ? In very general terms, the basic problem that both classical Newtonian mechanics and quantum mechanics seek to address can be stated very simply: if the state of a dynamic system is known initially and something is done to it, how will the state of the system change with time in response ? In this chapter, we will give a brief overview of, first, how Newtonian mechanics goes about solving the problem for systems in the macroscopic world and, then, how quantum mechanics does it for systems on the atomic and subatomic scale. We will see qualitatively what the differences and similarities of the two schemes are and what the domain of applicability of each is. Brief overview of classical mechanics To answer the question posed above systematically, we must first give a more rigorous formulation of the problem and introduce the special language and terminology (in double quotation marks) that will be used in subsequent discussions. For the macroscopic world, common sense tells us that, to begin with, we should identify the “system” that we are dealing with in terms of a set of “static properties” that do not change with time in the context of the problem. For example, the mass of an object might be a static property. The change in the “state” of the system is characterized by a set of “dynamic variables.
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wavefunctions or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?
During the past two or three centuries western philosophy and science have confirmed each other in their ontological attitude towards external reality. The particular opinion that physical objects have an existence completely independent of observation was established as the necessary basis for all scientific investigation. The discovery in quantum physics that the phenomena ultimately constituting the stability of the material world cannot be separated from the instruments of observation was necessarily felt disastrous to the scientific world-picture, and many philosophers and scientists, including celebrated physicists, are still trying by all means to save ontology in quantum physics. The motive power behind this activity is the belief that the objectivity of science can be maintained only if the elementary particles of matter can be objectified in the usual way. The present chapter deals with the fundamental conditions in quantum physics which entail a complete breakdown of the conceptual frame of classical mechanics
Quantum physics was born to describe the curious and common-sense denying micro-universe within the atom. Today, physicists tell us that it is actually the most accurate way to describe everything that exists, including ourselves. They tell us that we live in “a quantum world.” This world is made of energy, not “bits of matter,” and everything and everyone who exists in this world is actually an evolving pattern of dynamic energy. The quantum world is also made of relationships, and everything and everyone is in relationship with, is “entangled” with, everything and everyone else. This is “quantum holism.” The quantum world is indeterminate, and thus unpredictable, creatively “feeling” its way into the future through self-organization. It is a world where questions are more important than answers, and we people who ask those questions “co-authors of reality.” These and other key defining elements of the quantum world will be discussed in this chapter, and contrasted with the defining elements of the earlier, Newtonian physics and Newtonian world.
This chapter begins by explaining why physics is the fundamental of all natural sciences. Throughout most its history, atoms were hardly the center of attention in physics. Once called natural philosophy, physics originated in the study of the motion of inanimate objects. From those studies emerged a body of knowledge, including various natural laws, that today we call ‘classical’ physics. Newton's laws of motion, the basis of the science of mechanics, come to mind, as does his law of universal gravitation. These laws are obeyed by objects that in some sense are ‘large’ and, in fact, the laws were discovered after careful observation of the behavior of such objects. The discussion then turns to the focus of the book—the quantum world—where the laws of physics turn out to be different from the laws of classical physics used to explain phenomena in the macroscopic world of everyday life. The book discusses a number of mostly recent experiments on quantum mechanical foundations, most of them involving light at the level of a few photons—sometimes only one.