Chapter 10, more than any other, makes this textbook unique. It explains the physics underlying quantum phenomena, with the aim of giving the student a clearer picture of quantum behavior and its causes, and thus making it easier for them to understand the further reading. The phenomenological approach of stochastic quantum mechanics, inspired by Nelson’s theory, shows the Markovian nature of the quantum description. The discussion then points to the vacuum or zero-point field mentioned in Chapter 2, as the source of the quantum stochasticity and characteristic wave-like phenomena. The theory thus developed, stochastic electrodynamics, is shown to provide a first-principles explanation for the operator formalism and related quantum postulates. The chapter concludes with a brief introduction of the hydrodynamic quantum analogue of a walking droplet, a striking macroscopic example of a particle-wave system capable of expressing quantum-like features under appropriate conditions.
Chapter 10, more than any other, makes this textbook unique. It explains the physics underlying quantum phenomena, with the aim of giving the student a clearer picture of quantum behavior and its causes, and thus making it easier for them to understand the further reading. The phenomenological approach of stochastic quantum mechanics, inspired by Nelson’s theory, shows the Markovian nature of the quantum description. The discussion then points to the vacuum or zero-point field mentioned in Chapter 2, as the source of the quantum stochasticity and characteristic wave-like phenomena. The theory thus developed, stochastic electrodynamics, is shown to provide a first-principles explanation for the operator formalism and related quantum postulates. The chapter concludes with a brief introduction of the hydrodynamic quantum analogue of a walking droplet, a striking macroscopic example of a particle-wave system capable of expressing quantum-like features under appropriate conditions.
Chapter 1 begins by introducing the quantum world as part of the physical world, not in opposition to or separate from the classical world. It then introduces the basic tools needed to work with quantum mechanics, and describes the scope and purpose of this textbook. It discusses how despite its successes, current quantum mechanics lacks adequate explanations for important observed atomic properties, suggesting an incompleteness of the theory. After a brief overview of its main interpretative issues , the chapter concludes with an introduction of the vacuum or zero-point field as the physical element that restores causality and serves to complete the quantum picture by providing a causal explanation of characteristic quantum phenomena.
In this chapter, which covers part of the course given at ELAF, a straight-forward procedure is presented that leads from the basic postulates of stochastic electrodynamics to the usual formalism of quantum theory. The theory thus developed is called linear stochastic electrodynamics, to underline that one of its basic features is the (asymptotic) linear response of atomic systems to the background field. The chapter starts with a brief discussion of some open questions in quantum theory and of the possibility to find an answer to them by resorting to the zeropoint radiation field as the source of the quantum behavior of matter. The basic properties of this field are discussed, and a brief enumeration is made of some of the positive results and vital shortcomings of standard stochastic electrodynamics. After identifying the source of these shortcomings in the assumption that the background field is not altered by its interaction with matter, linear stochastic electrodynamics is developed and shown to lead, under certain approximations, to a consistent picture of both matter and field quantization. In the concluding part, it is shown that also the electron spin can be considered to be generated by the interaction of the particle with the zeropoint field; in particular, the two-valuedness of the spin projection is associated with the existence of just two independent states of polarization of the field.
Quantum mechanics is a theory to explain and predict the behavior of particles such as electrons, protons, neutrons, atomic nuclei, atoms, and molecules, as well as the photon–the particle associated with electromagnetic radiation or light. From quantum theory we obtain the laws of chemistry as well as explanations for the properties of materials, such as crystals, semiconductors, superconductors, and superfluids. Applications of quantum behavior give us transistors, computer chips, lasers, and masers. The relatively new field of molecular biology, which leads to our better understanding of biological structures and life processes, derives from quantum considerations. Thus, quantum behavior encompasses a large fraction of modern science and technology. Quantum theory was developed during the first half of the twentieth century through the efforts of many scientists. In 1926, E. Schrödinger interjected wave mechanics into the array of ideas, equations, explanations, and theories that were prevalent at the time to explain the growing accumulation of observations of quantum phenomena. His theory introduced the wave function and the differential wave equation that it obeys. Schrödinger's wave mechanics is now the backbone of our current conceptional understanding and our mathematical procedures for the study of quantum phenomena. Our presentation of the basic principles of quantum mechanics is contained in the first three chapters. Chapter 1 begins with a treatment of plane waves and wave packets, which serves as background material for the subsequent discussion of the wave function for a free particle.
During the last decades there has been a relatively extensive attempt to develop the theory of stochastic electrodynamics (SED) with a view to establishing it as the foundation for quantum mechanics. The theory had several important successes, but failed when applied to the study of particles subject to nonlinear forces. An analysis of the failure showed that its reasons are not to be ascribed to the principles of SED, but to the methods used to construct the theory, particularly the use of a Fokker-Planck approximation and perturbation theory. A new, non perturbative approach has been developed, called linear stochastic electrodynamics (LSED), of which a clean form is presented here. After introducing the fundamentals of SED, we discuss in detail the principles on which LSED is constructed. We pay attention to the fundamental issue of the mechanism that leads to the quantum behaviour of field and matter, and demonstrate that indeed LSED is a natural way to the quantum formalism by demanding its solutions to comply with a limited number of principles, each one with a clear physical meaning. As a further application of the principles of LSED we derive also the Planck distribution. In a final section we revisit some of the most tantalizing quandaries of quantum mechanics from the point of view offered by the present theory, and show that it offers a clear physical answer to them.
Introduction to the Maths and Physics of Quantum Mechanics details the mathematics and physics that are needed to learn the principles of quantum mechanics. It provides an accessible treatment of how to use quantum mechanics and why it is so successful in explaining natural phenomena. This book clarifies various aspects of quantum physics such as ‘why quantum mechanics equations contain “I”, the imaginary number?’, ‘Is it possible to make a transition from classical mechanics to quantum physics without using postulates?’ and ‘What is the origin of the uncertainty principle?’. A significant proportion of discussion is dedicated to the issue of why the wave function must be complex to properly describe our “real” world. The book also addresses the different formulations of quantum mechanics. A relatively simple introductory treatment is given for the “standard” Heisenberg matrix formulation and Schrodinger wave-function formulation and Feynman path integrals and second quantization are then discussed. This book will appeal to first- and second-year university students in physics, mathematics, engineering and other sciences studying quantum mechanics who will find material and clarifications not easily found in other textbooks. It will also appeal to self-taught readers with a genuine interest in modern physics who are willing to examine the mathematics and physics in a simple but rigorous way. Key Features: Written in an engaging and approachable manner, with fully explained mathematics and physics concepts Suitable as a companion to all introductory quantum mechanics textbooks Accessible to a general audience
The Copenhagen interpretation has been the subject of much criticism, notably by De Broglie and Einstein, because it contradicts the principles of causality and realism. The aim of this essay is to study the wave mechanics as an alternative to traditional quantum mechanics, in the continuity of the ideas of Louis de Broglie: the pilot wave theory of De Broglie (where each particle is associated with a wave which guides it), De Broglie-Bohm theory, stochastic electrodynamics (where the stochastic character of particles is caused by the energy field of the fluctuating vacuum), and the analogies between quantum mechanics and hydrodynamics.