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Morgan & Claypool Publishers eBooks

Newton relativity and one-particle Galilean quantum theory

W. H. Klink, S. Wickramasekara

Published Mar 1, 2015• 0 citations
Publisher

Abstract

Mathjax On | Off Abstract As stated in the introduction, the principle of relativity does not determine what particular relativity is applicable to a given dynamical theory. Of the three possibilities we consider in this series of works, namely Newton, Einstein, and de Sitter relativities, Newton relativity is the simplest and was the first to be formulated. Perhaps for that reason, it is also the most intuitive.

DOI
10.1088/978-1-6270-5624-3ch2

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Mathjax On | Off Abstract As stated in the introduction, the principle of relativity does not determine what particular relativity is applicable to a given dynamical theory. Of the three possibilities we consider in this series of works, namely Newton, Einstein, and de Sitter relativities, Newton relativity is the simplest and was the first to be formulated. Perhaps for that reason, it is also the most intuitive.
The history of how quantum mechanics was developed is a fascinating one and underlies the focus of this book; namely, given the rules that the founders of quantum mechanics developed, is it possible to find principles that lead to the structure of quantum mechanics as it was historically formulated? This is the first book in a series of works considering what particular relativity is applicable to a given dynamical theory. The series considers Newton, Einstein, and de Sitter relativities, while this book examines the unitary irreducible representations of the Galilei group and see how they provide the framework for Galilean quantum theory.
Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the behavior of the quantum world baffling and strange. This book is the first in a series of three that argues that relativity and symmetry determine the structure of quantum theory. That is to say, the structure of quantum theory is what it is because of relativity and symmetry. There are different types of relativity, each leading to a particular type of quantum theory. This book deals specifically with what we call Newton relativity, the form of relativity built into Newtonian mechanics, and the quantum theory to which it gives rise, which we call Galilean (often misleadingly called non-relativistic) quantum theory. Key Features:* Meaning and significance of the term of relativity; discussion of the principle of relativity.* Relation of symmetry to relativity. Significance of the notion of representations of symmetry transformations in formulating a quantum theory.* Representations of Galilean symmetry and how they lead to the most common form of quantum theory.* Extension of Newtonian relativity to accelerating quantum systems and broadened quantum theory.
Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the behavior of the quantum world baffling and strange. This book is the first in a series of three that argues that relativity and symmetry determine the structure of quantum theory. That is to say, the structure of quantum theory is what it is because of relativity and symmetry. There are different types of relativity, each leading to a particular type of quantum theory. This book deals specifically with what we call Newton relativity, the form of relativity built into Newtonian mechanics, and the quantum theory to which it gives rise, which we call Galilean (often misleadingly called non-relativistic) quantum theory. Key Features: • Meaning and significance of the term of relativity; discussion of the principle of relativity. • Relation of symmetry to relativity. Significance of the notion of representations of symmetry transformations in formulating a quantum theory. • Representations of Galilean symmetry and how they lead to the most common form of quantum theory. • Extension of Newtonian relativity to accelerating quantum systems and broadened quantum theory.
Abstract Einstein’s lasting conviction that quantum mechanics was not a theory of principle did not impede him from recognizing that this theory was highly successful. As early as 1927, he publicly expressed his judgment that wave mechanics is ‘in amazing agreement with the facts of experience’ [ E1]. In 1936 he wrote, ‘It seems clear … that the Born statistical interpretation of the quantum theory is the only possible one’ [E2], and in 1949 declared, ‘The statistical quantum theory [is] the most successful theory of our period’ [E3]. Then why was he never convinced by it? I believe Einstein indirectly answered this question in his 1933 Spencer lecture-perhaps the clearest and most revealing expression of his way of thinking in later life. The key is to be found in his remarks on Newton and classical mechanics. In this lecture [E4], Einstein noted that ‘Newton felt by no means comfortable about the concept of absolute space, … of absolute rest … [and] about the introduction of action at a distance.
Mathjax On | Off Abstract In the preceding chapter, we showed how one-particle quantum states can be obtained from unitary irreducible representations of the Galilei group, the transformation group of Newton relativity. Since the Galilei group defines transformations amongst inertial reference frames, this description of one-particle quantum states is limited to inertial observers. In particular, observers who are accelerating are excluded in this description. This motivates the question of whether it is possible to provide a description of one-particle quantum states that holds for non-inertial observers by expanding the notion of Newton relativity to include non-inertial reference frames.
This paper is about a new paradigm shift in physics. According to Einstein, Newton’s theory of gravity is a first approximation of general relativity, which is Einstein’s theory of gravity, in the limit, which is when gravitational fields are weak and the velocities of masses (relative to a coordinate system) are small compared to the velocity of light. Since Schrödinger was aware of de Broglie’s relation when he formulated his quantum wave mechanics, it is acceptable to enforce the application of de Broglie’s relation in Schrödinger’s quantum wave mechanics. This enforcement leads to a new paradigm shift in physics.