Quantum Theory without Reduction,

Cini

• Publisher: CRC Press
• Year: 2017
• eBook ISBN: 9781351420341
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Quantum theory offers a strange, and perhaps unique, case in the history of science. Although research into its roots has provided important results in recent years, the debate goes on. Some theorists argue that quantum theory is weakened by the inclusion of the so called "reduction of the state vector" in its foundations. Quantum Theory without Reduction presents arguments in favor of quantum theory as a consistent and complete theory without this reduction and as a theory capable of explaining all known features of the measurement problem. This collection of invited contributions defines and explores different aspects of this issue, bringing an old debate into a new perspective and leading to a more satisfying consensus about quantum theory. The book will be of interest to researchers in theoretical physics and mathematical physics involved in the foundations of quantum theory. Scientists, engineers, and philosophers interested in the conceptual problems of quantum theory will also find this work stimulating.

Principle of Stationarity in the Action Functional and the Theory of Measurement

R. FUKUDA

1. FLUCTUATION AND MACROVARIABLES

The measurement problem in quantum mechanics is certainly one of the profound problems in the theoretical physics. It has a long history and for the present status we refer for instance to the proceedings of the 2nd ISQM edited by Namiki et.al. (1986). Those of the 3rd ISQM will appear soon (1989). In this paper we start from the following observation which is somewhat different from the conventional approach.

The classical Newtonian mechanics does not have any measuring problem, any dynamical variables q_i(i=1~N) satisfying the deterministic equation of motion. If the system is discussed quantum mechanically, q_i satisfies the same equation of motion as the classical one but it is now the operator equation since q_i is an operator due to the canonical commutation relation between q_i and the momentum p_i. The non-commutativity is the source of the quantum fluctuations and these uncontrollable fluctuations are the cause of the measurement problem in quantum mechanics.

If we can find the fluctuationless variables in quantum system, the problem of measurement becomes parallel with that of the classical system. Therefore the solution to our measurement problem is the search for...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• List of Contributors
• Where is the Problem?
• Experiment and Quantum Measurement Theory
• A Consistent Interpretation of Quantum Mechanics
• The Measurement Process in the Individual Interpretation of Quantum Mechanics
• Principle of Stationarity in the Action Functional and the Theory of Measurement
• Quantum (Statistical) Mechanics, Measurement and Information
• State Vector Collapse as a Classical Statistical Effect of Measurement
• Consecutive Quantum Measurements
• No-collapse Versions of Quantum Mechanics
• An Attempt to Understand the Many-worlds Interpretation of Quantum Theory
• Uncertainty and Measurement