Quantum mechanics is widely believed to be inconsistent with local realism because J.S. Bell proved the contradiction between quantum mechanics and the hidden variable theories based on reality and locality of matter. As described herein, the relation between quantum mechanics and local realism is discussed. This paper presents the question of whether any version of local realism is contradicted by quantum mechanics. The answer is negative. An interpretation is proposed by which the contradiction is explained using physical variables of two types: (1) physical variables of the first type, such as positions and angles (i.e. coordinates), are realistic variables and always possess definite values independently of measurements; (2) those of the second type, such as momenta, angular momenta, and spins (i.e., conserved quantities), are non-realistic variables, which possess no value before measurement. Value definiteness of the first type provides a reliable basis to physical reality of matter, and non-reality of the second type might solve the problem of inconsistency between quantum mechanics and local realism.
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio
∣x∣/∣v∣ between the space coordinate
x and the velocity
v. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schrodinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function
ϕ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio
∣x∣/∣v∣ between the space coordinate
x and the velocity
v. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schrödinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function
ϕ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.