Abstract

This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties, and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version.

Highlights

  • Quantum mechanics was originally developed for the world of atoms and electrons, where it has been very successful

  • It is even paradoxical because the bodies of the everyday world are composed of atoms and electrons, which ought to be described by quantum mechanics

  • Similar results can be obtained for further thermodynamic properties such as specific heat, elasticity coefficient, etc

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Summary

Introduction

Quantum mechanics was originally developed for the world of atoms and electrons, where it has been very successful. According to Bohr, realism applies only to the results of quantum measurements, which can be described by the relation between objective classical properties of real classical preparation and registration apparatuses. Some structural properties can be measured directly by a registration (on individual quantum systems) and their values are real numbers. We shall not attempt to obtain from quantum mechanics the sharp trajectories that is a concept of general language part of Newtonian mechanics, but rather try to model the observed fuzzy trajectories of specific classical systems (Section 4), or to analyse different specific registration apparatuses first and try to formulate some features common to all (Section 5). It seems that the objective properties of quantum systems, if there are any, cannot be directly related to individual registrations, as they can in classical theories.

Part I
States
Mathematical preliminaries
76. There is a useful relation between faces and projections
General rules
Observables
Joint measurability
Contextuality
Superselection rules
Galilean group
Closed systems
Time translations
Composition of quantum systems
Tensor product of Hilbert spaces
Entanglement
Composition of identical systems
Identical subsystems
Cluster separability
Mathematical theory of D-local observables
Separation status
Change of separation status
State reduction
Part II
Quantum models of classical properties
Modified correspondence principle
Maximum entropy assumption in classical mechanics
Classical ME packets
Definition and properties
Classical equations of motion
Quantum ME packets
Calculation of the state operator
Diagonal representation
Quantum equations of motion
Classical limit
A model of classical rigid body
P2 2M0
Maximum-entropy assumption
The length of the body
The bulk motion
Joint measurement of position nd momentum
Quantum models of preparation and registration
Old theory of measurement
Example
Attempts at improvement of the old theory
New theory of measurement
Models of direct registrations
Ideal detectors
Non-ideal detectors
Particle tracks in detectors
General assumption for models of direct registration
Comparison with other changes of separation status
Scattering on macroscopic bodies
Linear superposition of large quantum systems
Conclusions
Full Text
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