of Quantum Theory

An elementary introduction to the statistical (ensemble) interpretation of quantum
theory ^{1} .

1 Motivation

2 Uncertainty Relations

2.1 Preparation and Measurement

2.2 Uncertainty from ”unsharp observables”

2.3 Individual and statistical predictions

2.4 Empirical support

3 Wave-Particle Duality

4 The Classical Limit

4.1 Two kinds of limit relations between classical theories

4.2 What is the ’standard limit’ of Schrödinger’s equation ?

4.3 The significance of the limit for the interpretation of quantum theory

5 Copenhagen Interpretation

5.1 Completeness requires metaphysics

5.2 An immediate consequence: The ’measurement problem’

5.3 Incompatible observables require more metaphysics

5.4 Even more metaphysics and several meanings of completeness

5.5 The EPR paper - the collapse of the Copenhagen interpretation

5.6 EPR, Bell, ”completeness”, and how the collapse became a paradox

6 Statistical Interpretation

6.1 ’No-go’ for hidden variables is not ’no-go’ for the statistical interpretation

6.2 Two attacks on the statistical interpretation

6.3 Wave function of single system by measurement ?

6.4 A list of publications related to the statistical interpretation

7 Statistical Quantization

8 Summary

9 Conclusion

References

2 Uncertainty Relations

2.1 Preparation and Measurement

2.2 Uncertainty from ”unsharp observables”

2.3 Individual and statistical predictions

2.4 Empirical support

3 Wave-Particle Duality

4 The Classical Limit

4.1 Two kinds of limit relations between classical theories

4.2 What is the ’standard limit’ of Schrödinger’s equation ?

4.3 The significance of the limit for the interpretation of quantum theory

5 Copenhagen Interpretation

5.1 Completeness requires metaphysics

5.2 An immediate consequence: The ’measurement problem’

5.3 Incompatible observables require more metaphysics

5.4 Even more metaphysics and several meanings of completeness

5.5 The EPR paper - the collapse of the Copenhagen interpretation

5.6 EPR, Bell, ”completeness”, and how the collapse became a paradox

6 Statistical Interpretation

6.1 ’No-go’ for hidden variables is not ’no-go’ for the statistical interpretation

6.2 Two attacks on the statistical interpretation

6.3 Wave function of single system by measurement ?

6.4 A list of publications related to the statistical interpretation

7 Statistical Quantization

8 Summary

9 Conclusion

References

Copyright © 2012 U. Klein

version 02, 11.12.2012

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.