of Quantum Mechanics

This paper was originally published in Reviews of Modern Physics **58**, 647-688, July
(1986). It is copyrighted (©1986) by John G. Cramer and the American
Institute of Physics and may not be reproduced without permission. Reproduction of single printed copies for personal non-commercial use is authorized.

See also *"An Overview of the Transactional Interpretation of Quantum Mechanics",* published in the International Journal of Theoretical Physics **27**, 227 (1988).

The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen Interpretation (CI) of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI), is presented. The basic element of TI is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The TI is explicitly nonlocal and thereby consistent with recent tests of the Bell Inequality, yet is relativistically invariant and fully causal. A detailed comparison of the TI and CI is made in the context of well known quantum mechanical gedanken experiments and "paradoxes". The TI permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the CI. The TI is shown to provide insight into the complex character of the quantum mechanical state vector and the mechanism associated with its "collapse". The TI also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law [P=], basic elements of the CI.^{*}

- 1.0 Introduction
- 2.0 What is the Copenhagen Interpretation?
- 2.1 Identity: What is the state vector?
- 2.2 Complexity: Why is the state vector a complex quantity?
- 2.3 Collapse: How and why does the state vector abruptly change?
- 2.4 Nonlocality: How are Correlations of Separated Parts of the State Vector Arranged?
- 2.5 Completeness: Do Canonically Conjugate Variables have Simultaneous Reality?
- 2.6 Predictivity: Why Cannot the Outcome of an Individual Quantum Event Be Predicted?
- 2.7 The Copenhagen Interpretation and the Uncertainty Principle

- 3.0 The Transactional Interpretation of Quantum Mechanics
- 3.1 Advanced Waves and Wheeler-Feynman Absorber Theory
- 3.2 The Emitter-Absorber Transaction Model
- 3.3 The Transactional Model and Relativistic Quantum Mechanics
- 3.4 The Transactional Interpretation
- 3.5 The Transactional Interpretation and the Formal Notation of QM
- 3.6. Identity and Complexity in the Transactional Interpretation
- 3.7 Collapse and Nonlocality in the Transactional Interpretation
- 3.8 Completeness and Predictivity in the Transactional Interpretation
- 3.9 Relativity and Causality in the Transactional Interpretation
- 3.10 The Arrow of Time in the Transactional Interpretation

- 4.0 Examples of Application of the Transactional Interpretation
- 4.1 Renninger's Negative-Result Gedanken Experiment
- 4.2 Wheeler's Delayed-Choice Experiment
- 4.3. Schrödinger's Cat and Wigner's Friend
- 4.4. Transmission of Photons through Non-Commuting Polarizing Filters
- 4.5 The Freedman-Clauser Experiment and Herbert's Paradox
- 4.6 The Hanbury-Brown-Twiss Effect
- 4.7 The Albert-Aharonov-D'Amato Predictions

- 5.0 Conclusion
- A.0 Alternative Interpretations of Quantum Mechanics
- A.1 Hidden Variable Theories
- A.2 Semiclassical Interpretations
- A.3 "Collapse" Interpretations
- A.4 The Many-Worlds Interpretation
- A.5 Advanced-Action Interpretations
- A.6 Stapp's Nonlocal Model

- List of Figures
- Footnotes
- References
- List of citations of this paper in the literature
since its publication in 1986.

*This page was created by John G. Cramer on 7/1/96.
*