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In Section 1.1 we set out the ground rules by which an interpretation of quantum mechanics could be judged, assuming that no experimental tests are possible. The suggested criteria were economy, compatibility, plausibility, and insightfulness. In the succeeding sections we examined the Copenhagen interpretation and the transactional interpretation in the way that they deal with the problems of quantum mechanics and can be applied to experiments and gedanken experiments.

In the context of economy we have shown that the CI is somewhat less compact than the TI because CI1, CI2, and CI4 are essentially independent and seemingly unrelated elemental postulates of the interpretation. On the other hand the transactional model which is the essential content of TI4 brings with it the uncertainty principle (TI1) and the statistical interpretation (TI2) as consequences of the model.

In the context of compatibility we have shown that the SV collapse model implicit in CI4, if the SV is taken to be a mathematical description of the state of an extended system which is common to all observers of the system (CI4a), is descriptionally inconsistent with relativistic invariance and/or causality, and also appears to manifestly violate time reversal invariance at the descriptional level. The TI applied to the same system is fully consistent with relativistic invariance and macroscopic causality. While the TI implicitly involves an arrow of time in its account of the statistical interpretation (TI2), this arrow has been accounted for elsewhere in terms of a boundary condition model (Cramer, 1983).

The criterion of plausibility is admittedly more subjective than the other criteria. However, the author feels that the assertion of the TI that the advanced solutions of the relativistic QM wave equations play a role in quantum events (TI4) is intrinsically more plausible than the assertion of the CI that the solutions of these equations are somehow mathematical descriptions of knowledge (CI4). This is reinforced by the evidence of the deep-rooted philosophical and epistemological problems implicit in the "our knowledge" assertion.

Finally, in the context of insightfulness we have shown that by providing an explicit nonlocal mechanism for describing quantum events the TI has provided new insights into the reality behind the QM formalism. In doing so, it has also shown that a synthesis is possible between the ideas of Heisenberg and Bohr which emphasized the intrinsic uncertainty and complementarity of quantum processes, and the ideas of Einstein which emphasized the need to view the reality behind the formalism with an interpretation which is compatible with our understanding in other areas of physics.

Despite these advantages, there are many who will find the use of advanced waves in the transaction model difficult to accept because there is no experimental evidence for the existence of such a phenomenon. And certainly there are others who will feel that the whole notion of considering alternative interpretations of quantum mechanics when there is no possible experimental means of deciding between one interpretation and another is a kind of philosophizing which has no place in physics.

We answer such criticisms by reiterating that interpretation does have an important role on our understanding of physical theory, even if it is untestable at the experimental level, and that as far as possible, an interpretation should interpret (rather than decline to do so). What is presented here is a paradigm shift in the mode of quantum mechanical interpretation. As Kuhn (1962) has made clear, such paradigm shifts are always difficult because of the intellectual gear changing which is required. A shift away from the Copenhagen interpretation may be particularly difficult because of its traditional role in the teaching of quantum mechanics over five decades. But the value of new interpretational insights into physical processes should not be underestimated. Experience in many fields of physics has shown that progress and new ideas and approaches are stimulated by the ability to clearly visualize physical phenomena. Schrödinger described quantum mechanics as "a formal theory of frightening, indeed repulsive, abstractness and lack of visualizability" (Heisenberg, 1927). The visualization of quantum phenomena has been denied us for half a century, not by the abstract QM formalism but by the Copenhagen interpretation. The transactional interpretation of the same formalism now makes this long-sought visualization possible.

This work was supported in part by the Division of Nuclear Sciences of the U. S. Department of Energy. Teaching University of Washington undergraduates about quantum phenomena provided much of the stimulation and original inspiration for the ideas presented here. The opportunity for much of the contemplation and writing was provided by a sabbatical leave supported jointly by the University of Washington and the Hahn-Meitner Institute of Berlin. The author is indebted to many individuals for valuable discussions and correspondence, helpful suggestions, and good advice (sometimes ignored), and to many institutions for the opportunity to present these ideas at various stages of evolutionary development to varied audiences.

Among the individuals who deserve particular mention are (alphabetically): David Boulware, Wil Braithwaite, John Clauser, Kevin Coakley, Jorrit deBoer, Ernest Henley, Dieter Gross, Nick Herbert, Max Jammer, Hans Krappe, Dan Larsen, Albert Lazzarini, Chris Morris, Rudolph Moessbauer, Riley Newman, Rick Norman, Pierre Noyes, Rudi Peierls, Dennis Sciama, Saul-Paul Sirag, Derek Storm, Dan Tieger, John Wheeler, and Larry Wilets. Among the institutions which have made possible the presentation of these ideas in colloquia, seminars, and discussions are Carnegie-Mellon University, Michigan State University, the University of Washington, Los Alamos National Laboratory, the Esalen Institute, the University of Munich, the Hahn-Meitner Institute - Berlin, the Demokritos Laboratory for Nuclear Research - Athens, the Ruhr University - Bochum, and the University of Cologne. Thanks are due Bill Warren for the Schrödinger's Cat illustration. Finally, the author is deeply indebted to his wife Pauline B. Cramer, a pragmatic mechanical engineer, for many discussions, for the injection of much common sense, and for a great deal of encouragement.

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