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The Transactional Interpretation of Quantum Mechanics

by John G. Cramer

1.0 Introduction

"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. ... On the other hand, I think it is safe to say that no one understands quantum mechanics. ... Do not keep saying to yourself, if you can possibly avoid it, `But how can it be like that?', because you will get `down the drain' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."
R. P. Feynman (1967a)

It has been over half a century since that remarkable period of 1925-27 when modern quantum mechanics suddenly emerged from the work of Heisenberg (1925, 1927), de Broglie (1926, 1927a, 1927b), Schrödinger (1926a, 1926b, 1926c, 1926d, 1927a, 1927b), and Born (1926a, 1927b, 1927), and quickly replaced Newtonian mechanics and the "old quantum theory" of Planck, Einstein, and Bohr as the standard theory for dealing with all microscopic phenomena. The mathematical formalism of quantum mechanics, though refined and generalized in the intervening decades, has never been seriously challenged either theoretically or experimentally and remains as firmly established today as it was in the 1930's.

And yet over the entire period since the original development of quantum mechanics there has been controversy surrounding its interpretation. The questions of the meaning of the mathematics and of the underlying reality behind the laws and procedures of quantum mechanics have been a battlefield for five decades, and no truce is yet in sight. The controversy has, in fact, recently been intensified. The "spooky actions at a distance" which Einstein (1947) perceived in quantum mechanics seem to have been demonstrated by the theoretical work of J. S. Bell (1964, 1966) and the experimental work which has followed from it (Freedman, 1972; Clauser, 1978; Aspect, 1982a, 1982b). This body of work (Clauser, 1978; Stapp, 1971, 1982) makes a compelling case that quantum mechanics (and nature) cannot simultaneously have the properties of "locality" and "contrafactual definiteness", but rather must lack one or the other (or both).

1.0.1 Contrafactual Definiteness

The term contrafactual definiteness {footnote 1} (CFD) used here was introduced by Stapp (1971; see also Herbert, 1978) as a minimal assumption. It means that for the various alternative possible measurements (perhaps of non-commuting variables) which might have been performed on a quantum system, each would have produced a definite (but unknown and possibly random) observational result and further that this set of results is an appropriate matter for discussion. CFD is actually a rather weak assumption and is often employed by practicing physicists in investigating and discussing quantum systems. It is completely compatible with the mathematics of quantum mechanics but is in some conflict with the positivistic element of the Copenhagen Interpretation (Section 2.0) and with certain other interpretations (Appendix A.4).

The term locality {footnote 2} means that the separated parts of the system described are assumed to remain correlated only so long as they retain the possibility of speed-of-light contact and that when isolated from such contact the separated parts can retain correlations only through "memory" of previous contact. The term nonlocality implies the converse of this, e.g., correlations established faster-than-light across spacelike or negative timelike intervals. One should make the distinction between nonlocal enforcement of correlations, which is at issue here, and nonlocal communication, which (although sometimes confused with the former) is a far stronger condition. This distinction will be clarified later.

1.0.2 Nonlocality and Formalism

The mathematics of quantum mechanics does not deal explicitly with such nonlocal correlations. It does, however, require that any separated measurements of the properties of an extended system be treated as parts of the same quantum mechanical "state", regardless of the degree of separation of the measurements in time and/or space. This common-state requirement could be interpreted as a kind of de facto nonlocality, but that association is not conventionally made in applying the CI to the mathematics.

Mermin (1985) has suggested that on the question of whether there is some fundamental problem with quantum mechanics signalled by tests of Bell's inequality, physicists can be divided into a majority who are "indifferent" and a minority who are "bothered". If there were a prevailing view among this concerned minority as to the resolution of the above dichotomy, CFD vs. locality, it would probably be that CFD, although pragmatically useful in practical applications and discussions of quantum mechanics, must be philosophically abandoned to positivism because the alternative of nonlocality is unacceptable. It is perceived by some that nonlocality must be in direct conflict with special relativity because it could be used, at least at the level of gedanken experiments, for "true" determinations of relativistic simultaneity and must be in conflict with causality {footnote 3} because it offers the possibility of backward-in-time signalling. But this view is at best questionable. While it is clear that nonlocal communication between observers could lead to such conflicts, the minimum nonlocal correlations required to invalidate the Bell locality postulate are compatible with both relativity and causality.

The alternative approach to the dichotomy, and that which is advocated in the present work, is to retain CFD while abandoning locality. Contrary to what might be expected, this does not require any revision of the mathematical formalism of quantum mechanics, but only a revision of the interpretation of the formalism. The transactional interpretation of quantum mechanics (TI), which is the new interpretation presented below, is explicitly nonlocal but is also relativistically invariant and fully causal. It is consistent with all of the familiar theoretical predictions and experimental demonstrations of conventional quantum mechanics {footnote 4}, and indeed provides new insights into some of the more counter-intuitive aspects of the quantum mechanical formalism, as will be discussed in Chapter 4.

1.0.3 Overview of Contents

In the body of this paper we will review the Copenhagen interpretation and the interpretational problems of the quantum mechanical formalism which it is designed to resolve. We will then present the transactional interpretation and examine the way in which it deals with the same problems. Finally, we will consider a number of new and traditional gedanken experiments and interpretational paradoxes as illustrative examples of the applications and power of the TI. We will find that the transactional interpretation deals with these problems in a deeper and more intuitive way.

In the main body of the present paper we will not consider other alternatives to the Copenhagen interpretation that have been proposed, but rather will reserve discussion of some of these for an appendix. Further, we will not consider the rather orthogonal approach of quantum logic, which would bypass considerations of interpretation and supply instead a revision of conventional logic better suited to the quantum mechanical formalism. We find here that standard logic can meet the needs of the quantum mechanical formalism when a proper interpretation of that formalism is provided.

1.1 Ground Rules

In the present paper, when we explicitly examine a formalism of quantum mechanics in the context of interpretation, we will restrict our consideration to Schrödinger-Dirac formalism (Dirac, 1930) of wave mechanics. Although that formalism is perhaps less elegant than some of its alternatives, we find it to be the most transparent to interpretation. Because of the complete equivalence (Schrödinger, 1926c) between the wave mechanics formalism and its principal alternatives, no loss of generality is incurred through this restriction. For reasons which will be discussed later, we will assume that the wave equations describing the system under consideration are relativistically invariant.

The task which we have undertaken here is a critical comparison of the Copenhagen interpretation with the new transactional interpretation presented below. Interpretations of a physical theory cannot normally be subjected to experimental verification. For this reason, it will be necessary to use criteria other than appeal to experiment to make any sort of critical comparison. We would like to list those criteria explicitly here:

  1. Economy (Occam's Razor): It is preferable in constructing the interpretation to use a minimum number of independent postulates.
  2. Compatibility: It is preferable that the non-observable constructs of the interpretation be compatible with physical laws, even when such laws are not directly related to the theory being interpreted, i.e., quantum mechanics. In the present case we will employ the laws of relativistic invariance, macroscopic causality, and time reversal invariance in this context. [The violation of this criterion, i.e, the violation of a physical law by an interpretational construct, is what is sometimes called an "interpretational paradox". These are to be avoided.]
  3. Plausibility: It is preferable that the mechanisms, if any, employed by the interpretation should be physically plausible. Common sense is not always a reliable guide in physics, but it can often help in making a relative choice between otherwise equal alternatives.
  4. Insightfulness: It is preferable that an interpretation provide insight into the underlying mechanisms of nature behind the mathematical formalism. Providing insight into the fundamental processes of nature is an important function of an interpretation. For example, the interpretational concept of field lines introduced by Faraday, while unnecessary to the formalism of electrodynamics, provides a rich and powerful medium for gaining insights into the operation of electromagnetic phenomena.

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