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**A.0 Alternative Interpretations of Quantum Mechanics**

In the discussion in the main body of this paper we have focused on the orthodox formalism of quantum mechanics and on its interpretation by the Copenhagen and transactional approaches. In doing this we have not discussed the efforts of individuals and groups who have investigated other ways of dealing with the interpretational problems of the quantum mechanical formalism. For a comprehensive review of such efforts the reader is referred to the excellent survey provided by Jammer (1974). Here we briefly summarize some of the alternative interpretations and theories which have had a significant impact on the field and consider these in the framework of the discussion of interpretational problems in Section 2 of this paper.

The hidden variable alternatives to the formalism of quantum mechanics (Belinfante, 1973; Jammer, 1974) have been aimed primarily at the problems of completeness and predictivity (see Sections 2.5 and 2.6) and have conventionally started from the assumption of locality. By asserting the existence of unobserved variables which would eliminate the indeterminacy of quantum mechanics if their values were known, they have attempted to demonstrate that quantum mechanics is an incomplete theory.

Hidden variable theories are able to deal at some level with some of the interpretational problems of Section 2 by avoiding SV collapse through the use of deterministic hidden variables. The SV is treated as an average and incomplete description of the system, and so the "knowledge" issue does not arise. The Bell inequality experiments have at a stroke invalidated all hidden variable theories which are based on the locality assumption. While a hidden variable theory could, in principle, be constructed which was nonlocal and compatible with the Bell inequality experimental results, such a approach would lose much of its intrinsic classical appeal and would run the risk of conflicts with relativity and causality. It remains to be seen whether any new hidden variable theory can successfully come to terms with nonlocality, the experimental results, and the relativity/causality dilemma.

**A.2 Semiclassical Interpretations**

Perhaps the most widely "accepted" semiclassical interpretation is the "disturbance model" (Herbert, 1985). This is the notion, often introduced as a pedagogical tool in elementary textbooks on modern physics, that canonically conjugate variables of a particular system under study, e.g., position and momentum, can "actually" have simultaneous well-defined values, but that the act of making a measurement of one of these variables "disturbs" the other so that no knowledge of it can be obtained. Heisenberg reportedly used this model in his early thinking (Rosenfeld, 1971a) but later discarded it when he realized its inadequacy. The disturbance model has been refuted again and again, most recently by the experimental tests of Bell's Inequality, but remains as a widely held interpretation of quantum mechanics used by a sizable segment of the community of practicing physicists. A second early and unsuccessful semiclassical interpretation, that of Schrödinger has already been discussed in Section 2.

The "guide wave" interpretation (GWI) of de Broglie, which is also a semiclassical interpretation, was invented very early in the development of quantum mechanics (about 1925) and is said to be responsible for stimulating the development of the Schrödinger equation and for the emphasis on the wave aspects of quantum mechanics which were so important to the early development.

The GWI suggests a specific underlying mechanism for the interplay of waves and particles in a quantum event. It has been described in a number of publications of de Broglie (1926, 1927a, 1927b, 1960, 1964, 1968). For example, de Broglie (1968) gave the following summary:

"... a particle is a very small object which is constantly localized in space and a wave is a physical process which is propagated in space in the course of time according to a given equation of propagation. ... The wave has a very low amplitude and does not carry energy, at least not in a noticeable manner. The particle is a very small zone of highly concentrated energy incorporated in the wave, in which it constitutes a sort of generally mobile singularity. By reason of this incorporation of the particle in the wave, the particle possesses an internal vibration which, as it moves, remains constantly in phase with the vibration of the wave. ... the mean path of the particle is determined according to the shape of the wave by a certain 'guidance law', but this motion has superimposed on it continual fluctuations corresponding to a hidden variable behavior of the particles."

From this summary it should be apparent that the GWI presents a very different view of quantum events from that of the Copenhagen interpretation. The "wave" in the above description is the SV itself, which has a definite but limited reality in that it can physically travel through space but it cannot carry energy, momentum, etc. The collapse does not occur, but is replaced by the action of the particle which "rides" the SV and arrives with the largest probability at the locations where the SV has the largest amplitude, the general properties of the SV being separated from those of the specific particle which tracks it.

The problem of complexity is not addressed, but is not serious because the SV is given only limited reality. The predictivity of the picture is a problem, since the particle does not follow the path of greatest amplitude of the SV, as might be expected, but rather follows the wave in a random "thermodynamic" way.

The most serious problem of the GWI is that it makes no provision for nonlocalities of the second kind and is implicitly local. It is therefore inconsistent with the Bell inequality experiments. There are also grounds for believing that it may be inconsistent with the formalism of quantum mechanics. Recent papers (Garuccio et al, 1981, 1982) have asserted that there are experimental tests which can distinguish the predictions of the GWI from those of orthodox quantum mechanics. This is because in certain situations involving the interference of incoherent sources the GWI would predict interference effects which are absent in orthodox calculations.

From a certain point of view, the GWI can be taken as a kind of preliminary version of the TI presented here. It is completely consistent with the TI in most of its aspects, and its principal shortcomings are its lack of a nonlocal mechanism which can account for correlations in separated measurements and the ad hoc way that the particle and its properties are introduced. But if de Broglie's particle is identified with the transaction of the TI then the picture presented is very close that presented in Section 3 above. Thus the penetrating intuitive insight of de Broglie was not only crucial to the early development of quantum mechanics, but it also came very close to the nonlocal interpretation presented here.

**A.3 "Collapse" Interpretations**

As discussed in Section 2.3, the abrupt and discontinuous collapse of the SV implied by the formalism of quantum mechanics and its treatment by the CI have been the source of many of the interpretational problems. Therefore, there have been a number of attempts to provide a more plausible account of the SV collapse process.

One of the early alternative collapse models was suggested first by Darwin (1929) but was more widely publicized through the work of von Neumann (1932), London and Bauer (1939), and Wigner (1962). Wigner in particular popularized the model, and we quote him to describe it:

Wigner goes on to introduce what has become known as the Wigner's Friend paradox which was discussed in Section 4.6 above. He uses this gedanken experiment to illustrate the plausibility of his model and the implausibility of several alternatives."... the result of an observation modifies the wave function of a system. The modified wave function is, furthermore, in general unpredictable before the impression gained at the interaction has entered our consciousness: it is the entering of an impression into our consciousness which alters the wave function because it modifies our appraisal of the possibilities of different impressions which we expect to receive in the future. It is at this point that the consciousness enters the theory unavoidably and unalterably."

This "consciousness" interpretation, while it is a reasonable working hypothesis for an observer who does not wish to find himself dissolved into the state vector of the system which he is measuring, does beg a number of question: Did the SV of the universe remain uncollapsed until the first consciousness evolved? Where is the borderline between consciousness and unconsciousness? Will "smart" measuring instruments eventually achieve the ability to collapse SV's, and how will one know when they do? And so on ...

Schrödinger (1935) suggested an alternative to the consciousness interpretation which he called the principle of state distinction, and which asserts: "states of a microscopic system which could be told apart by macroscopic observation are distinct from each other whether observed or not". In other words, the SV collapses as soon as some macroscopic record of the result of a measurement is made, whether a conscious observer looks a that record or not. Heisenberg (1960) and others have suggested a variant of this position which asserts that as soon as the quantum measurement passes from the domain of reversible processes into the domain of thermodynamic irreversibility the SV collapses.

The latter two "collapse triggers" are more appealing to most physicists than the former because they avoid giving some special significance to consciousness and because, as pointed out by Weisskopf (1959, 1980), they correspond more closely to the operating assumptions which practicing physicists use in thinking about how quantum measurements are done. However, these models also beg the question of borders: Where precisely is the border between macrophysics and microphysics and the border at which irreversibility begins? This point seems particularly troublesome when one realizes that present experimental techniques permit the result of a quantum measurement to be "recorded" in the spin orientation of a single electron in a Penning trap or in the trapping of a single magnetic flux quantum in a split superconducting ring.

Indeed, in the context of the latter apparatus this point has been made more quantitative by recent work. Leggett (1980) has carefully considered the question of macroscopic quantum effects. He has introduced a semi-quantitative measure called "disconnectivity" for characterizing the degree to which a quantum system is isolated from effects which would average away any coherent quantum interference phenomena. He has shown that this is a useful criterion for separating the macrocosm from the microcosm, i.e., classical from quantum phenomena. He finds that while many experiments, and in particular the Schrödinger's Cat gedanken experiment, do indeed have a very small disconnectivity which places them in the classical domain, there remains a class of possible macroscopic experiments which satisfy the criterion of high disconnectivity and which should exhibit quantum interference effects at the macroscopic level. Of particular interest are experiments involving macroscopic quantum tunneling (MQT) of magnetic flux in a superconducting Josephson junction, because this collective behavior involves many degrees of freedom as well as macroscopic dissipation. Recent experiments (Voss, 1981; Ouboter, 1982) have confirmed some of Leggett's predictions for MQT in this macroscopic junction phase of Josephson junctions. The border between macro- and microphysics seems to have become less sharp with the improvement of such experimental techniques making the issue of collapse less clear.

Another problem with these collapse models is they are not full interpretations of quantum mechanics. They have focused only on the cause of collapse and have provided no insights into the related interpretational problems listed in Section 2. In particular, the nonlocal aspects of the SV collapse which have become the focus of the recent Bell inequality tests are not clarified by these interpretations.

**A.4 The Many-Worlds Interpretation**

In 1957 at a conference on gravitation, Hugh Everett, III (1957) and his thesis supervisor at Princeton, Prof. John A. Wheeler (1957) presented related papers on Everett's thesis research, which has come to be known (DeWitt, 1970; DeWitt and Graham, 1973) as the Everett-Wheeler, Everett-Wheeler-Graham, or many-worlds interpretation (MWI) of quantum mechanics. Like the interpretations discussed in Section A.3, the MWI addresses the problem of collapse. But unlike the other interpretations the MWI asserts that collapse never occurs. Instead each component of the SV of a quantum event represents a separate and equal physically real reality. In other words, with each quantum event the universe splits into a number of branch universes, each containing a different possible outcome for the event. What we perceive as collapse is, in the MWI, simply a result of the fact that our consciousness took a particular path through these branches and therefore observed one set of results instead of another of the myriad possibilities. And presumably other copies of our consciousness are observing all of the other possible outcomes in other branch universes.

This is perhaps the most "heroic" of the efforts to deal with the problem of collapse. It addresses identity by giving the SV the status of objective reality, for the electron in each branch universe is identical with its component in the original SV. Complexity is not addressed, and is presumably more troublesome for the MWI than the CI because the SV is a physical entity. Locality is not specifically addressed in Everett's paper, but he labels the locality problem stated by Einstein, Podolsky and Rosen (1935) as a "fictitious paradox" and asserts that it can be easily investigated and clarified with the MWI.

From one point of view this is perhaps true, for in a situation with two separated measurements the "earlier" of the two measurements will, in the MWI, split the universe containing the second measurement such that its outcome is always correlated properly with that of the first. From this point of view the MWI is compatible with nonlocality. However, from another point of view the MWI would appear to have severe problems in this area. With each splitting of the universe, spatial regions megaparsecs distant from an event locus are instantaneously split into alternate realities due to the distant quantum event. It would seem that both the propagation speed of the splitting and its simultaneity are manifestly inconsistent with relativistic invariance.

The MWI is interesting from another point of view. It represents an interpretation of quantum mechanics to which the assumption of contra-factual definiteness (CFD) as discussed in Section 1.0 does not apply. The MWI characterizes our world as one of many equally real alternatives, and so some alternative experiment which might have been performed would not have a single definite outcome as CFD asserts, but rather would have had all possible outcomes, one for each branch universe split off by the measurement. Thus the CFD assumption is not applicable to the MW. Therefore, in the context of the MWI, the Bell inequality experimental results can be taken as an experimental demonstration of the invalidity of CFD rather than locality.

The MWI also has an intrinsic time asymmetry. In its description, the universe splits only in the future time direction, and never in the past time direction. Thus there is an intrinsic arrow of time built into the interpretation which is inconsistent, as has been said for the CI, with the even-handedness with which microphysics deals with the flow of time. And perhaps this kind of approach is just what William of Occam had in mind in warning that hypotheses should not be multiplied beyond necessity.

**A.5 Advanced-Action Interpretations**

In addition to the present work, two other approaches to the interpretation of quantum mechanics have appeared in the literature which have suggested the use of advanced waves. The first of these is the "advanced action" interpretation (AAI) of Costa de Beauregard (1953, 1965, 1976, 1977a, 1977b, 1978, 1979a, 1979b), as discussed in a series of papers. He points out that the timelike symmetry of electrons and positrons in the Feynman picture can, in principle, account for the nonlocal structure of quantum mechanics as applied to electrons and positrons in a creation-annihilation event.

The approach, however, has a number of deficiencies. In a recent paper, Garuccio and his coworkers (1980) have pointed out that the AAI employs negative energy solutions of the Dirac equation which are assumed to propagate in the positive time direction, an impossibility due to the complementarity of the time and energy variables [see (Cramer, 1980) for a discussion of this point]. They also argue that the AAI violates causality and energy conservation. Indeed there would appear to be causality problems with the AAI approach, for Costa de Beauregard (1980) has suggested the AAI as an explanation for parapsychological phenomena.
Selleri and Vigier (1980) have argued that the AAI is inconsistent with quantum electrodynamics because it implies a rejection of Feynman's D_{c} propagator.

A second interpretation using advanced waves was suggested by Davidon (1976), who proposed that:

Since the time-dependent Schrödinger equation, (see Section 3.3) being first order in its time derivative, does not"an operator which factors into a tensor product of advanced and retarded solutions of the time-dependent Schrödinger equation"could lead to"a local and objective description ... for each of the remote parts in an Einstein-Podolsky-Rosen situation."

Both of these advanced wave approaches, from the point of view of the present work, were on the right track, but missed the crucial role of the transaction in mediating the transfer of energy, momentum, etc., and in erasing all residual traces of the advanced waves. Without this key concept, these interpretations lead inevitably to causality paradoxes and inconsistency with QM predictions and experimental observations.

Stapp (1975, 1977, 1980) has proposed a very general nonlocal model which we regard as a precursor of the present work. It is not an interpretation because it does not propose any specific mechanism for quantum events. Rather, it is a world-model similar to that originally proposed by A. N. Whitehead, but suitably modified to deal with the manifest nonlocality demonstrated by the tests of the Bell inequality.

A particular feature of this work is that although the elemental events considered connect loci of spacetime across spacelike intervals, the events retain a sequentiality which is independent of reference frame, and which proceeds from the past to the future. Thus the model is atemporal (like the TI) but it preserves a sequentiality which is consistent with causality and with our perception of the causal arrow of time.

The Transactional Interpretation is fully consistent with Stapp's model but goes beyond it in providing a specific and plausible mechanism through which Stapp's nonlocal sequentiality can operate. In particular, if one makes the equivalence between the transaction concept defined above and Stapp's elemental quantum event concept, then the TI provides a meaningful context in which Stapp's very general but rather non-specific world-model can be seen in operation.

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