Open System for Geniuses - by Chronostalker

Let’s discuss Cramer’s “Overview of the Transactional Interpretation“. The paper was published in the International Journal of Theoretical Physics 27, 227 (1988). This journal is known from its rather liberal attitude to the quality of the papers that are being accepted. Some papers are very good and innovative, some are speculative and controversials, some are simply wrong. But in almost every issue one can find something of interest. After a short introduction Cramer proceeds to the first section "Summary of the Transactional Interpretation". Let us analyze this summary, paragraph after paragraph, and let us see what makes sense and what not.

Albert Einstein distrusted quantum mechanics (QM) in part because he perceived in its formalism what he called “spooky actions at a distance'’[2]. The action-at-a-distance characteristic that worried Einstein is now called nonlocality. It is generally acknowledged to be inextricably embedded in the quantum mechanics formalism. Let us then define our terms. Locality means that isolated parts of any quantum mechanical system out of speed-of-light contact with other parts of that system are allowed to retain definite relationships or correlations only through memory of previous contact. Nonlocality means that in quantum mechanical systems relationships or correlations not possible through simple memory are somehow being enforced faster-than-light across space and time. Close examination of the correlations present in recent experimental tests of Bell’s inequality provide concrete examples of such nonlocality.

Einstein did not reject quantum mechanics because its "spooky action at a distance". He simply noticed that QM is incomplete. In particular he was unhappy with the role that is being played by "chance": “God does not play dice" - he would say to Bohr, and Bohr would respond: “Einstein, stop telling God what to do". Nonlocality is not generally acknowledged to be inextricably embedded in the quantum mechanics formalism. The title of a standard textbook by Rudolf Haag, one of the seniors of quantum field theory, and a founder of algberaic approach, is "Local quantum physics". In Concluding Remarks to the Second Edition of Local Quantum Physics Haag writes:

The conceptual structure proposed above incorporates the essential message of quantum-physics and does not seem to be at odds with known experimental findings. At the present stage it is not clear whether this structure should be regarded only as an idealization suitable in a certain regime of phenomena or whether a fundamental theory based on this picture can be developed. This would demand a more general definition of events and links, in other words a deeper understanding of the "division problem". It might demand a finer division of "decisions of nature", related to the quantum of action rather than to collision processes between-stable structures. The relation of events to space-time must be clarified. It is here that some differences from the standard formalism will be manifested. One of the factors in favor of the picture presented is precisely this point.- It seems ultimately unsatisfactory to accept space-time as a given arena in which physics has to play. This feature persists even in general relativity where a 4-dimensional space-time continuum is a priori assumed and only its metric structure depends on the physical situation. In particular, in the absence of all matter and all events there would still remain this continuum, void of significance. This aspect was one of the factors that motivated the author to introduce the notion of "event" as a basic concept with the ultimate aim of understanding space-time geometry as the relations between events [Haag 90a]. The other motivation was, of course, the desire to separate the laws of quantum physics from the presence of an observer [Haag 90b]. In this respect it appears that theorists discussing quantum processes inside a star or in the early universe necessarily transcend Bohr’s epistemology.

Usually the orthodox interpretation is then silently ignored but there are some efforts to build a rational bridge from the standard formalism to such areas of physical theory, most prominently the work by Gell-Mann and Hartle [Gen 90, 94]. It uses the concept of "consistent histories" introduced by Griffiths [Griff 84] and extended by Omnes [Omnes 1994]. One criticism of this concept is that consistent histories embodying some established facts are highly non-unique. This led Omnes to the distinction between "reliable properties" and truth.
Still another motivation comes from the following consideration. The general mathematical structure of standard quantum theory is extremely flexible. Its connection to physical phenomena depends on our ability to translate the description of circumstances (e.g., experimental apparatus) to a specification of operators in Hilbert space. Apart from the case of very simple systems, the success in this endeavor is due to the fact that for most purposes no precise mathematical specification is needed. Thus, for the treatment of collision processes in quantum field theory it suffices to give a division of "all" observables into subsets which relate to specified space-time regions. However, in addition to-this classification of observables one uses the postulate of strict relativistic causality. Some consequences of this postulate have been verified by the check of dispersion relations to regions with an extension far below 10-13 cm. On the other hand it seems highly unlikely that the construction of an instrument of intrinsic size of, say, 10-15 cm and the control of its placement to such an accuracy could be possible even in principle, i.e., that we may assume the existence of such observables. But it is not unlikely that we can attribute to high energy events a localization of this order of magnitude though we have no means of verifying this in the individual case. Thus the indirect check by means of dispersion relations could be explained by the existence of sharply localized events rather than sharply localized observables.
The realization of a specific result in each individual measurement has been recognized by many authors as a challenge to the theory of measurement which cannot be explained using only the dynamic law of quantum theory applied to the interaction of a quantum system with a macroscopic device but needs an additional postulate. In the words of Omnes this is "a law of nature unlike any other". In a series of papers Blanchard and Jadczyk suggested a formalism in which irreversibility is introduced in the dynamics of the coupling of a quantum system with a classical one and thereby obtained a (phenomenological) description of this aspect of measurements (see, e.g., [Blanch 93, 95]).
The evolutionary understanding of reality was proposed many years ago by A.N. Whitehead [Whitehead 1929]. His writings have influenced philosophers and theologians, but few physicists. A notable exception are the papers by H.P. Stapp in which he outlines a theory of events having many features in common with the evolutionary picture described above [Stapp 77, 79]. It is a pity that these seminal papers did not receive the attention they deserve and unfortunate that I became aware of them too late to incorporate an adequate discussion of this work. The first two postulates in [Stapp 77] are identical with those underlying the evolutionary picture. Differences in views concern his postulate 3 (momentum conservation) and the meaning of causal independence. Especially the discussion of the EPR-effect in [Stapp 79] differs from the treatment above and leads to a different assessment of the lessons. In physics D. Finkelstein suggested an approach to the space-time problem based on similar concepts [Fink 68]. C.F. von Weizsacker tried for many years to draw attention to the fundamental difference between facts as related to the past and possibilities as related to the future and argued that for this reason the statistical statements in physics must always be future directed [Weiz 73].
‘Whatever the ultimate fate of these ideas, we should recognize that the standard formalism of quantum physics is not sacrosanct and will probably be modified in future theories. With regard to the interpretation there is no basic disagreement with the epistemological analysis of Niels Bohr but an appeal to accept that physical theory always transcends the realm of experience, introducing concepts which can never be directly verified by experience though they must be compatible with it.

When discussing Bell’s inequality Haag writes (pp. 107-108)

Axiom E combines several features abstracted from conventional field theoretic models. The main principle expressed by it is the causal structure of events. Two observables associated with space-like separated regions are compatible. The measurement of one does not disturb the measurement of the other. The operators representing these observables must commute.
To avoid possible confusion it must be stressed that this has nothing to do with the discussion around the Einstein-Podolsky-Rosen paradox and Bell’s in-equality. There one is dealing with the joint probability distribution of measure­ments on two far separated particles coming from a common root e.g. as decay products of an unstable particle. If a neutral particle decays into two oppositely charged ones it will surprise nobody that a charge measurement on one of the decay products suffices to tell us the charge of the other one, no matter how far away it is. This is due to the correlation resulting from charge conservation, not to a causal influence between the charge measurements in space-like separated regions. The total experiment includes, of course, the preparation of the state of the unstable particle, by which the charge (resp. spin) are fixed. If, instead of the charge, we consider the angular momentum, the situation becomes indeed more curious. Instinctively one would like to associate with each of the particles (once they are sufficiently separated) an "objective", "real" state which determines the probability of finding a specific result in the subsequent measurement of the angular momentum component in any chosen direction. As Bell has shown [Bell 64] this picture, together with angular momentum conservation, demands that a certain inequality must hold for the joint probability distributions for such measurements on the two particles. This inequality is not satisfied in the quantum mechanical description. Very fine experiments have been performed to check this inequality. They appear to speak for quantum mechanics and against the inequality. What is the message of this? It does not relate to a physical influence propagating faster than light but it illustrates in a particularly drastic way that the concept of a materially defined "physical system" has to be handled with extreme care. This latter is a mental construct whose correspondence to "reality" is (sometimes) questionable (compare [d’Espagnat 1979]). We shall give a thorough discussion of this problem in Chapter VII. Here we note only that the existence of correlations between far space-like separated events does not contradict the limitation of causal influences to time-like directions as de­manded by axiom E.

Thus we see that Cramer’s statement about non-locality is at least misleading.

To be continued…