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3. Differences between the Transactional and the Copenhagen Interpretations


In this section I want to focus on the differences between the transactional interpretation and the Copenhagen interpretation. I have decided to do this with a question and answer format, asking an interpretational question implicit in the quantum mechanics formalism and then providing answers from the points of view of both the Copenhagen interpretation (CI) and the transactional interpretation (TI). The answers given are based on my understanding of both interpretations, and there is perhaps room for other views of how the CI might answer the questions posed. Where there was this sort of disagreement during the discussion session of this Conference, I will try to indicate this.

Q1: Does the wave described by the state vector have physical reality?

CI: The state vector does not describe a real physical wave moving through space, but rather a mathematical representation of the knowledge of an observer.

TI: To the extent that the formalism contains state vectors represented in position space (as opposed to momentum space or other parameter spaces), the formalism is describing real physical waves moving through space which are the first steps in the formation of transactions. The completed transaction describes the exchanged particle.

Discussion: It was pointed out in the Conference discussion that for some quantum mechanical systems (e.g. an ensemble of particles with spin) there is no known formalism capable of representing the system in position space. Therefore, it was argued, it is inappropriate to discuss ``waves physically present in space''. This is a very relevant observation, for the interpretation of a formalism cannot and should not go where the formalism itself does not venture. The TI, when applied to a formalism representing waves in position space, can interpret them as physically present in space. When applied to momentum space formalisms, etc, the issue of physical presence is moot, since it is not clear that ``physical presence'' in an arbitrary parameter space is a meaningful concept.

Q2: Are physical interactions involving observers different from other physical interactions?

CI: Yes. Physical interactions with an observer are qualitatively different from other physical interactions because they produce observer knowledge and cause state vector collapse.

TI: No. Physical interactions involving an observer are completely equivalent to any other physical interactions. A change in observer knowledge is a necessary consequence of state vector collapse, not a cause.

Discussion: In the Conference discussion Prof. von Weizsäcker disagreed with this dichotomy. His point was that there is no distinction made in the formalism between observer interactions and any other interactions. That is of course correct, but my point here is that there is a difference in these interactions at the interpretational level precisely because the Copenhagen interpretation treats observer interactions differently, (e.g, by using them to collapse the state vector), even though the QM formalism does not.

Q3: Can one ask interpretational questions about aspects of the formalism that are not observable?

CI: No. One should confine one's attention to the observables and to statical predictions of their values; discussion of non-observables is meaningless.

TI: Yes. One can discuss most of non-observable constructs of the quantum mechanics formalism, and can even visualize nonlocal quantum processes.

Discussion: As discussed in my review article[1], the positivistic aspect of the Copenhagen interpretation can be considered detachable, but the discussions at this Conference indicate that it remains an important aspect of the CI, at least to some of the attendees.

Q4: Is the state vector unique in the sense that only one state vector is required to describe a given physical system?

CI: No. A separate state vector is required for each observer of a given physical system.

TI: Yes. A single state vector describes a physical system, no matter how may observers make measurements on it.

Discussion: It was demonstrated in my review article[1] that at the interpretational level a paradox arises if one assumes (1) the CI account of state vector collapse and (2) that a single state vector describes a system involving two separated measurement events not lying in the same light cone. The conclusion is that the only consistent use of the Copenhagen interpretation is to attribute separate state vectors to measurements which do not share the same light cone. This does not necessarily count against the Copenhagen interpretation, but it is a point which is not widely appreciated. The transactional interpretation, on the other hand, describes all quantum events in terms of a unique state vector, even when measurements are involved which do not share the same light cone.

Q5: Is the interpretation capable of extension to developing relativistic quantum mechanics or quantum gravity formalisms?

CI: It is not obvious that such an extension is possible for the CI. Time and space are treated non-relativistically, and definite simultaneity is implied by the knowledge interpretation.

TI: There are no apparent obstacles to such an extension. Time and space are treated relativistically, and Lorentz invariance is effectively built into the transactional interpretation.

Discussion: The Copenhagen interpretation was developed specifically for interpreting the non-relativistic Schrödinger formalism. The structure of Newtonian space-time is deeply embedded in its approach, perhaps inextricably so. Further, attempts to apply the CI to systems involving no observers, for example the quantum dynamics of Big Bang era or the state vector of the universe as a whole, would seem to be at odds with the knowledge interpretation's need for external observers to provide state vector collapse.

next up previous
Next: Equivalence Mapping of Up: An Overview of the Previous: Summary of the

John G. Cramer
Tue Apr 30 12:12:30 PDT 1996