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.

Tue Apr 30 12:12:30 PDT 1996