Dear Dr. Towler,
Let me try to answer your question about why, in the 10 or so
years since it was published, the transactional interpretation has
not received more attention from those who write books about the
interpretation(s) of quantum mechanics.
First I would have to say that I do not understand it either.
Perhaps it's my fault for not putting more effort into promoting the
transactional interpretation once it was in print and for not sending
complaining letters to authors of review articles and books who have
not given it enough (or any) attention. It did, by the way, receive
considerable attention in a book by John Casti and in a recent biography
of Erwin Schroedinger.
The interpretation of quantum mechanics is not my principal
area of research. In fact, as an experimentalist I find quantum
interpretation to be a very frustrating area because of its insulation
from experimental tests. Therefore, once the ideas behind the TI were
fully elucidated, I did not feel it necessary to continue with further
publications on the subject. I feel, perhaps naively, that sufficiently
good ideas should be able stand on their own and should not require a
sales pitch. In 1986, shortly after the RMP article appeared, I did
write a letter to the Scientific American offering do write a popular
article about the transactional interpretation. However, they never
even replied to my letter. I was somewhat irritated and dropped the
idea of a large popular-language article. However, in my science-fact
columns published in Analog Magazine (see http://www.npl.washington.edu/av).
I have dealt with various aspects of the TI and quantum interpretation
a number of times. Eventually I may do my own book on the subject.
Last summer, on the 10th anniversary of the RMP publication, I did
a citation index search on the TI papers, and I have placed the results
at the end of the version of the TI paper that is on WorldWideWeb (see
http://www.npl.washington.edu/tiqm). There are some references, but far
fewer that I would have expected by now when I wrote the paper.
Perhaps I should mention that the Everett-Wheeler interpretation
of quantum mechanics had a similar history. It was published in Reviews
of Modern Physics in 1957 and largely ignored until 1971, when Bryce DeWitt
published an article about it in Physics Today. Since then, the
Everett-Wheeler interpretation has been embraced by the much of the
theoretical community (in spite of its conspicuous inadequacy in dealing
with the problem of nonlocality) and the various versions which include
"decoherence" as a substitute for wave function collaps are widely
discussed in the literature. Perhaps QM interpretations, like wines, have
to be aged for 15 years before the paradigm shifts they bring are palatable.
As for fundamental objections, I'm not aware of any fatal ones.
Below I list some of the objections and criticisms that have been raised,
along with my responses:
(1) From Carl von Weiszacker at the 1988 New Orleans QM conference:
"The TI differs from the Copenhagen Interpretation only in using different
terms for the same quantum constructs, so that the difference between the
two is basically semantic."
My reply to this, published in the 1988 "Overview" paper, is that
while there may (or may not) be a 1:1 correspondence between terms in the
TI and CI, the causal relations in some cases are clearly inverted,
particularly for issues involving the role of the observer. The CI gives
the illusion that the observer has a mysterious central role in the quantum
process while the TI demonstrates that the observations of the observer are
only a side effect of the central transaction.
(2) A question raised by someone named Levine at the 1988 New Orleans
QM conference and recently repeated by one Jack Sarfatti of Berkeley,
(who seems to have achieved some status on the Net from the sheer volume
of his diatribes):
"Some quantum mechanical systems (e.g. an ensemble of fermions with spin 1/2)
have no known formalism capable of representing the system in position space
and can be formulated only in a multidimensional momentum phase space.
Therefore, it is inappropriate to discuss `waves physically present in space'
as portrayed in the TI, and so the TI cannot be considered as a general
interpretation."
I've always found this objection rather silly. Of course it is
always possible to represent a quantum system in momentum space, where the
formalism and solutions may be more tractable. Does this mean that there is
no possible (if intractable) representation of the system in configuration
space and that the same waves cannot be considered to exist in space? Of
course not. That's what multidimensional Fourier transformations are for.
(3) An objection raised by several field theorists:
"The TI interprets the solutions of wave equations, e.g., the Schroedinger,
Dirac, and Klein-Gordon equations. However, modern quantum field theory
does not use or need wave equations, relativistic or otherwise, and so the
TI is not applicable."
I think the argument, like the one above, starts from mathematical
convenience and ends with undue generalization. It has not been demonstrated
that any aspect of quantum field theory CANNOT be converted to a
representation in terms of relativistic wave equations and their solutions.
There are even some indications in the literature (e.g., Konopinski) that
quantum field theory, with its embarrassment of infinities ans self-energies
that must be renormalized away, could profit from a representation in terms
of a time-symmetric (advanced + retarded) formalism as suggested by the TI.
(4) Another objection raised by Jack Sarfatti:
"Figures 2-5 of the RMP paper show the waves propagating along 45-degree
space-time trajectories, i.e., traveling at the speed of light. Further,
Gribbin has argued that in the light-cone reference frame there is no
space-time interval between the emission and absorption events, so they
are superimposed, facilitating the TI handshake. Therefore, the TI is
implicitly only about photons and cannot be applied to massive particles
like electrons. Also, Dirac has taught us that time-reversed electrons are
positrons, so their wave representations can't be combined in an advanced-
retarded handshake."
The photon argument is bogus. The figures in the RMP paper use 45
degree trajectories because essentially all of the EPR experiments that have
demonstrated the intrinsic nonlocality of QM employ photons. This does NOT
mean that the trajectories of the advanced and retarded waves HAVE to be at
45-degrees in a Minkowski diagram. Clearly, massive particles will have
steeper timelike trajectories, which presents no problems to the application
of the interpretation. Gribbin's zero-interval observation is interesting
but was not contained in the TI paper and is not a part of the interpretation.
The positron argument is also bogus. Representing charged particles
with advanced and retarded solutions requires four kinds of waves which are
characterized by positive or negative charge and positive or negative energy,
all of which are solutions, for example, of the Dirac equation. The
advanced-retarded handshake for an transaction involving the emission and
absorption of an electron will use a negative charge with positive energy
wave and a positive charge with negative energy wave, the latter reinterpreted
as a positive energy electron according to the usual Dirac rules.
These are all the "fundamental objections" to the TI of which I am
aware. None are particularly damaging, and the first two have been addressed
in a journal publication with no published refutations. In this context I
should also mention that Steve Gull of Cambridge, in a recent FOP publication
about the Clifford Algebra version of the Dirac equation, remarked as a sort
of aside that the TI could not be applied to the solutions he was looking at.
I sent him E-mail (which I know he received) asking for a clarification of
that statement, but in ~6 months he has not replied. If you know him, perhaps
you could encourage him to do so.
Anyhow, that's about all I can say about the status of the
transactional interpretation. I'd be interested in hearing how your
presentation goes at Cambridge. Please keep me informed.
Best regards,
John G. Cramer
Professor of Physics
University of Washington