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.

At the interpretational level, the nonlocality of the quantum mechanics formalism is a source of some difficulty for the Copenhagen interpretation. It is accommodated in the CI through Heisenberg's ``knowledge interpretation'' of the quantum mechanical state vector as a mathematical description of the state of observer knowledge rather than as a description of the objective state of the physical system observed. For example, Heisenberg in a 1960 letter to Renninger wrote[3], ``The act of recording, on the other hand, which leads to the reduction of the state, is not a physical, but rather, so to say, a mathematical process. With the sudden change of our knowledge also the mathematical presentation of our knowledge undergoes of course a sudden change.'' The knowledge interpretation's account of state vector collapse and nonlocality is internally consistent but is regarded by some (including the author) as subjective and intellectually unappealing. It is the source of much of the recent dissatisfaction with the Copenhagen interpretation.

The author has proposed an alternative and more objective interpretation
of the quantum mechanics formalism called the * transactional interpretation*
(TI). It employs an explicitly nonlocal ``transaction'' model for quantum events.
This model describes any quantum event as a ``handshake'' executed through an
exchange of advanced and retarded waves and is based on time symmetric
Lorentz-Dirac electrodynamics and on ``absorber theory'' originated by Wheeler
and Feynman. In the absorber theory description any emission process makes
advanced waves (schematically represented by the time dependence )
on an equal basis with ordinary ``retarded'' waves (). Both advanced
and retarded waves are valid orthogonal solutions of the electromagnetic wave
equation, but in conventional electrodynamics the advanced solutions are
conventionally rejected as unphysical or acausal. Wheeler and Feynman used a
more subtle boundary condition mechanism to eliminate the non-causal effects of
the advanced solutions.

In the Wheeler-Feynman picture when the retarded wave is absorbed at some time in the future, a process is initiated by which canceling advanced waves from the absorbers erase all traces of advanced waves and their ``advanced'' effects, thereby preserving causality. An observer not privy to these inner mechanisms of nature would perceive only that a retarded wave had gone from the emitter to the absorber. The absorber theory description, unconventional though it is, leads to exactly the same observations as conventional electrodynamics. But it differs in that there has been a two-way exchange, a ``handshake'' across space-time which led to the transfer of energy from emitter to absorber.

This advanced-retarded handshake is the basis for the transactional interpretation of quantum mechanics. It is a two-way contract between the future and the past for the purpose of transferring energy, momentum, etc, while observing all of the conservation laws and quantization conditions imposed at the emitter/absorber terminating ``boundaries'' of the transaction. The transaction is explicitly nonlocal because the future is, in a limited way, affecting the past (at the level of enforcing correlations). It also alters the way in which we must look at physical phenomena. When we stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been traveling for a hundred years to reach our eyes, but the advanced waves generated by absorption processes within our eyes have reached a hundred years into the past, completing the transaction that permitted the star to shine in our direction.

It is a serious interpretational problem for the Copenhagen interpretation that it characterizes as mathematical descriptions of the knowledge of observers the solutions of a simple second-order differential equation relating momentum, mass, and energy. Similarly, it is a problem for the transactional interpretation that it uses advanced solutions of wave equations for retroactive confirmation of quantum event transactions. While this provides the mechanism for its explicit nonlocality, the use of advanced solutions seems counterintuitive and contrary to common sense, if not to causality. Can this account of a quantum event be truly compatible with the austere formalism of quantum mechanics?

From one perspective the advanced-retarded wave combinations used in the transactional description of quantum behavior are quite apparent in the Schrödinger-Dirac formalism itself, so much so as to be almost painfully obvious. Wigner's time reversal operator is, after all, just the operation of complex conjugation, and the complex conjugate of a retarded wave is an advanced wave. What else, one might legitimately ask, could the ubiquitous notations of the quantum wave mechanics formalism possibly denote except that the time reversed (or advanced) counterparts of normal (or retarded) wave functions are playing an important role in a quantum event? What could an overlap integral combining with represent other than the probability of a transaction through an exchange of advanced and retarded waves? At minimum it should be clear that the the transactional interpretation is not a clumsy appendage gratuitously grafted onto the formalism of quantum mechanics but rather a description which, after one learns the key to the language, is found to be graphically represented within the quantum wave mechanics formalism itself.

The latter half of my review article[1] provides examples
of the use of the transactional interpretation in analyzing the accumulated
curiosities and paradoxes (the EPR paradox, Schrödinger's cat, Wigner's
friend, Wheeler's delayed choice, Herbert's paradox, etc.) that have lain for
decades in the quantum mechanics Museum of Mysteries. It is shown that the TI
removes the need for half-and-half cats, frizzy universes with split ends,
observer-dependent reality, and ``knowledge'' waves. It removes the observer from
the formalism and puts him back in the laboratory where he belongs.

Tue Apr 30 12:12:30 PDT 1996