ran@ho95e.UUCP (RANeinast) (11/20/86)
The July, 1986 issue of Reviews of Modern Physics had an article in it called "The Transactional Interpretation of Quantum Mechanics", by John Cramer. This is a new way of looking at QM that, to my mind, is a cleaner and much more logical way of looking at QM, and resolves the many "paradoxes" associated with QM. This is so revolutionary an interpretation that I would have expected that some of the other journals (Science, Nature, Science News, New Scientist) would have mentioned it, but I haven't seen anything. Since I've been out of physics for about 5 years, I don't know if this is because it's considered utter hogwash, or if just nobody's really noticed it yet. In the rest of this posting, I'll try to address the highlights of the interpretation. Maybe those of you out there with the background will want to read the complete article in RMP (particularly since I'm sure I can't explain it anywhere near as well as Cramer did). Maybe those of you out there with ties to the physics world can let me know what they think of it. ----- It should be stressed that a new interpretation does not change the formalism of QM. All calculations are done as always. It's just how you think about what's going on that is different. Other interpretations of QM that you may be familiar with are the "collapse" interpretation (the knowledge of the observer is what makes the wave function collapse, so that Schrodinger's cat isn't dead until we open the box and observe it) and the many-worlds interpretation (each time a QM "choice" is to be made, the world lines split, making an infinity of universes with each possible outcome). The basic idea comes from Wheeler-Feynman electrodynamics. All relativistic wave equations have what are called "advanced" and "retarded" wave solutions. The "retarded" solutions are the usual ones you are familiar with. The "advanced" solutions are waves that travel backwards in time with negative energy. These solutions are usually discarded as "unphysical". Wheeler and Feynman showed that a consistent electrodynamics exists using the advanced waves also. Consider a simple one-dimensional exchange of a photon between two electrons. The usual (retarded waves only) interpretation has the first electron emitting a retarded (forward in time) wave. When that wave hits the second electron, it vibrates, creating an additional retarded wave exactly out of phase with the first (canceling the first wave in the future), so that the resultant is no wave after the absorption. The Wheeler-Feynman electrodynamics includes the advanced waves. The exchange is described in a pseudo-time sequence. Here, the first electron emits both an advanced and retarded wave, the advanced wave going into the past, and the retarded wave going into the future. In the future, the second electron vibrates when the retarded wave hit is, and creates both advanced and retarded waves. The retarded wave cancels the first wave after the absorption. Meanwhile, the second advanced wave travels backwards in time to the first electron, and cancels the first advanced wave before the original emission. The final result is exactly the same as for the usual case. Wheeler and Feynman showed that this canceling always takes place exactly as necessary, and in three dimensions, it's the boundary conditions that enforce it. For QM, the situation is similar. At the start of the transaction (using pseudo-time as before), a particle sends out a retarded Offer Wave, which disperses and diminishes as it goes, and its possible target responds to the retarded Offer Wave with an advanced Confirmation Wave, which travels back in time to the original particle. Boundary conditions ensure there are no stray waves before or after the event. What's the probability of a particular transaction occurring? Well, the amplitude of the Offer Wave is attenuated to Psi(x) by the intervening medium, and then the amplitude of the Confirmation Wave is the same, since it traverses through the exact same medium, only backwards, BUT THE CONFIRMATION WAVE IS TIME REVERSED, giving Psi*(x). Thus, the probability of completing the Offer/Confirmation with that target is just Psi*(x)Psi(x) [ta-da!]. Finally, we have an explanation as to why the probability in QM is given by the absolute square of the wave function. The way the paradoxes are resolved is that the particles involved in completing the transaction are communicating through time with each other, and thus know the details of the experiment that is being performed. If after two photons are sent out in opposite directions, one experimenter decides to check for circular polarization, and the other for horizontal, the results correlate correctly (that is, as QM says they should) because the complete transaction involved the final states measured. [You'll have to read the RMP article for more lucid explanations of the paradoxes]. Note that faster-than-light communication is still disallowed, but that long distance correlations are still enforced. All "signals (offer/confirmation)" travel relativistically (some forward in time, some backwards), but never faster than light. The correlations are maintained by the handshaking through time. This interpretation of QM has a very strong flavor of the story "By His Bootstraps" by R. A. Heinlein. Things happen in the future the way they do because the past knows whats going to happen, and going back to the past just brings the future about the way it was going to be [the more I read that sentence, the more convinced I am that I didn't say it very well, but I don't think I can say it better]. There is also a strong flavor of inevitability here, since once a transaction is set up across time, its completion is inevitable, yet freedom (free-will?) exists, since the beginning of the transaction chooses in a probabilistic sense from among all the targets (that satisfy the proper boundary conditions). ----- Whew! I'm sure I haven't done justice to the transaction interpretation, but the more I think about it, the more I like it. Any thoughts out there? -- ". . . and shun the frumious Bandersnatch." Robert Neinast (ihnp4!ho95c!ran) AT&T-Bell Labs