The "transactional" interpretation of Quantum Mechanics was devised by John Cramer in 1986 to provide a complete and consistent interpretation of Quantum Mechanics without introducing new elements.The story begins in 1925 when, de facto, Heisenberg made a metaphysical revolution by surrendering the concept of reality in favor of the concept of observables: we can't know what really exists, we can only know what we can observe. Kastner points out that Heisenberg's metaphysical move was essential to discovering a theory that turned out to correctly predict observation.
Sometimes one has to surrender conventional beliefs in order to understand the world. Many thinkers, and Bohr in particular, drew the conclusion that reality cannot be known (a` la Kant), not realizing that reality doesn't necessarily have to be "classical" reality: there could exist a different, non-classical, kind of reality. One has to study carefully what the math is saying.
Heisenberg wrote: "One might perhaps call [the statistical nature of quantum theory] an objective tendency or possibility, a "potentia" in the sense of Aristotelian philosophy... The probability wave of Bohr, Kramers, Slater... was a quantitative version of the old concept of "potentia" in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality." (in the Gifford Lectures of 1956, published in "Physics and Philosophy", 1958) As the author of this book puts it: "There are real physical events that transcend the boundaries of the observable universe".
The story continues with a theory formulated by the US physicists John Wheeler and Richard Feynman in the 1940s for classical electrodynamics. From a purely mathematical viewpoint, Maxwell's equations of electromagnetism have two possible solutions: a retarded solution and an advanced one. If one reads those equations literally, any electrically charged particle generates both waves that will arrive after the emission as well as other, perfectly symmetrical, waves that will arrive before the emission. Since the latter make no sense in a world driven by the causality principle (that the effect of an action cannot preceed the action), the advanced solutions were routinely discarded.
However, Wheeler and Feynman found a formally beautiful way to retain them as part of reality. Charged particles were traditionally considered only as radiation emitters. Wheeler and Feynman viewed them as both emitters and absorbers: charged particles emit their radiation half as retarded and half as advanced. The principle of causality is not violated if one retains both the retarded waves that travel from emitter to absorber and the advanced waves that travel from absorber to emitter. In other words, Wheeler and Feynman described a radiation process as a "transaction" in which the emitter of the radiation and the absorber of the radiation exchange waves: the emitter sends a "retarded" wave to the absorber, and simultaneously the absorber sends an "advanced" wave to the emitter. An observer perceives only that a retarded wave has traveled from the emitter to the absorber.
Technically, advanced waves have "eigenvalues" of negative energy and frequency, and they propagate in the negative time direction. Advanced waves are basically the time-reversed counterparts of normal (or retarded) waves. Both "advanced" and "retarded" waves are valid orthogonal solutions of the electromagnetic wave equation, but in conventional electrodynamics the advanced solutions are usually ignored as unnatural, because they violate the law of causality, and only "retarded" solutions are retained. Wheeler and Feynman proposed that the time symmetry in the wave equation reflects a property of nature, that both types of waves actually occur.
In 1970 Paul Davies extended the Wheeler-Feynman model to Quantum Mechanics ("A Quantum Theory of Wheeler-Feynman Electrodynamics"). The problem with this model of particle interaction was that it was difficult to compute.
Cramer interpreted the retarded component of the Wheeler-Feynman as an "offer wave", and the advanced component of the Wheeler-Feynman as a "confirmation wave". Traditionally, only the emission process had been considered real. Cramer gave reality to the absorption process too. Cramer showed that this "transactional" interpretation had one monumental advantage: it derived the Born Rule (that the probability of an event is proportional to the square of the wave function corresponding to that event), something that had historically been an accidental discovery with no rational explanation other than the fact that it works. Furthermore, the measurement process is no longer mysterious: it corresponds with the moment when "all confirmation waves are returned to the emitter from all absorbers capable of responding". Measurements are simply the consequences of transactions, that include both emissions and absorptions.
In other words, Cramer viewed any quantum event as a "handshake" executed through an exchange of advanced and retarded waves. The exchange of a quantum of energy between a present emitter and a future absorber occurs through a Wheeler-Feynman exchange of advanced and retarded waves. The emitter sends an "offer" wave to the absorber (forward in time). The absorber then returns a "confirmation" wave to the emitter (backwards in time). The transaction is then completed with an "handshake" across space-time, which leads to the transfer of energy from emitter to absorber.
Cramer's "transaction" is explicitly non-local because the future is affecting the past. Einstein's apparent paradox is therefore solved without resorting to a knowledge-based interpretation.
What the US physicist Ruth Kastner has done is to remedy some problems of the original Cramer theory. The technicalities are for quantum scientists only, but the metaphysical implications are for everybody: Kastner takes the retarded and the advanced waves as being both "real". The key concept, somewhat aligned with David Lewis' "possible worlds", is that possibilities exist, although not in spacetime.
"Physical" and "actual" are not the same thing: "actual" is a physical entity that is also experienced, but there are physical entities that are never experienced, and therefore never "actual". There is a sort of meta-reality that takes place in what Kastner calls "the pre-spatiotemporal realm".
In this realm Cramer's offer and confirmation waves (the results of emissions and absorptions) are not simply mathematical tools but real events. This realm, it turns out, is Hilbert space. Hilbert space is therefore "real" in Kastner's recasting of ontology. If Quantum Theory is interpreted as a theory about possibilities in this sense, a lot of "oddities" get simplified.
Kastner's transactions are not quite classical trajectories. They are more like Feynman's sum-over-paths.
Throughout the book Kastner points out several examples of physical theories that are, after all, no less counter-intuitive than assuming the reality of Hilbert space. For example, we all treat atoms as real, although we can't see them. But the most powerful argument comes towards the end, when she reviews the "collapse" of the quantum wave, an instantaneous phenomenon that seems to defy the principle of Relativity (according to which what is instantaneous for me may not be for you if you are in motion relative to me). This collapse, that is routinely observed in millions of experiments around the world, is empirically real but it is not quite an event: it is not located anywhere in spacetime. It is "sub-empirical".
The last sections of the book are more philosophical in nature than scientific. Kastner elaborates on the notion of possibility (her possibilities are less real than events in the actual world but more real than mere suppositions). Transactions, not particles, are her fundamental ontological entities. But this is only the tip of the iceberg: any "object" or observed event is the result of a large number of transactions.
Reality is neither objective nor subjective but "intersubjective". The very persistence of an object through time is due to the fact that transactions keep happening whose result is a cohesive macroscopic phenomenon. Kastner also salvages free will, that most interpretations of Quantum Mechanics sacrifice to the altar of indeterminacy and randomness.
There is a lot to absorb in this stimulating book.