Wikipedia has a short entry on the theory, which basically involves the idea of the quantum world being governed by "offer waves" that travel forward in time meeting up with "confirmation waves" that travel backward in time.
The paper talks about the "Quantum Liar Experiment", which has this consequence:
Elitzur and Dolev refer to this as the “quantum liar” experiment because, in their words: “The very fact that one atom is positioned in a place that seems to preclude its interaction with the other atom leads to its being affected by that other atom. This is logically equivalent to the statement: ‘This sentence has never been written.”’An issue with the transactional interpretation is the nature of the waves. It seems Cramer says they are physical waves, but the author of this new paper has a different take:
Clearly, when we consider experiments like the QLE in the usual conceptual way, we encounter nothing but paradoxes and contradictions, which are always the hallmark of a constraining paradigm. We can break through the impasse by viewing offer and confirmation waves not as ordinary physical waves but rather as “waves of possibility” that have access to a larger physically real space of possibilities.In the conclusion, it's said:
...TI continues to provide an elegant and natural account of quantum phenomena, provided that we consider offer and confirmation waves as residing in a “higher” physical space corresponding to the configuration space of all particles involved. This space can be considered as a physically real space of possibilities; thus “real” is not equivalent to “actual.” This is admittedly a bold new ontological picture in the context of quantum theory interpretations, but it should be seriously considered because it accomodates the formalism of quantum theory, including its implicit time-symmetric aspects, in a natural way. As a side-benefit, it also provides further insight into the origins of “quantum wholeness.” In this picture, actualized phenomena constitute just the “tip of the iceberg” of a space of physically real possibilities.What does it all mean? I don't know, but I like the phrase "physically real space of possibilities", becuase I am sure there must be theological fodder in it! (Sounds to me like somewhere God would live.)