The Quantum Handshake: Entanglement, Nonlocality and Transactions by John Cramer.
The transactional interpretation of quantum theory is probably the most neglected interpretation of quantum theory (I know, you would have thought all interpretations of quantum theory would be fodder for gossip mags and the glitterati!) Invented by John Cramer it was inspired by the Wheeler-Feynman absorber theory of electromagnetism. In this later theory Wheeler and Feynman examine the consequences of taking both advanced and retarded solutions of electromagnetism seriously. You may recall from your hours spent reading Jackson (I will not link to the blasphemous third edition) that when solving Maxwell’s equations of electromagnetism you end up in the tricky situation of having solutions to the equations that seem to go the wrong way in time. When you wiggle (accelerate) a charge there are solutions to the electromagnetic fields which are waves propagating away from the charge into the future (called retarded waves). But there are also solutions that have waves essentially propagating backwards into the past (called advanced waves). Of course this should make you head hurt, and so the normal thing to do is disregard the advanced waves. What Wheeler and Feynman attempted to do was to not make a theory of electromagnetism without this kludge of disregarding advanced waves. They were in a sense successful, able to show that in essence they could recover the retarded only electromagnetism via an assumption that all emissions must result in absorption.
What Cramer’s transactional interpretation does is to attempt to use advanced (backwards in time) solutions to the relevant quantum mechanical equations to help us overcome our difficulties understanding quantum theory. Roughly this works as follows, an emitter at some time emits and “offer” wave. In nonrelativistic quantum theory this is just the normal wave function for Schrodigner’s equation. At some later time an absorber interacts with this offer wave. In particular the absorber sends a wave backwards in time to the emitter, in nonrelativistic quantum theory this is the solution to the complex conjugate of Schrodinger’s equation. The emitter then receives this “confirmation” wave. Now, interestingly, if one thinks about the amplitude of the wave function at the emitter, it will be the norm squared of the wave function at the absorber. An emitter can receive many “confirmation” waves from future absorbers. In order to change this into reality, a “transaction” must be established: a choice is made so that only one of the confirmation wave “survives”. Because the emitter has access to the amplitudes, we can see that this choice could be made so as to follow Born’s probability law, at least in so much as the information necessary to get the correct probability law is at the emitter. Supporters of the transactional interpretation like to say that the interpretation “derives” Born’s law, though I find this slightly wanting in this area since I still wonder how probabilities arise here, why is a field norm squared turned into the probability that a transaction is chosen?
The nice thing about the transactional interpretation is that it can help one attempt to reason about seemingly paradoxical setups in quantum theory. For example in a Bell experiment, one can reason about the probabilities that violate local realistic theories, by imagining backwards in time propagation of measurement directions to an original emitter, who because they receive confirmation offers from spacelike separated detectors in the future, can make the same probabilities arise as those in quantum theory. The thing I most like about the interpretation is that it attempts to keep locality of information propagation intact, at the price of these backwards propagating solutions.
“The Quantum Handshake: Entanglement, Nonlocality and Transaction” is a gentle introduction to the transactional interpretation. I begins with a description of the history of quantum theory and conceptual problems that arose. It then introduces the transactional interpretation. And then comes my favorite part of the book, which is where Cramer applies the interpretation to just about every paradoxical quantum experiment ever proposed. In my view this is the best part of the book, an amazing collection of these different issues and what led people to get confused. In each Cramer attempts to show how the transactional interpretation would deal with these issues. But it is a seriously good list of the experiments that makes this book worth picking up, even if you are not likely to be converted to Cramer’s view of the world. The book also includes a bit on an objection to the transactional interpretation due to Maudlin. This involves, Cramer’s approach, an additional assumption about the hierarchy of transactions, which is interesting to ponder.
Recommended for quantum theory buffs and anyone who want’s to beat their head up against understanding quantum theory.