The transactional interpretation of quantum mechanics (TIQM) describes quantum interactions in terms of a standing wave formed by both retarded ("forward-in-time") waves, in addition to advanced ("backward-in-time") waves. It was first proposed in 1986 by John G. Cramer, who argues that it helps in developing intuition for quantum processes. He also suggests that it avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and also resolves various quantum paradoxes. TIQM formed a minor plot point in his science fiction novel Einstein's Bridge.
More recently, he has also argued TIQM to be consistent with the Afshar experiment, while claiming that the Copenhagen interpretation and the many-worlds interpretation are not. The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations was explored in the Wheeler–Feynman absorber theory. Cramer revived their idea of two waves for his transactional interpretation of quantum theory. While the ordinary Schrödinger equation does not admit advanced solutions, its relativistic version does, and these advanced solutions are the ones used by TIQM.
In TIQM, the source emits a usual (retarded) wave forward in time, but it also emits an advanced wave backward in time; furthermore, the receiver also emits an advanced wave backward in time and a retarded wave forward in time. The phases of these waves are such that the retarded wave emitted by the receiver cancels the retarded wave emitted by the sender, with the result that there is no net wave after the absorption point. The advanced wave emitted by the receiver also cancels the advanced wave emitted by the sender, so that there is no net wave before the emitting point either. In this interpretation, the collapse of the wavefunction does not happen at any specific point in time, but is "atemporal" and occurs along the whole transaction, and the emission/absorption process is time-symmetric. The waves are seen as physically real, rather than a mere mathematical device to record the observer's knowledge as in some other interpretations of quantum mechanics.
Advances over previous interpretations
TIQM is explicitly non-local and, as a consequence, logically consistent with counterfactual definiteness (CFD), the minimum realist assumption. As such it incorporates the non-locality demonstrated by the Bell test experiments and eliminates the observer dependent reality that plagues the Copenhagen Interpretation. Greenberger–Horne–Zeilinger state the key advance over Everett's Relative State Interpretation is to regard the conjugate state vector of the Dirac formalism as ontologically real, incorporating a part of the formalism that, prior to TIQM, had been interpretationally neglected. Having interpreted the conjugate state vector as an advanced wave, it is claimed that the origins of the Born rule follow naturally from the description of a transaction.
Being "atemporal", TIQM assigns ontological priority to events in pseudo time. This appears to have acted as the foremost inhibition to mainstream acceptance of the interpretation and underpins Maudlin's (1996,2002) objection. Kastner (2010) has determined that inclusion of pseudotime is not a requirement of the transactional mechanism.
||The neutrality of this section is disputed. (November 2010)|
TIQM faces a number of common criticisms. The following is partial list and some replies:
1. “TI is not mathematically precise.”
Offer waves (OW) obey the Schrödinger equation and confirmation waves (CW) obey the complex conjugate Schrödinger equation. A transaction is a genuinely stochastic event, and therefore does not obey a deterministic equation. Outcomes based on actualized transactions obey the Born rule and, as noted in Cramer (1986), TI provides a derivation of the Born rule rather than assuming it as in standard quantum mechanics (QM).
2. “TI does not generate new predictions / is not testable / has not been tested.”
TI is an exact interpretation of QM and so its predictions must be the same as QM. Like the many-worlds interpretation (MWI), TI is a ‘pure’ interpretation in that it does not add anything ad hoc but provides a physical referent for a part of the formalism that has lacked one (the advanced states implicitly appearing in the Born rule). Thus the demand often placed on TI for new predictions or testability is a mistaken one that misconstrues the project of interpretation as one of theory modification.
3. “It is not made clear where in spacetime a transaction occurs.”
One clear account is given in Cramer (1986), which pictures a transaction as a four-vector standing wave whose endpoints are the emission and absorption events. Other possible accounts are being explored in which the formation of a transaction is an aspatiotemporal process, or one taking place on a level of possibility rather than actuality.
4. “Maudlin (1996, 2002) has demonstrated that TI is inconsistent.”
Maudlin (see below) raised an interesting challenge for TI which has been addressed by (at least) four different authors, all of which have presented ways for TI to remain viable in the face of this challenge:
- Berkovitz, J. (2002). ``On Causal Loops in the Quantum Realm,” in T. Placek and J. Butterfield (Ed.), Proceedings of the NATO Advanced Research Workshop on Modality, Probability and Bell's Theorems, Kluwer, 233–255.
- Cramer J. G. (2005). “The Quantum Handshake: A Review of the Transactional Interpretation of Quantum Mechanics,” presented at “Time-Symmetry in Quantum Mechanics” Conference, Sydney, Australia, July 23, 2005.
- Kastner, R. E. (2006). “Cramer's Transactional Interpretation and Causal Loop Problems,” Synthese 150, 1–14.
- Marchildon, L. (2006). “Causal Loops and Collapse in the Transactional Interpretation of Quantum Mechanics,” Physics Essays 19, 422.
5. It is not clear how the transactional interpretation handles the quantum mechanics of more than one particle.
- Daniel F. Styer, Miranda S. Balkin, Kathryn M. Becker, Matthew R. Burns, Christopher E. Dudley, Scott T. Forth, Jeremy S. Gaumer, Mark A. Kramer, David C. Oertel, Leonard H. Park, Marie T. Rinkoski, Clait T. Smith and Timothy D. Wotherspoon (2002) "Nine formulations of quantum mechanics," American Journal of Physics 70, 288–297.
- The Transactional Interpretation of Quantum Mechanics by John Cramer. Reviews of Modern Physics 58, 647–688, July (1986)
- An Overview of the Transactional Interpretation by John Cramer. International Journal of Theoretical Physics 27, 227 (1988)
- A Farewell to Copenhagen?, by John Cramer. Analog, December 2005.
- Hugh Everett, Relative State Formulation of Quantum Mechanics, Reviews of Modern Physics vol 29, (July 1957) pp 454–462.
- Avshalom C. Elitzur, Eliahu Cohen: The Retrocausal Nature of Quantum Measurement Revealed by Partial and Weak Measurements, AIP Conf. Proc. 1408: Quantum Retrocausation: Theory and Experiment (13–14 June 2011, San Diego, California), pp. 120–131, DOI http://dx.doi.org/10.1063/1.3663720 (abstract)
- Y. Aharonov, P. G. Bergmann, J. L. Lebowitz, Phys. Rev. B, vol. 134, pp. 1410 ff., 1964
- Yakir Aharonov, Lev Vaidman: Protective measurements of two-state vectors, in: Robert Sonné Cohen, Michael Horne, John J. Stachel (eds.): Potentiality, Entanglement and Passion-At-A-Distance, Quantum Mechanical Studies for A. M. Shimony, Volume Two, 1997, ISBN 978-0792344537, pp. 1–8, p. 2
- Cramer's Transactional Interpretation and Causal Loop Problems, Synthese, Vol 150, Iss1, May 2006.
- The Quantum Liar Experiment, R E Kastner, Studies in History and Philosophy of Modern Physics, Vol41, Iss2, May 2010.
- Tim Maudlin, Quantum Non-Locality and Relativity, Blackwell Publishers 2002, ISBN 0-631-23220-6 (discusses a gedanken experiment designed to refute the TIQM)
- R. E. Kastner, Why Everettians Should Appreciate the Transactional Interpretation, argues that TIQM provides a better solution to quantum puzzles than Many-Worlds interpretations. http://arxiv.org/abs/1001.2867.
- John Gribbin, Schrödinger's Kittens and the Search for Reality : solving the quantum mysteries has an overview of Cramer’s interpretation and says that “with any luck at all it will supersede the Copenhagen interpretation as the standard way of thinking about quantum physics for the next generation of scientists.”
- Pavel V. Kurakin, George G. Malinetskii, How bees can possibly explain quantum paradoxes, Automates Intelligents (February 2, 2005). (This paper tells about a work attempting to develop TIQM further)
- Cramer's Transactional Interpretation and Causal Loop Problems (quant-ph/0408109) by Ruth E Kastner, an argument that Maudlin's experiment is not fatal for TIQM.
- Kastner has also applied TIQM to other quantum mechanical issues in  "The Transactional Interpretation, Counterfactuals, and Weak Values in Quantum Theory" and  "The Quantum Liar Experiment in the Transactional Interpretation"