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The transactional interpretation of quantum mechanics (TIQM) is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward-in-time) and advanced (backward-in-time) waves. The interpretation was first proposed by John Cramer in 1986. The author argues that it helps in developing intuition for quantum processes, avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and resolves various quantum paradoxes.^[1][2] Cramer uses TIQM in teaching quantum mechanics at the University of Washington in Seattle.

The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations was proposed by Richard Feynman and John Archibald Wheeler in 1945 (cited in original paper by J. Cramer). They used the idea to solve the problem of the self-energy of an electron. 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.

Suppose a particle (such as a photon) emitted from a source could interact with one of two detectors. According to TIQM, the source emits a usual (retarded) wave forward in time, the "offer wave", and when this wave reaches the detectors, each one replies with an advanced wave, the "confirmation wave", that travels backwards in time, back to the source. The phases of offer and confirmation waves are correlated in such a way that these waves interfere positively to form a wave of the full amplitude in the space-time region between emitting and detection events, and they interfere negatively and cancel out elsewhere in space-time (i.e., before the emitting point and after the absorption point). The size of the interaction between the offer wave and a detector's confirmation wave determines the probability with which the particle will strike that detector rather than the other one. 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, the region of space-time where offer and confirmation waves interact. 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.

John Cramer has argued that the transactional interpretation is consistent with the outcome of the Afshar experiment, while the Copenhagen interpretation and the many-worlds interpretation are not.^[3]

• Wheeler–Feynman absorber theory

1. ^ The Transactional Interpretation of Quantum Mechanics by John Cramer. Reviews of Modern Physics 58, 647-688, July (1986)
2. ^ An Overview of the Transactional Interpretation by John Cramer. International Journal of Theoretical Physics 27, 227 (1988)
3. ^ A Farewell to Copenhagen?, by John Cramer. Analog, December 2005.

• Tim Maudlin, Quantum Non-Locality and Relativity, Blackwell Publishers 2002, ISBN 0-631-23220-6 (discusses a gedanken experiment designed to refute the TIQM)

• 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 Kastneran, an attempt to refute Maudlin's refutation