Path integral and transactional interpretation

Jareth Baca, Ajit Hira, J. A. de Freitas Pacheco +2 more

Ruth E. Kastner

J. G. Cramer

Daniel F. Styer, Miranda S. Balkin, Kathryn M. Becker +10 more

Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton–Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.

John A. Colosi

H. Fearn

This paper explains the delayed choice quantum eraser of Kim et al. (A delayed choice quantum eraser, 1999 ) in terms of the transactional interpretation (TI) of quantum mechanics by Cramer (Rev Mod Phys 58:647, 1986 , The quantum handshake, entanglement, nonlocality and transactions, 1986 ). It is kept deliberately mathematically simple to help explain the transactional technique. The emphasis is on a clear understanding of how the instantaneous “collapse” of the wave function due to a measurement at a specific time and place may be reinterpreted as a relativistically well-defined collapse over the entire path of the photon and over the entire transit time from slit to detector. This is made possible by the use of a retarded offer wave, which is thought to travel from the slits (or rather the small region within the parametric crystal where down-conversion takes place) to the detector and an advanced counter wave traveling backward in time from the detector to the slits. The point here is to make clear how simple the transactional picture is and how much more intuitive the collapse of the wave function becomes if viewed in this way. Also, any confusion about possible retro-causal signaling is put to rest. A delayed choice quantum eraser does not require any sort of backward in time communication. This paper makes the point that it is preferable to use the TI over the usual Copenhagen interpretation for a more intuitive understanding of the quantum eraser delayed choice experiment. Both methods give exactly the same end results and can be used interchangeably.