3.7 Collapse and Nonlocality in the Transactional Interpretation
In the TI the collapse of the state vector is interpreted as the completion of the transaction started by the OW and the CW exchanged between emitter and absorber. The emergence of the transaction from the SV does not occur at some particular location in space or at some particular instant of time, but rather forms along the entire four-vector which connects the emission locus with the absorption locus (or loci in the case of multiple correlated particles). The transaction employs both retarded and advanced waves which propagate, respectively, along positive and negative lightlike (or timelike) four-vectors. Since the sum of these four-vectors can span spacelike and negative timelike or lightlike intervals, the "influence" of the transaction in enforcing the correlations of the quantum event is explicitly both nonlocal and atemporal.
Fig. 5 shows an example of such combinations of four-vector for a two photon transaction corresponding to an event in the Freedman-Clauser experiment. Note that although all of the waves in the transaction lie along lightlike world lines, the "influence" which enforces the correlations between the two polarization measurements spans a spacelike interval and is therefore nonlocal. This nonlocality is an explicit feature of the TI arising from the use of advanced waves.
Schrödinger (1935), in analyzing the EPR paradox, concluded that at least part of the problem lay in the way time is used in quantum mechanics (in the context of the CI). The CI treats time in an essentially classical non-relativistic way, and as we have seen in Section 2.5, this leads to inconsistencies with relativity or causality in any non-subjective CI description of collapse in, for example, the Freedman-Clauser experiment. The root of the inconsistencies lies in the implicit assumption of the CI that the SV collapse occurs at a particular instant at which a particular measurement is made and "knowledge" is gained, that before this instant the SV is in its full uncollapsed state, and that there can be a well-defined "before" and "after" in the collapse description. In the TI the collapse, i.e., the development of the transaction, is atemporal and thus avoids the contradictions and inconsistencies implicit in any time-localized SV collapse.
Further, the TI description does not need to invoke arbitrary collapse triggers such as consciousness, etc., because it is the absorber rather than the observer which precipitates the collapse of the SV, and this can occur atemporally and nonlocally across any sort of interval between elements of the measuring apparatus. This will be discussed further in the context of gedanken experiments in Section 4.
