STM-D-0983Paper2001Published and peer-reviewed

The transactional interpretation of quantum mechanics

John G. Cramer

Abstract and summary · read the original at the source

In one page

Quantum mechanics works perfectly and nobody agrees on what it means. John Cramer, a nuclear physicist at the University of Washington, published a picture in 1986 he called the transactional interpretation, and this conference paper is his own restatement of it. He starts from something already sitting in the equations. The relativistic wave equations have two families of solutions, one running forward in time and one running backward, and the usual treatment quietly keeps only the first. Cramer keeps both. An atom about to emit sends out an offer wave; every potential absorber answers with a confirmation wave running back to the moment of emission; the two lock into a handshake across spacetime, and the completed handshake is the photon. Nothing travels backward as a signal, because the advanced waves cancel everywhere outside the interval between emission and absorption — which is exactly why the picture predicts what standard quantum mechanics predicts. What it buys is a mechanism for the parts the textbooks decline to explain.

Why it matters hereChapter 2 treats the vacuum as a real structured medium whose modes are physically present rather than bookkeeping, and Cramer’s reading gives the wave function that same status — a real wave in space, not a ledger of somebody’s knowledge. Chapter 13 needs pictures in which nonlocality, the arrow of time and the electromagnetic field are one story, and the transaction is the tidiest of them.

What it claims

01Under the Dirac and Wheeler-Feynman assumption of time-symmetric radiation, the advanced field produced by the absorber is exactly cancelled everywhere outside the interval between emission and absorption, so no advanced effect — no backward-in-time signalling, no negative-energy radiation — survives; time-symmetric electrodynamics is completely equivalent in all observables to the conventional description, which is why no experiment distinguishes them.Reviews of Modern Physics 58, section III.A and III.B, pages 659 to 661, Equations 3 to 5
Settled physics
02The emitter produces an offer wave that travels to the absorber; the absorber returns a confirmation wave to the emitter; and the transaction completes as a handshake across spacetime. The process is atemporal, and the step-by-step telling of it is a pedagogical convention, not a sequence in time — the only observables come from the superposition of all steps in the final transaction.Reviews of Modern Physics 58, page 661, the paragraph beginning ’The above, in a simplified one-dimensional form’, and footnote 14
Published and peer-reviewed
03The interpretation is visible in the formalism rather than added to it: for simple systems complex conjugation is equivalent to time reversal, so the complex conjugate wave function is the advanced confirmation wave to the ordinary wave function’s retarded offer wave, and the familiar products and overlap integrals of quantum mechanics read directly as sums of offer-and-confirmation echoes over all space.Reviews of Modern Physics 58, section III.E, page 666, Equations 11a to 11c
Published and peer-reviewed
04Cramer states the interpretation as five elements. The uncertainty principle and the statistical interpretation carry over from Copenhagen unchanged but become consequences of the transaction model rather than independent postulates; all physical processes have equal status, and the observer, the measurement and the apparatus have no special standing; and the state vector is a real physical wave with spatial extent, identical with the offer wave, while the particle and the collapsed state vector are identical with the completed transaction.Reviews of Modern Physics 58, section III.D, pages 665 to 666, elements T-1 to T-5
Published and peer-reviewed
05The account is explicitly nonlocal, and therefore consistent with the tests of the Bell inequality, while remaining relativistically invariant and fully causal — Cramer argues that the collapse model implicit in the Copenhagen interpretation is descriptionally inconsistent with relativistic invariance and causality, and that the transactional description applied to the same system is not.Reviews of Modern Physics 58, Abstract, and section V, Conclusion, page 681
Published and peer-reviewed
06What to watch: Cramer sets his own criteria — economy, compatibility, plausibility and insightfulness — precisely because he holds that no experiment presently separates the two interpretations, and he says so in the conclusion. The observation that would settle it is any result that distinguishes the predictions rather than the pictures, which is the boundary Cramer himself went on to probe in his later work on whether quantum nonlocality permits a signal.Reviews of Modern Physics 58, section V, page 681; and page 661 on the intrinsic untestability of time-symmetric electrodynamics
What to watch

Read it · abstract

Abstract

The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a “handshake” between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or “transaction” in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually “visible” in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to “quantum paradoxes.”

John G. Cramer, The transactional interpretation of quantum mechanics, AIP Conference Proceedings 573, pages 132 to 138 (2001), from the Fourth International Conference on Computing Anticipatory Systems, Liège. The published paper is at doi.org/10.1063/1.1388683.

Abstract of the 1986 original

The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and “paradoxes.” The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as “mathematical representations of knowledge” as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its “collapse.” It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P = ψψ*), basic elements of the Copenhagen interpretation.

John G. Cramer, The transactional interpretation of quantum mechanics, Reviews of Modern Physics 58, pages 647 to 687, July 1986. The published article is at doi.org/10.1103/RevModPhys.58.647, and the author hosts a scan of it openly at faculty.washington.edu/jcramer.

(Abstracts only — no other text of either paper is reproduced here; see the rights note above. On this site, Cramer’s talk at the NASA Breakthrough Propulsion Physics workshop appears in the proceedings at /library/stm-df8f3b69bc; the causal-interpretation fluid model is at /library/stm-ad7a00b6f5; the zero-point-field reading of the quantum ontology is at /library/stm-9409ed6eff; the stochastic-electrodynamics route to the same questions is at /library/stm-aed90bbe0c and /library/stm-e18be5e77d; and the Defense Intelligence reference document on entanglement and nonlocality is at /library/stm-e094621316.)

The way in

https://doi.org/10.1063/1.1388683TWO PAPERS, ONE IDEA. The identifier on this record is the conference restatement — John G. Cramer, The transactional interpretation of quantum mechanics, AIP Conference Proceedings 573, pages 132 to 138, from the Fourth International Conference on Computing Anticipatory Systems held at Liege in 2000. The original is Reviews of Modern Physics 58, 647 to 687 (1986), DOI 10.1103/RevModPhys.58.647, a forty-one page review article. Both are cited; this page is about the interpretation, not about either printing of it. TEXT. The AIP proceedings paper is closed and no repository copy exists, so the abstract reproduced below is the author’s own as deposited with the publisher and carried by OpenAlex. Cramer hosts the 1986 Reviews of Modern Physics article openly on his University of Washington faculty page at faculty.washington.edu/jcramer; that file was fetched on 2026-09-08 and is a page-image scan with no text layer, so it was rasterised at 300 dots per inch and read by optical character recognition. The American Physical Society holds copyright in it, so only its abstract is reproduced here — but every claim below is located against that article’s own section numbers, page numbers and equation numbers, read from the scan rather than from the conference summary. Cramer’s affiliations on the 1986 paper are the Department of Physics, University of Washington, Seattle, and the Bereich Kern- und Strahlenphysik of the Hahn-Meitner-Institut fur Kernforschung, Berlin.

How to cite it

John G. Cramer (2001) The transactional interpretation of quantum mechanics. doi:10.1063/1.1388683

Where it sits in the curriculum

What the vacuum is The unified picture