The transactional interpretation of quantum mechanics (TIQM) takes the

wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...

of the standard quantum formalism, and its complex conjugate, to be retarded (forward in time) and advanced (backward in time) waves that form a quantum interaction as a Wheeler–Feynman handshake or transaction. It was first proposed in 1986 by

John G. Cramer John Gleason Cramer, Jr. (born October 24, 1934) is a Professor Emeritus of Physics at the University of Washington in Seattle, Washington, known for his development of the Transactional Interpretation of Quantum Mechanics. He has been an activ ...

, who argues that it helps in developing intuition for quantum processes. He also suggests that it avoids the philosophical problems with the

Copenhagen interpretation The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, as feat ...

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 The Afshar experiment is a variation of the double-slit experiment in quantum mechanics, devised and carried out by Shahriar Afshar while at the private, Boston-based Institute for Radiation-Induced Mass Studies (IRIMS). The results were presente ...

, while claiming that the Copenhagen interpretation and the

many-worlds interpretation The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum ...

are not. The existence of both advanced and retarded waves as admissible solutions to

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...

was explored in the

Wheeler–Feynman absorber theory The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assu ...

. Cramer revived their idea of two waves for his transactional interpretation of quantum theory. While the ordinary

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...

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, who is later in time, also emits an advanced wave backward in time and a retarded wave forward in time. A quantum event occurs when a "handshake" exchange of advanced and retarded waves triggers the formation of a transaction in which energy, momentum, angular momentum, etc. are transferred. The quantum mechanism behind transaction formation has been demonstrated explicitly for the case of a photon transfer between atoms in Sect. 5.4 of Carver Mead's book ''Collective Electrodynamics''. In this interpretation, the

collapse of the wavefunction In quantum mechanics, wave function collapse occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an ''observat ...

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 An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraord ...

. Philosopher and writer Ruth Kastner argues that the waves exist as possibilities outside of physical spacetime and that therefore it is necessary to accept such possibilities as part of reality. Cramer has used TIQM in teaching quantum mechanics at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seatt ...

Seattle Seattle ( ) is a seaport city on the West Coast of the United States. It is the seat of King County, Washington. With a 2020 population of 737,015, it is the largest city in both the state of Washington and the Pacific Northwest region o ...

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 A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the ...

and eliminates the observer-dependent reality that has been criticized as part of the

. Cramer states that the key advances over Everett's Relative State Interpretation are that the transactional interpretation has a physical collapse and is time-symmetric. Cramer also states that the TI is consistent with but not dependent upon the notion of an Einsteinian block universe. Kastner claims that by considering the product of the advanced and retarded wavefunctions, the

Born rule The Born rule (also called Born's rule) is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of findi ...

can be explained ontologically.Kastner, R. E. The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility (CUP, 2012) The transactional interpretation is superficially similar to the two-state vector formalism (TSVF) which has its origin in work by Yakir Aharonov,

Peter Bergmann Peter Gabriel Bergmann (24 March 1915 – 19 October 2002) was a German-American physicist best known for his work with Albert Einstein on a unified field theory encompassing all physical interactions. He also introduced primary and secondar ...

and

Joel Lebowitz Joel Louis Lebowitz (born May 10, 1930) is a mathematical physicist widely acknowledged for his outstanding contributions to statistical physics, statistical mechanics and many other fields of Mathematics and Physics. Lebowitz has published ...

of 1964. However, it has important differences—the TSVF is lacking the confirmation and therefore cannot provide a physical referent for the Born Rule (as TI does). Kastner has criticized some other time-symmetric interpretations, including TSVF, as making ontologically inconsistent claims. Kastner has developed a new ''Relativistic Transactional Interpretation'' (RTI) also called ''Possibilist Transactional Interpretation'' (PTI) in which space-time itself emerges by a way of transactions. It has been argued that this relativistic transactional interpretation can provide the quantum dynamics for the causal sets program.

Debate

In 1996, Tim Maudlin proposed a

thought experiment A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anc ...

involving Wheeler's delayed choice experiment that is generally taken as a refutation of TIQM. However Kastner showed Maudlin's argument is not fatal for TIQM. In his book, ''The Quantum Handshake'', Cramer has added a hierarchy to the description of pseudo-time to deal with Maudlin's objection and has pointed out that some of Maudlin's arguments are based on the inappropriate application of Heisenberg's knowledge interpretation to the transactional description. Transactional Interpretation faces criticisms. The following is partial list and some replies:

References

;Further reading * John G. Cramer, ''The Quantum Handshake: Entanglement, Nonlocality and Transactions'', Springer Verlag 2016, . * Ruth E. Kastner, ''The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility,'' Cambridge University Press, 2012. * Ruth E. Kastner, ''Understanding Our Unseen Reality: Solving Quantum Riddles,'' Imperial College Press, 2015. * Tim Maudlin, ''Quantum Non-Locality and Relativity'', Blackwell Publishers 2002, (discusses a '' gedanken experiment'' designed to refute the TIQM; this has been refuted in Kastner 2012, Chapter 5) * Carver A. Mead, ''Collective Electrodynamics: Quantum Foundations of Electromagnetism'', 2000, . *

John Gribbin John R. Gribbin (born 19 March 1946) is a British science writer, an astrophysicist, and a visiting fellow in astronomy at the University of Sussex. His writings include quantum physics, human evolution, climate change, global warming, the orig ...

, '' 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.”

External links

* John G. Cramer, Professor Emeritus of Physics at the University of Washington, presents "The Quantum Handshake Explored.
YouTube video dated 1 Feb 2018
* Pavel V. Kurakin, George G. Malinetskii

Automates Intelligents (February 2, 2005). (This paper tells about a work attempting to develop TIQM further) * Kastner has also applied TIQM to other quantum mechanical issues i

"The Transactional Interpretation, Counterfactuals, and Weak Values in Quantum Theory" an

"The Quantum Liar Experiment in the Transactional Interpretation" {{Quantum mechanics topics Interpretations of quantum mechanics Quantum measurement Quantum field theory Theoretical physics

Advances over previous interpretations

Debate

See also

References

External links