Transactional interpretation
Encyclopedia
The transactional interpretation of quantum mechanics
(TIQM) describes quantum interactions in terms of a standing wave
formed by retarded (forward-in-time) and advanced (backward-in-time) waves. It was first proposed in 1986 by John G. Cramer
, who 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. More recently he has also argued TIQM to be consistent with the Afshar experiment
, while claiming that the Copenhagen interpretation
and the many-worlds interpretation
are not.
The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations
was explored in the Wheeler–Feynman absorber theory. 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.
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 also emits an advanced wave backward in time and a retarded wave forward in time. The phases
of these waves are such that the retarded wave emitted by the receiver cancels the retarded wave emitted by the sender, with the result that there is no net wave after the absorption point. The advanced wave emitted by the receiver also cancels the advanced wave emitted by the sender, so that there is no net wave before the emitting point either. 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, 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.
1. “TI is not mathematically precise.”
Offer waves (OW) obey the Schrödinger equation and Confirmation waves (CW) obey the complex conjugate Schrödinger equation. A transaction is a genuinely stochastic event, and therefore does not obey a deterministic equation. Outcomes based on actualized transactions obey the Born Rule
and, as noted in Cramer (1986), TI provides a derivation of the Born Rule
rather than assuming it as in standard quantum mechanics
(QM).
2. “TI does not generate new predictions / is not testable / has not been tested.”
TI is an exact interpretation of QM and so its predictions must be the same as QM. Like the many-worlds interpretation
(MWI), TI is a ‘pure’ interpretation in that it does not add anything ad hoc but provides a physical referent for a part of the formalism that has lacked one (the advanced states implicitly appearing in the Born Rule
). Thus the demand often placed on TI for new predictions or testability is a mistaken one that misconstrues the project of interpretation as one of theory modification.
3. “It is not made clear where in spacetime a transaction occurs.”
One clear account is given in Cramer (1986), which pictures a transaction as a four-vector standing wave whose endpoints are the emission and absorption events. Other possible accounts are being explored in which the formation of a transaction is an a-spatiotemporal process, or one taking place on a level of possibility rather than actuality.
4. “Maudlin (1996, 2002) has demonstrated that TI is inconsistent.”
Maudlin (see below) raised an interesting challenge for TI which has been addressed by (at least) four different authors, all of which have presented ways for TI to remain viable in the face of this challenge:
5. It is not clear how the transactional interpretation handles the quantum mechanics of more than one particle.
Cramer uses TIQM in teaching quantum mechanics at the University of Washington
in Seattle
.
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...
(TIQM) describes quantum interactions in terms of a standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
formed by retarded (forward-in-time) and advanced (backward-in-time) waves. It was first proposed in 1986 by John G. Cramer
John G. Cramer
John G. Cramer is a professor of physics at the University of Washington in Seattle, the United States. When not teaching, he works with the STAR detector at the new Relativistic Heavy Ion Collider at Brookhaven National Laboratory, and the particle accelerator at CERN in Geneva, Switzerland...
, who argues that it helps in developing intuition for quantum processes, avoids the philosophical problems with the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
and the role of the observer, and resolves various quantum paradoxes. More recently he has also argued TIQM to be consistent with the Afshar experiment
Afshar experiment
The Afshar experiment is an optical experiment, devised and carried out by Shahriar Afshar in 2001, which investigates the principle of complementarity in quantum mechanics...
, while claiming that the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
and the many-worlds interpretation
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
are not.
The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
was explored in the Wheeler–Feynman absorber theory. Cramer revived their idea of two waves for his transactional interpretation of quantum theory. While the ordinary Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
does not admit advanced solutions, its relativistic
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
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 also emits an advanced wave backward in time and a retarded wave forward in time. The phases
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of these waves are such that the retarded wave emitted by the receiver cancels the retarded wave emitted by the sender, with the result that there is no net wave after the absorption point. The advanced wave emitted by the receiver also cancels the advanced wave emitted by the sender, so that there is no net wave before the emitting point either. 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, 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.
Debate
TIQM faces a number of common criticisms. The following is partial list and some replies:1. “TI is not mathematically precise.”
Offer waves (OW) obey the Schrödinger equation and Confirmation waves (CW) obey the complex conjugate Schrödinger equation. A transaction is a genuinely stochastic event, and therefore does not obey a deterministic equation. Outcomes based on actualized transactions obey the Born Rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...
and, as noted in Cramer (1986), TI provides a derivation of the Born Rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...
rather than assuming it as in standard quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
(QM).
2. “TI does not generate new predictions / is not testable / has not been tested.”
TI is an exact interpretation of QM and so its predictions must be the same as QM. Like the many-worlds interpretation
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
(MWI), TI is a ‘pure’ interpretation in that it does not add anything ad hoc but provides a physical referent for a part of the formalism that has lacked one (the advanced states implicitly appearing in the Born Rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...
). Thus the demand often placed on TI for new predictions or testability is a mistaken one that misconstrues the project of interpretation as one of theory modification.
3. “It is not made clear where in spacetime a transaction occurs.”
One clear account is given in Cramer (1986), which pictures a transaction as a four-vector standing wave whose endpoints are the emission and absorption events. Other possible accounts are being explored in which the formation of a transaction is an a-spatiotemporal process, or one taking place on a level of possibility rather than actuality.
4. “Maudlin (1996, 2002) has demonstrated that TI is inconsistent.”
Maudlin (see below) raised an interesting challenge for TI which has been addressed by (at least) four different authors, all of which have presented ways for TI to remain viable in the face of this challenge:
- Berkovitz, J. (2002). ``On Causal Loops in the Quantum Realm,” in T. Placek and J. Butterfield (Ed.), Proceedings of the NATO Advanced Research Workshop on Modality, Probability and Bell's Theorems, Kluwer, 233-255.
- Cramer J. G. (2005). “The Quantum Handshake: A Review of the Transactional Interpretation of Quantum Mechanics,” presented at “Time-Symmetry in Quantum Mechanics” Conference, Sydney, Australia, July 23, 2005. Available at: http://faculty.washington.edu/jcramer/PowerPoint/Sydney_20050723_a.ppt
- Kastner, R. E. (2006). “Cramer's Transactional Interpretation and Causal Loop Problems,” Synthese 150, 1-14.
- Marchildon, L. (2006). “Causal Loops and Collapse in the Transactional Interpretation of Quantum Mechanics,” Physics Essays 19, 422.
5. It is not clear how the transactional interpretation handles the quantum mechanics of more than one particle.
- Daniel F. Styer, Miranda S. Balkin, Kathryn M. Becker, Matthew R. Burns, Christopher E. Dudley, Scott T. Forth, Jeremy S. Gaumer, Mark A. Kramer, David C. Oertel, Leonard H. Park, Marie T. Rinkoski, Clait T. Smith and Timothy D. Wotherspoon (2002) "Nine formulations of quantum mechanics," American Journal of Physics 70, 288-297.
Cramer uses TIQM in teaching quantum mechanics at the University of Washington
University of Washington
University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...
in Seattle
Seattle, Washington
Seattle is the county seat of King County, Washington. With 608,660 residents as of the 2010 Census, Seattle is the largest city in the Northwestern United States. The Seattle metropolitan area of about 3.4 million inhabitants is the 15th largest metropolitan area in the country...
.
Further reading
- Tim Maudlin, Quantum Non-Locality and Relativity, Blackwell Publishers 2002, ISBN 0-631-23220-6 (discusses a gedanken experiment designed to refute the TIQM)
- R. E. Kastner, Why Everettians Should Appreciate the Transactional Interpretation, argues that TIQM provides a better solution to quantum puzzles than Many-Worlds interpretations. http://arxiv.org/abs/1001.2867.
- John GribbinJohn GribbinJohn R. Gribbin is a British science writer and a visiting Fellow in astronomy at the University of Sussex.- Biography :John Gribbin graduated with his bachelor's degree in physics from the University of Sussex in 1966. Gribbin then earned his master of science degree in astronomy in 1967, also...
, Schrödinger's Kittens and the Search for RealitySchrödinger's Kittens and the Search for RealitySchrödinger's Kittens and the Search for Reality is a book by John Gribbin, published in 1996, which attempts to explain the mysteries of modern quantum mechanics in a popular-scientific way...
: 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
- 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 Kastner, an argument that Maudlin's experiment is not fatal for TIQM.
- Kastner has also applied TIQM to other quantum mechanical issues in http://philpapers.org/rec/KASTTI "The Transactional Interpretation, Counterfactuals, and Weak Values in Quantum Theory" and http://arxiv.org/abs/0906.1626 "The Quantum Liar Experiment in the Transactional Interpretation"