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arXiv:1204.6636

The transaction as a quantum concept

Leonardo Chiatti

Published Apr 24, 2012• 15 citations
arXivHTMLPDF

Abstract

This essay intends to present a novel approach to the concept of "transaction" in quantum physics. Breaking with Cramer's original theory, the transaction is not connected to the simultaneously retarded and advanced spacetime propagation of classical fields, as in the spirit of Wheeler-Feynman electrodynamics. Instead, the transaction is seen as an archetypal structure intrinsic within the quantum formalism. The present approach is advantageous in that, while preserving the essential point of Cramer's theory, is also fully consistent with the standard quantum formalism. In particular, it has the advantage of avoiding the introduction of elements which are completely extraneous to quantum formalism (such as the propagation of real physical waves in four-dimensional spacetime, the phase difference between offer and confirmation waves which is necessary for the elimination of "tails", the echoing mechanism, etc.)

DOI
10.48550/arxiv.1204.6636

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This essay intends to present a novel approach to the concept of "transaction" in quantum physics. Breaking with Cramer's original theory, the transaction is not connected to the simultaneously retarded and advanced spacetime propagation of classical fields, as in the spirit of Wheeler-Feynman electrodynamics. Instead, the transaction is seen as an archetypal structure intrinsic within the quantum formalism. The present approach is advantageous in that, while preserving the essential point of Cramer's theory, is also fully consistent with the standard quantum formalism. In particular, it has the advantage of avoiding the introduction of elements which are completely extraneous to quantum formalism (such as the propagation of real physical waves in four-dimensional spacetime, the phase difference between offer and confirmation waves which is necessary for the elimination of "tails", the echoing mechanism, etc.)
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 ($P=\ensuremath{\psi}{\ensuremath{\psi}}^{*}$), basic elements of the Copenhagen interpretation.
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.”
The classical Wheeler-Feynman absorber theory with a postulate of Lorentz-invariant zero-point electromagnetic radiation is proposed to explain quantum phenomena in a similar manner to that of stochastic electrodynamics. For this purpose, Cramer's model of a 'Minimum emitter-absorber transaction' is extended to the case where zero-point radiation exists, in the context of the classical Wheeler-Feynman theory. The Einstein-Podolski-Rosen paradox and the quantum levels of a charged simple harmonic oscillator are derived from the theory. It is shown that the condition for a transaction plays an essential role, such as in the radiative balance of a simple harmonic oscillator.
The transactional interpretation of quantum mechanics, following the time-symmetric formulation of electrodynamics, uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate to understand quantum phenomena by means of transactions. A transaction occurs between an emitter and a specific absorber when the emitter has received advanced waves from all possible absorbers. Advanced causation always raises the specter of paradoxes, and it must be addressed carefully. In particular, different devices involving contingent absorbers or various types of interaction-free measurements have been proposed as threatening the original version of the transactional interpretation. These proposals will be analyzed by examining in each case the configuration of absorbers and, in the special case of the so-called quantum liar experiment, by carefully following the development of retarded and advanced waves through the Mach-Zehnder interferometer. We will show that there is no need to resort to the hierarchy of transactions that some have proposed, and will argue that the transactional interpretation is consistent with the block-universe picture of time.
By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws ofmore » motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle.« less