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Quantum dynamics without the wavefunction

Rafael D Sorkin

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When suitably generalized and interpreted, the path integral offers an alternative to the more familiar quantal formalism based on state vectors, self-adjoint operators and external observers. Mathematically one generalizes the path-integral-as-propagator to a quantal measure μ on the space Ω of all 'conceivable worlds', and this generalized measure expresses the dynamics or law of motion of the theory, much as Wiener measure expresses the dynamics of Brownian motion. Within such 'histories-based' schemes new and more 'realistic' possibilities open up for resolving the philosophical problems of the state-vector formalism. In particular, one can dispense with the need for external agents by locating the predictive content of μ in its sets of measure zero: such sets are to be 'precluded'. But unrestricted application of this rule engenders contradictions. One possible response would remove the contradictions by circumscribing the application of the preclusion concept. Another response, more in the tradition of 'quantum logic', would accommodate the contradictions by dualizing Ω to a space of 'co-events' and effectively identifying reality with an element of this dual space.


PACS

03.65.Ca Formalism

03.65.Ta Foundations of quantum mechanics; measurement theory

03.67.-a Quantum information

05.40.Jc Brownian motion

03.65.Fd Algebraic methods

MSC

81S40 Path integrals (See also 58D30)

81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)

81P15 Quantum measurement theory

Subjects

Computational physics

Statistical physics and nonlinear systems

Quantum information and quantum mechanics

Dates

Issue 12 (23 March 2007)

Received 24 October 2006

Published 7 March 2007



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