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arXiv:math-ph/9807034 · Physical Review A

Temporal quantum theory

Oliver Rudolph

Published Feb 1, 1999• 1 citation
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Abstract

We propose a framework for temporal quantum theories for the purpose of describing states and observables associated with extended regions of space-time quantum mechanically. The proposal is motivated by Isham's history theories. We discuss its relation to Isham's history theories and to standard quantum mechanics. We generalize the Isham-Linden information entropy to the present context.

DOI
10.1103/physreva.59.1045

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We propose a framework for temporal quantum theories for the purpose of describing states and observables associated with extended regions of space-time quantum mechanically. The proposal is motivated by Isham's history theories. We discuss its relation to Isham's history theories and to standard quantum mechanics. We generalize the Isham-Linden information entropy to the present context.
These lecture notes cover the important developments in histories approach to quantum mechanics with overall content and emphasis somewhat different from other reviews and books on the subject.The idea of Houtappel, Van Dam and Wigner of employing objects based on primitive concepts of physical theories is discussed in some detail and the fact that histories are such objects is emphasized. Application of histories formalism to the problem of understanding the quasiclassical domain is treated in some detail. Other topics discussed include generalized histories-based quantum mechanics and its application to the quantum mechanics of space-time,generalization of the notion of time sequences employing partial semigroups,quasitemporal structures, history projection operator (HPO) formalism, the algebraic scheme of Isham and Linden, an axiomatic scheme for quasitemporal histories-based theories and symmetries and conservation laws in histories-based theories.
The Theory of Temporal Relativity proposes a unified theoretical framework that extends Special and General Relativity into the complex domain, integrating aspects of Quantum Mechanics within a single geometrical structure. The theory introduces a generalized Hilbert-space geometry and interprets quantum states as observer-dependent, arising from complex temporal relations between reference frames. Theory of Temporal Relativity is a theoretical framework proposing a unified extension of Special and General Relativity into the complex domain, with the goal of incorporating aspects of Quantum Mechanics within a consistent geometrical model. The theory generalizes Hilbert-space geometry and relativistic invariance to complex coordinates, introducing observer-dependent descriptions of physical quantities and a reinterpretation of quantum states as complex-phase relations between reference frames. Within this model, fundamental constants such as c, G, and h are not strictly universal but can exhibit apparent local variations arising from the observer’s position in the complex spacetime manifold. These variations preserve global covariance and CPT symmetry while reconciling quantum non-locality with relativistic kinematics. The framework predicts experimentally testable effects, including measurable phase shifts in interferometric experiments, possible frequency modulations in non-inertial systems, and small local deviations of physical constants detectable in condensed-matter and gravitational contexts. The supplementary work, “Quantum Uncertainty, Planck’s Constant, and Ontological Insights from Complex Spacetime Geometry and Local Metric Deformations”, develops the principle of Temporal Relativity as a foundational element of the theory. It formalizes the connection between quantum uncertainty, metric deformations, and complex temporal structures, within an alternative logical framework (AU). This extension provides both an ontological interpretation of the wavefunction and a basis for the emergence of quantum indeterminacy from geometric causes. Together, these works present a coherent attempt to unify the relativistic and quantum domains under a single complex-geometric view of spacetime, maintaining mathematical rigor while providing clear experimental pathways for empirical validation.
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