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The European Physical Journal Plus

An exploration of a special case in the relationship between Fisher information and quantum potential in the causal interpretation of quantum mechanics

Tim C Jenkins

Published Jan 1, 2021• 1 citation
Publisher
DOI
10.1140/epjp/s13360-020-01050-y

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Thermomagnetic properties, and its effects on Fisher information entropy with Schioberg plus Manning-Rosen potential are studied using NUFA and SUSYQM methods in the presence of the Greene-Aldrich approximation scheme to the centrifugal term. The wave function obtained was used to study Fisher information both in position and momentum spaces for different quantum states by the gamma function and digamma polynomials. The energy equation obtained in a closed form was used to deduce numerical energy spectra, partition function, and other thermomagnetic properties. The results show that with an application of AB and magnetic fields, the numerical energy eigenvalues for different magnetic quantum spins decrease as the quantum state increases and completely removes the degeneracy of the energy spectra. Also, the numerical computation of Fisher information satisfies Fisher information inequality products, indicating that the particles are more localized in the presence of external fields than in their absence, and the trend shows complete localization of quantum mechanical particles in all quantum states. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. The energy equations obtained from the NUFA and SUSYQM were the same, demonstrating a high level of mathematical precision.

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On a refinement of Heisenberg uncertainty relation by means of quantum Fisher information

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Journal of Mathematical Analysis and Applications•Sep 18, 2010•34 citations
We extend the Informational Gravity framework (Papers I-II) to quantum mechanics. Papers I and II established the nodes of the causal network (informationally bound energy) and defined their spatial relationships through bidirectional causal connectivity. This paper identifies the connections: massless interactions as timeless field potentials that link nodes without temporal extension. This identification yields a taxonomy of physical relationships - causal connections, entanglement, and the absence of connection - that proposes to reframe the EPR paradox without invoking nonlocality, accommodates Bell inequality violations within its ontological categories, provides an account of delayed choice experiments, and aims to dissolve the measurement problem by proposing that every interaction between a timeless connection and a time-bound system (any system with mass and proper time) constitutes a projection - removing the need for a special category of "measurement." An independent result - that finite informational capacity of a discrete network grounds a structural reading of the uncertainty principle - connects quantum indeterminacy to the framework's foundational structure. The framework does not modify quantum mechanics but offers an interpretive ontology in which its features become natural consequences of a causal network rather than irreducible axioms. We argue that this ontology renders the Many Worlds interpretation unnecessary.
Thermomagnetic properties, and its effects on Fisher information entropy with Schioberg plus Manning-Rosen potential are studied using NUFA and SUSYQM methods in the presence of the Greene-Aldrich approximation scheme to the centrifugal term. The wave function obtained was used to study Fisher information both in position and momentum spaces for different quantum states by the gamma function and digamma polynomials. The energy equation obtained in a closed form was used to deduce numerical energy spectra, partition function, and other thermomagnetic properties. The results show that with an application of AB and magnetic fields, the numerical energy eigenvalues for different magnetic quantum spins decrease as the quantum state increases and completely removes the degeneracy of the energy spectra. Also, the numerical computation of Fisher information satisfies Fisher information inequality products, indicating that the particles are more localized in the presence of external fields than in their absence, and the trend shows complete localization of quantum mechanical particles in all quantum states. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. The energy equations obtained from the NUFA and SUSYQM were the same, demonstrating a high level of mathematical precision.