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A conceptually rigorous validation of the discovery of force as a fundamental quantum observable

Raheem Adom

Published Apr 22, 2026• 0 citations
Publisher

Abstract

In a recent study (Adom R., Int. J. Quantum Found., 12 (2025) 379), I developed a mathematical formulation of force as an essential quantum observable, connecting its quantum wave equation to the violation of translational symmetries that govern the behavior of open quantum systems in a particularly coherent manner. In this letter, I demonstrate that, following the same methodological principles that underpin the well-established quantum wave equations, the proposed force wave equation constitutes a theoretically sound framework that emerges naturally when energy-momentum exchange, instigated by force, is viewed as the fundamental organizing principle for non-relativistic quantum dynamics. This validates the conceptual and mathematical foundations of the framework.

DOI
10.1209/0295-5075/ae5ad3/pdf

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In a recent study (Adom R., Int. J. Quantum Found., 12 (2025) 379), I developed a mathematical formulation of force as an essential quantum observable, connecting its quantum wave equation to the violation of translational symmetries that govern the behavior of open quantum systems in a particularly coherent manner. In this letter, I demonstrate that, following the same methodological principles that underpin the well-established quantum wave equations, the proposed force wave equation constitutes a theoretically sound framework that emerges naturally when energy-momentum exchange, instigated by force, is viewed as the fundamental organizing principle for non-relativistic quantum dynamics. This validates the conceptual and mathematical foundations of the framework.
Abstract In a recent study ( Adom R. , Int. J. Quantum Found. , 12 (2025) 379), I developed a mathematical formulation of force as an essential quantum observable, connecting its quantum wave equation to the violation of translational symmetries that govern the behavior of open quantum systems in a particularly coherent manner. In this letter, I demonstrate that, following the same methodological principles that underpin the well-established quantum wave equations, the proposed force wave equation constitutes a theoretically sound framework that emerges naturally when energy-momentum exchange, instigated by force, is viewed as the fundamental organizing principle for non-relativistic quantum dynamics. This validates the conceptual and mathematical foundations of the framework.
This paper introduces a theoretical framework that bridges the conceptual divide between quantum mechanics and relativity by proposing a fundamental building block of the universe: the “Space-Time* quantum.” The theory posits that every object possesses an inherent property, Time* — defined as the reciprocal of its intrinsic frequency. The Space-Time* quantum is a composite entity, consisting of a timeless space energy and a kinetic Time* energy. This framework provides a new perspective on wave-particle duality, the double-slit experiment, and quantum entanglement. It re-examines the principles of Special Relativity, offering a conceptual and visual explanation of phenomena such as time dilation and length contraction as a consequence of changes in the Space-Time quanta. The theory also provides an alternative view on the origin of the universe and the nature of gravity, suggesting that gravitational effects arise from an energy deficiency rather than a curvature of spacetime. This paper establishes a conceptual foundation for further mathematical development to test and validate these new insights.
Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.
This paper presents a novel derivation of Schrödinger's equation from first principles based on quantum information dynamics rather than traditional quantization procedures. Working within the Pentagonal Quantum Information Substrate (PQIS) framework, we demonstrate that the wave function and its evolution equation emerge naturally from the dynamics of information processing in a discrete network with pentagonal (D₅) symmetry. Through rigorous mathematical analysis, we establish that information depth distributions project onto configuration space as wave functions, while their evolution through the network yields precisely the Schrödinger equation. We formally derive the Planck constant ℏ as J·χ₍ₐᵥₖ₎·ℓ₍ₚ₎, connecting quantum behavior to fundamental network parameters, and show how the Hamiltonian operator emerges from information exchange terms in the QIS action. Our derivation accounts for all essential quantum features including superposition, interference, probability interpretation, and measurement collapse through the meltdown mechanism. Quantum corrections for finite-sized systems and relativistic extensions are also presented. This work suggests that quantum mechanics is not a fundamental description but rather an emergent approximation of more basic information dynamics, with significant implications for our understanding of quantum foundations and potential paths toward quantum gravity.
Classical mechanics and quantum mechanics have long been framed as binary opposites—but this dichotomy has yielded no real benefits, only persistent confusion. The fundamental equations of quantum mechanics cannot logically demarcate a clear boundary between the quantum and classical realms; in fact, the massm and potential energy V in the Schrödinger equation seamlessly traverse the divide between the microscopic and macroscopic. The electromagnetic potential energy in the Schrödinger equation can be replaced with the potential energy of interactive forces, which can further be converted into force itself using the relation F = V/r. Derivations have now produced a force operator and quantum mechanical equations that explicitly incorporate force—including a quantum formulation of Newton’s second law. These results provide direct evidence that quantum and classical mechanics are not incompatible, but complementary. By resolving the historical absence of "force" as a formal concept in quantum mechanics, we bridge the conceptual gap between macroscopic classical frameworks and microscopic quantum theory, challenging long-held perceptions of their irreconcilability. This unified approach explains why nanoscale particles exhibit quantum properties, simplifies calculations of quantum forces, and lays the groundwork for a generalized wave mechanics that unifies mechanical descriptions across all scales.