Dirac Equation vs ψ–Hamzah Equation: Superiority Analysis.

Abstract: All Articles are Available: Orcid ID: https://orcid.org/my-orcid?orcid=0009-0009-3175-8563 Science Open ID: https://www.scienceopen.com/user/2c98a8bc-b8bb-49b3-9c91-2f2986a7e16e Safe Creative register the work titled "The Theory of Intelligent Evolution, the Hamzah Equation, and the Quantum Civilisation". Safe Creative registration #2504151474836. .................................................................................................................................................................................................. This article presents a comprehensive comparison between the classical Dirac equation and the ψ–Hamzah equation, highlighting the advancements and superiorities of the latter in various scientific and philosophical contexts. The Dirac equation, a cornerstone of modern physics, describes spin-1/2 particles within the framework of special relativity and quantum mechanics. However, its limitations become evident when addressing complex concepts such as consciousness, information fields, quantum memory, and non-linear time. In contrast, the ψ–Hamzah equation, based on fractional derivatives, field memory, and non-linear ψ–time, offers a more sophisticated and dynamic approach to modeling physical phenomena. This equation not only incorporates traditional features like spinor structures and particle-antiparticle predictions but also extends its capability to model information dynamics, quantum memory, and multi-dimensional fractal fields. Moreover, ψ–Hamzah’s framework allows for deeper insights into quantum fields, the relationship between time and memory, and offers a more robust resistance to quantum noise. Through this comparative analysis, we explore how ψ–Hamzah not only enhances the classical Dirac model but also serves as a foundational tool for the future of quantum physics, artificial intelligence, cognitive sciences, and interdisciplinary scientific studies. The results highlight ψ–Hamzah's superiority in modeling complex systems, such as quantum consciousness, fractal geometries, and advanced physical theories like string theory and M-theory. Ultimately, this article proposes ψ–Hamzah as a next-generation computational and philosophical model that reshapes our understanding of the universe's fundamental structures.