Extended Theories of Gravity

<p>For over a century, we've faced a profound divide in physics: quantum mechanics and general relativity stubbornly refuse to speak the same language, while galaxies spin with a defiant disregard for our gravitational expectations. In this paper, I introduce Systemic Relativity & Logarithmic Gravity – a framework that rethinks how gravity operates by introducing logarithmic corrections that naturally vary with scale. This approach offers an alternative to dark matter while seamlessly recovering the Newtonian behavior we observe in everyday life.</p> <p>The key insight lies in what I call the system-dependent parameter λ – defined as the ratio between a system's gravitational binding energy and the fundamental Planck energy. Unlike other theories that apply fixed corrections (like MOND) or rely on arbitrary mathematical functions, this formulation explains why gravity behaves differently across cosmic scales as a natural consequence of each system's intrinsic properties.</p> <p>What's particularly striking is how these logarithmic gravitational modifications have independently emerged across seemingly disconnected fields – from black hole thermodynamics to quantum gravity approaches – suggesting we're glimpsing something fundamental about reality. The evidence is compelling: when I analyzed 175 galaxies from the SPARC database, the framework reduced rotational velocity prediction errors by half compared to standard Newtonian models. Even more impressively, when applied to the galaxy cluster Abell 2744, it accurately reproduces gravitational lensing patterns and mass distributions where other modified gravity theories struggle.</p> <p>This framework doesn't just explain observations – it makes testable predictions. I outline specific, falsifiable expectations for gravitational lensing and gravitational wave behavior that can be verified through upcoming observations with JWST, LIGO, and LISA. If I'm right that gravity is scale-dependent, then what we've been calling "dark matter" may simply be an artifact of our perspective – the result of applying fixed-scale thinking to a universe where gravity itself transforms across the cosmic hierarchy.</p> <blockquote> <p><br>The implications extend beyond cosmology to challenge our fundamental conception of physical law. Perhaps gravity isn't a universally fixed force but an emergent phenomenon that adapts to the systems it governs – a possibility that might finally bridge the quantum-cosmic divide that </p> </blockquote>