A Scale-Invariant Epistemic Unification of Physics via Information Geometry

The foundational principles of a scale-free, epistemically-grounded reality establish the philosophical and mathematical bedrock upon which the entire Scale-Invariant Epistemic Framework is constructed. This framework posits that physical reality is fundamentally scale-invariant, with no intrinsic minimum or maximum physical scales, and that our knowledge of this reality is inherently limited by epistemic constraints. The principle of universal scale invariance asserts that the laws of physics maintain consistent mathematical form across all observational scales, from the quantum to the cosmological, with dimensional quantities transforming predictably under scale transformations rather than possessing absolute values. This perspective challenges conventional approaches that introduce fundamental scales such as the Planck length, recognizing these as artifacts of incomplete theoretical descriptions rather than genuine features of physical reality. Simultaneously, the principle of epistemic humility acknowledges the intrinsic limits on observational knowledge imposed by quantum measurement constraints, cosmological horizons, and information-theoretic boundaries. These principles together form a coherent epistemological framework that respects both the scale-free nature of physical law and the fundamental limitations on what can be known about the universe. The mathematical implementation of these principles requires sophisticated tools from information geometry, renormalization group theory, and quantum information theory, which provide the language for describing physical phenomena in a manner that maintains consistent interpretation across different observational scales while explicitly acknowledging the boundaries of knowledge. This dual recognition—that physical reality is scale-free yet our knowledge of it is inherently limited—provides the foundation for a unified description of physics that resolves longstanding theoretical tensions while remaining grounded in empirical constraints.