No Protocol-Independent Mass: A General No-Go Theorem

Arc III — Matter Paper 3 Title No Protocol-Independent Mass: A General No-Go Theorem Zenodo DOI 10.5281/zenodo.18225855 This paper establishes a general no-go theorem demonstrating that no notion of mass can be both operationally meaningful and protocol independent in a universe with finite accessibility. Building on the accessibility-based definition of mass developed in earlier papers, the work proves that any attempt to assign a unique, observer- and protocol-independent mass parameter leads to contradictions once finite resolution, finite bandwidth, and composite internal structure are taken seriously. The theorem is formulated without assuming specific dynamics, spacetime geometry, or microscopic ontology. Instead, it relies only on minimal operational assumptions: that mass is inferred through probe–system interactions, that probes have finite accessibility, and that composite systems possess internal degrees of freedom inaccessible to external measurement at finite resolution. The result shows that apparent mass invariance in classical physics is an emergent approximation valid only in regimes where accessibility renormalization is negligible. In more general settings—including strongly composite systems, cloaked internal structure, or dark-sector interactions—mass necessarily becomes protocol dependent. This no-go theorem places strong constraints on extensions of gravity and particle physics that posit universal mass parameters and motivates the re-interpretation of dark matter and exotic mass phenomena as accessibility effects rather than new substances. Keywords No-go theorem; operational mass; protocol dependence; finite accessibility; composite systems; dark matter; foundations of physics; inference limits Notes (Optional / Internal) Arc III — Matter Formalizes impossibility results implied by Papers 1–2 Motivates: Information-Volume Collapse and the Inference Manifold of Physical Reality