The Meaning of Scale and Accumulation

Physical laws derive their authority from local precision and repeated empirical success. Yet many of the most persistent conceptual difficulties in physics arise not from failures of these laws, but from their extension beyond the conditions under which their application is conceptually justified. This paper argues that additivity—the assumption that physical effects accumulate linearly and without structural limitation—is not itself a law of nature, but a rule governing application whose validity is conditional. By distinguishing local dynamics from global accumulation, the paper clarifies how physical laws may remain exact while their cumulative extension requires regulation. This perspective preserves the thermodynamic arrow of time, avoids unnecessary ontological expansion, and restores conceptual discipline to the use of physical law across scale.