An Algebraic Foundation of Amended Dimensional Analysis
Abstract
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory of quantity spaces. Examples of dimensional analysis based on this approach are given, showing that it allows results obtained by traditional dimensional analysis to be strengthened. For example, the orbital period of a two-body system can be derived without use of equations of motion.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.