On the Foundation of Physics Admissibility

Key Points

• To establish admissibility as essential for well-defined comparison in physics, focusing on invariance and relational structures.
• Defined conditions for admissibility including invariance, refinement, composition, finite propagation, and closure.
• Analyzed the implications of these conditions on relational structures and comparisons.
• Derived a unique scalar comparison form based on the established constraints.
• Proved that alternatives relying on representation or descriptive scale are excluded.
• Established that the quadratic invariant structure in relativity and quantum theory is a necessary result.
• Demonstrated that any theory with scalar comparison must adhere to the identified constraints.

Abstract