Structural Tables in physics: A Roadmap for Revealing the Underlying structure of Physical Laws and Phenomena

Abstract This study addresses a fundamental problem in theoretical physics: the absence of a unified structural framework capable of explaining the emergence of physical quantities and the mathematical relations connecting them, while systematically identifying the origins of approximation terms and deviations from ideal behavior in physical laws. It is based on the premise that established physical laws do not necessarily represent the primary structure of physical phenomena, but rather final forms resulting from deeper structural organizations governing the interactions among fundamental physical quantities. To this end, the study proposes a new structural framework that reinterprets fundamental physical dimensions as primary structural quantities and employs a general structural equation to generate and organize all possible dimensional combinations into a set of structural physical tables. These tables are not used merely to classify physical quantities, but as an organized space from which physical relations can be derived through a unified set of operational rules, including the identification of interacting quantities, selection of structural coupling patterns, application of central and local symmetry, alignment, distribution, structural preservation, reduction, and constraint. The proposed methodology was tested on a broad range of physical laws and relations spanning mechanics, electromagnetism, gravitation, general relativity, heat transfer, thermodynamics, and the ideal-gas equation of state. The results demonstrate the possibility of reconstructing numerous established physical relations using the same methodological structure without modifying the general principles or introducing field-specific procedures. The applications also show that a given physical relation may emerge through several independent structural pathways that converge to the same physical form, suggesting that physical laws may represent intersections of deeper organizational structures rather than starting points of physical description. Furthermore, preserving the phenomenological structure of relations prior to conventional mathematical reduction may reveal intermediate quantities and dimensionless coefficients with potentially independent physical significance, providing a systematic basis for exploring physical variables or properties not yet directly characterized. The study does not claim that the proposed framework constitutes a complete physical theory or an alternative to existing models; rather, it presents a foundational methodology for investigating the structural level underlying physical laws and testing the possibility of a unified structure connecting physical quantities and natural relations across different domains.