Domain Projection: The Geometric Origin of Physical Constants and Laws

Physical constants such as Planck’s constant \(\:h\) and Boltzmann’s constant \(\:{k}_{B}\) are traditionally treated as fundamental invariants of nature, introduced as fixed parameters in physical theories. This paper introduces Domain Projection, an empirically constrained framework in which such constants are shown to arise from systematic geometric distortions generated during translation between distinct descriptive domains, rather than as intrinsic parameters of a physical substrate. The spectral domain, defined by directly measured frequency relations, encodes empirically accessible invariants recoverable as geometric properties of spectral relations. The representational domain, comprising constructs such as energy and temperature, corresponds to a secondary mapping imposed on spectral structure for descriptive and operational purposes. We show that translation between these domains is expressed as a composition of non-invertible, non-commuting mappings, whose failure to close produces residual geometric offsets. When appropriately rescaled, these offsets reproduce the numerical values of the ratio \(\:h/{k}_{B}\), and the Wien displacement factors (2.82 and 13.38) observed in blackbody radiation, without invoking quantization postulates, statistical mechanics, or thermodynamic assumptions. In addition, the Stefan–Boltzmann constant \(\:\sigma\:\) is obtained as a translation invariant associated with composed domain mappings, while the fine-structure constant \(\:\alpha\:\simeq\:1/137\) appears as a representational invariant. Within this framework, physical constants are reinterpreted not as ontological primitives, but as invariants embedded in the projection geometry, while physical laws are understood as second-order representations of spectral structure rather than direct mappings of the physical substrate. This approach provides a systematic method for identifying and classifying physical invariants grounded entirely in empirically accessible spectral relations.