Dimensional Projection Theory Based on Three-Dimensional Euclidean Substrate and Its Physical Applications

Whether higher-dimensional space exists objectively has long been a core research topic in modern theoretical physics. A great many physical phenomena cannot be fully described merely within the observable three-dimensional Euclidean space. Different from traditional higher-dimensional models that introduce spacetime curvature and compact curled dimensions, this paper constructs a nested higher-dimensional projection geometric model fully based on flat three-dimensional Euclidean space. It assumes that various higher-dimensional objects exist independently and objectively, regards time only as an auxiliary parameter rather than an independent spatial dimension, and confirms that observable phenomena in three dimensions are projection effects of higher-dimensional objects in three-dimensional space. The inherent physical meaning of integration is adopted to interpret the evolution law of dimensions. Two types of periodic and regular one-off dimension-raising motion configurations are defined from the three-dimensional observation perspective, and equivalent dimension raising is realized through splitting and nesting of extra orthogonal supplementary degrees of freedom. Focusing on higher-dimensional systems above three dimensions, this paper completes the deduction of wave configurations from four-dimensional to six-dimensional space in sequence, and provides a geometric interpretation for wave-particle duality based on the projection mechanism. A unified expression for the four fundamental interactions is derived relying on the 3D–6D basic framework. After further nesting and expansion to 7D and higher dimensions, multiple testable theoretical predictions in the field of gravity are put forward: it is deduced that black holes have a maximum critical mass and black holes with unlimited mass do not exist; the temperature correction formula for Hawking radiation deviating from the ideal blackbody spectrum is obtained; it is verified that the galactic dark matter effect originates from the enhancement effect of baryonic matter via high-dimensional gravitational projection, eliminating the need for WIMP-type dark matter particles with quantitative fitting of galactic rotation curves completed; the correction rule for the deflection angle of cosmic gravitational lensing is derived. This system supports infinite nested expansion of dimensions, adapts to large-scale cosmic and black hole astrophysical effects, expands the applicable scope of the theory, and provides a brand-new analytical idea for fundamental unsolved problems in gravitational research.