Fractal Spacetime and the Origin of Mass
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Recent advances in theoretical physics increasingly suggest that spacetime may not be smooth at fundamental scales, but instead exhibit fractal and scale-dependent structure. The Fractal Spacetime Dynamics (FSD) project investigates how such geometric irregularities can give rise to particle mass, energy distributions, and dark matter phenomena. This publication presents the latest developments in fractal spacetime modeling, connecting quantum fields, cosmology, and emergent gravity into a unified theoretical framework.
Theoretical Framework: Fractal Geometry in Fundamental Physics
Traditional physics assumes a smooth, differentiable spacetime manifold. FSD challenges this assumption by modeling spacetime as a fractal structure with scale-dependent dimensionality. At quantum scales, deviations from classical geometry introduce localized curvature irregularities that act as natural mass-generating mechanisms.
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Scale-Dependent Spacetime Dimensions
FSD introduces an effective spacetime dimension that varies with scale. While large-scale spacetime appears four-dimensional, microscopic regions exhibit fractional dimensional behavior, modifying quantum field propagation and particle self-energy.
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Fractal Consistency Law
The Fractal Consistency Law constrains how matter fields interact with irregular spacetime geometry. This law ensures stability of physical constants while allowing mass to emerge from geometric self-interaction rather than from external symmetry breaking.
Analysis I: Emergent Mass from Spacetime Irregularities
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Geometric Origin of Particle Mass
In the FSD framework, mass arises from localized geometric resistance to field propagation. Particles acquire effective rest mass as a consequence of interacting with fractal spacetime curvature, eliminating the need for fundamental mass parameters.
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Reproducing Standard Model Mass Hierarchies
Applying fractal scaling relations to Standard Model fields reproduces observed fermion mass hierarchies within a narrow parameter range. This suggests that mass differences may reflect geometric depth rather than arbitrary coupling constants.
Analysis II: Dark Matter and Vacuum Energy Implications
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Dark Matter as a Fractal Spacetime Effect
FSD predicts that regions of enhanced spacetime irregularity behave gravitationally like unseen mass. These effects naturally mimic dark matter halos without invoking new particle species, offering an alternative explanation consistent with galactic rotation curves.
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Vacuum Energy and Cosmic Acceleration
Fractal spacetime geometry modifies vacuum energy density at large scales, potentially explaining cosmic acceleration without fine-tuned cosmological constants. This provides a geometric pathway to understanding dark energy.
Discussion: Toward a Geometric Unification of Physics
The FSD approach reframes mass, dark matter, and vacuum energy as emergent properties of spacetime geometry. By shifting the origin of physical constants from particles to structure, fractal spacetime offers a promising route toward unifying quantum mechanics and gravity.
Conclusion: Fractal Geometry as a Foundation of Reality
Fractal Spacetime Dynamics provides a compelling theoretical framework in which geometry itself becomes the source of mass and cosmic structure. As observational precision improves, FSD offers testable predictions that may redefine our understanding of fundamental physics.
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