Beta Hypothesis: Relativistic dynamics as an effect of a geometric constraint

The Beta Hypothesis proposes a geometric reformulation of relativistic dynamics, where mass, energy, and momentum are not fundamental entities but manifestations of a local constraint imposed on the trajectory of a particle in a space with internal structure. The model considers physical space as a fiber bundle composed of ordinary spacetime and an additional cyclic internal dimension, along which the particle undergoes an additional wave-like motion. The central constraint of the model precisely links the observable motion component and the internal one, imposing that the total velocity is constant and equal to c. This condition is not related to transformations between observers but is a local physical relationship that structures the particle's dynamics. A key feature of the model is that the two directions of the fibered space are not equivalent: the observable base and the internal fiber possess different geometric metric scales. This geometric asymmetry is what gives rise to inertial mass and relativistic dynamics. When the metric symmetry between the two components is broken, energy cannot be freely interconverted between the base and the fiber, and a geometric resistance to changes in motion arises: this is how inertial mass emerges. Within the framework of the Beta Hypothesis: − Rest mass is linked to the period of internal oscillation; − Relativistic mass emerges from the helical structure of the constrained motion; − Momentum is the effect of the projection of this trajectory along the observable direction. All known effects of special relativity (such as time dilation and length contraction) naturally emerge from this constrained geometry without assuming Lorentz transformations or a predetermined global metric. The article develops this approach, proposing a unified and coherent vision of mass and energy as geometric effects, laying the foundation for a natural extension in a wave-like and quantum framework.