Shinayaka Geometry and Quantum Theory: Elastic Lines and the Fluctuating Paths of Particles

Quantum theory reveals that particle trajectories are not rigid and deterministic, but fluctuate under the principles of uncertainty and superposition. Shinayaka Geometry, by introducing the concept of elastic lines, offers a geometric model for such indeterminacy. This paper explores the relation between Shinayaka Geometry and quan- tum theory, emphasizing its connection to the uncertainty principle, the Feynman path integral, and tunneling phenomena. Elasticity in geometry is interpreted as a metaphorical and structural extension of the probabilistic nature of quantum mechanics.