The hanging string as a model of metric distortion
Alvin Meckler · American Journal of Physics · 1976
The identification of a string as a curve allows the statement of a physical postulate which has as an immediate consequence the differential equation of the curve. The applied force appears as the gradient of the tension. It is possible to rewrite the differential equation as an equation for a geodesic in a transformed space, with the tension now incorporated into the metric. The field equation can be chosen to be the equation relating the transformed scalar curvature to the tension. The geometrization of physics is traceable. By the same procedure, the differential equation of a light ray may be derived, and the index of refraction may be related to the distorted geometry.