Newtonian bending of light

Under purely Newtonian mechanics, if you take a particle of infinitesimal mass traveling at the speed of light, and it barely skims above the surface of the sun during a solar eclipse, the particle will deflect due to the sun's gravity, just like the way the sun causes orbits of the planets to curve. Therefore, the mere fact that the stars appeared displaced during the famous solar eclipse experiment did not prove Einstein's Theory of General Relativity because Newton's theory also predicts displacement.

Rather, it is the amount of displacement that matters. Einstein's theory predicts a different amount of displacement, or star light deflection, than Newton's theory does. I think this is because in Einstein's theory, matter causes space and time to curve, while Newton's law of gravitation, when thought about in a certain way, only deals with the curvature of space.

Therefore, the popular illustration of General Relativity, balls rolling around on deformable sheet, as well as the common explanation of the solar eclipse experiment, are all somewhat missing the point, as in their simpleness they could just as easily be an illustration or explanation of Newtonian mechanics.

The most significant conceptual difference between Einstein's theory of gravity and Newton's theory of gravity is that Einstein's predicts that gravity causes clocks to slow down.

Curved spacetime is a powerful and very appropriate mathematical tool for describing Einstein's theory of general relativity.