Einstein did not have adequate background in mathematics to adapt Riemannian geometry to physics. As a result, he has an incorrect theory of measurement that makes other errors inevitable. On the other hand, his equivalence principle is an ingenious stroke. These result in an inconsistent theory.
In Riemannnian geometry, the notion of "distance" is valid in mathemtics because there is no need to have a way to measure it. Because Einstein did not understand the mathematics, he adapted this notion without making the necessary modification for physics. However, in physics, the distance must be associated with measurements. Thus, an invalid notion of distance, as pointed out by Whitehead, would lead to inconsistency that inevitably leads to invalid interpretations in physics.
|