Barry Parker on Albert Einstein

“Under Grossman's guidance, Einstein studied and learned tensor analysis. The two men actually published several papers together, but the work at this stage was still a kind of groping in the dark—a mind-tormenting search for the one equation out of hundreds that was the correct one. ...Interestingly, the correct equation was actually considered briefly, but rejected by Einstein because he came to the mistaken conclusion that it violated causality. Then a further mistake led to the abandonment of the principle of covariance.”

“Pondering about the problem, Einstein thought about the beam of light curving around the limb of the sun; he soon realized that it was not the beam that was bent, but rather the space through which it traveled. Matter must somehow curve space and other matter must move through this curved space in the way we see it move—yet this way must be "natural." He decided the most natural way would be along a path that represented the shortest distance between two given points in space (this is called the geodesic in mathematics). This would mean that the sun curves the space around it and the planets move in this space along geodesics. These geodesics appear to us to be elliptical orbits, but in curved space they are actually straight lines.”

“From a simple point of view, then, Einstein's equation can be written: tensor A = tensor B, where tensor A describes the curvature of space and tensor B describes the matter that causes the curvature. In practice, B can also contain terms describing an electromagnetic field since electromagnetic fields represent energy, and energy is just another form of mass. Einstein's dissatisfaction centered on tensor B.”