The Theory of Relativity

Early in the 20th century, Einstein formulated two theories of relativity, which proposed a geometric model for gravity. His theories were long and complex, and they showed how objects behaved relative to one another. They are often used to explain the physics of the macroscopic world of planets and stars. One of the most important principles of his theory that lead to many ideas behind string theory was the concept that energy can be converted to mass and vice versa (we will discuss this in detail later). This conversion of energy to mass is commonly expressed in the equation e=mc^2.

The geometric model of gravity was theorized by Einstein after he found a major flaw in Newton’s theories about gravity. His theory was originally formulated to study light, setting the speed of light as a speed limit for objects in the universe.

According to Newton, if the sun were to burn out, Earth would exit its orbit immediately. Einstein disagreed, theorizing that it would take eight minutes, the time it takes light to reach earth from the sun, to exit orbit. Einstein believed this would hold true because gravity was a force created by the “stretching” of a “fabric” of spacetime. This stretched spacetime is similar to if one were to put a bowling ball on a trampoline. Because of the stretch in the trampoline that the ball would create, all smaller masses put on the trampoline would be attracted to it.

Einstein’s geometric model of gravity does not rely on traditional Euclidian geometry. Instead, it involves the geometry of contemporary scholars, such as Riemann. Riemann’s geometric models describe how shapes behave when they are drawn on curved surfaces. Another complex mathematical idea that is used in the theory of relativity is tensor calculus, the branch of calculus dealing with calculation using tensors. Tensors can best be described as quantities that posses certain properties, such as vectors. This mathematical system allowed Einstein to express physical laws without the use of a grid system.