Chapter 3: Albert Einstein and the Geometry of Space and Time

A New View of Gravity: The General Theory of Relativity

Albert Einstein, one of the most famous men of all-time, developed his special theory of relativity that discussed electromagnetism and mechanics. In his theory he postulated two things:

a) “The laws of physics are identical in any reference frame moving at a constant speed.”
b) “The speed of light is the same in all reference frames.”

Although Einstein’s special theory of relativity unified mechanical and electromagnetic forces, he did not discuss Newton’s proposed gravitational forces. Einstein’s general theory of relativity was developed after he made two cunning observations. First, he observed that the gravitational mass of an object is related to its inertial mass. Secondly, he observed that a gravitational field could be mimicked in gravity’s absence by accelerating a reference frame. Based on Newton’s theories, the gravitational force exerted on an object depends on the object’s mass, defined as the gravitational mass. Newton’s proposal was that objects respond to forces by accelerating. Newton’s second law states that force equals mass multiplied by acceleration. For example, an object twice the mass of another object will undergo half the acceleration if subjected to the same force. However, this is not so because we know that two objects dropped from the same height will hit the ground at the same time. Take the classic example of the brick and the feather for example. The brick has a larger gravitational mass and is pulled stronger by the gravitational force, however, the feather has a larger inertial mass, but it is not as quick to respond to a given force. The force applied to the brick is the same as the feather, but it responds at a much slower rate than the feather. That is why they have the same acceleration.

Einstein’s connection between gravity and accelerated reference frames led to his general theory of relativity. After his new development, he proposed the equivalence principle, which states “the laws of physics in a gravitational field are the same as in an accelerated reference frame.” With this knowledge, Einstein said that it was now possible to mimic the effects of gravity in a reference frame, which is not subjected to gravitational forces. The special theory of relativity notes that mass can be converted into energy. In the general theory of relativity, energy and mass respond to gravity. Gravity affects the motion of light. Based on this discovery, it is possible to detect the effect just by studying the stars.