# General Relativity - Page 1 of 2

Calculus

Special relativity changed the whole theme of space and time. Through special relativity, Einstein resolved the conflict of motion and the constancy of the speed of light. By the end of his special relativity, he realized that special relativity dictated. Special relativity dictated that nothing could outrun the speed of light. This, in turn, was against Newton's law of universal gravitation, proposed at the end of the seventeenth century. The problem with Newton's law of universal gravitation was that it predicts that bodies would exert forces on each other instantaneously. According to special relativity, however, nothing can travel faster than light. Therefore, instantaneous events are not allowed in nature. After years of extremely intense studies, Einstein resolved this dilemma, along with other puzzling dilemmas that special relativity dictated, in his stunning General Theory of Relativity. In this theory, Einstein once again revolutionized our understanding of space and time. He showed that the warp of space would produce all kind of weird effects on the space and time around them. We shall investigate that closely.

## Newton's Problem

Before the advent of general relativity, Newton's theory was lacking one important characteristic. Other than the instantaneousness dictated by Newton's law of universal gravitation, the law was lacking one important aspect: it did not explain what gravity is. It just dealt with gravity as it is. Although it can offer very accurate predictions about how objects move under the influence of gravity, it does not explain the force itself. The problem is set in the following example: how can two physical bodies exert gravitational forces on each other despite the presence of enormous distances between them? (As in the case of planets, for example). How does gravity carry out its mission? Newton was no fool. He realized this one missing aspect. In his monumental "Principles of Natural Philosophy", he wrote:

"It is inconceivable, that intimate brute matter, should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact. That Gravity should be innate, inherent and essential to matter so that one body may act upon another at a distance in a vacuum without the mediation of anything else, by and through which their action and force may be conveyed, from one to another, is to me so great an absurdity that I believe no Man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers".

## Einstein's Solution

In 1915, Einstein proposed General Relativity. He developed the theory to explain and try to solve the apparent conflicts between the laws of relativity and the laws of gravity. To modify such classical principles, such as gravity, required some hard work. Einstein began to learn differential geometry. He extensively used the geometry developed by Bernhard Riemann in the nineteenth century. The difference between Euclid's plane geometry and Riemann's geometry is that Riemann's includes all curved spaces in general. Einstein's genius came when he discovered that Reimannian geometry seemed magically designed to serve the physics of gravity. To resolve the conflicts between classical gravitational physics and relativity, Einstein developed an entirely innovative and smart approach to the concept of gravity. This was based on his new "Principle of Equivalence". The principle of equivalence boldly states that the effects and forces produced by gravity are in every way similar to the effects and forces produced by acceleration, so that it is theoretically impossible to distinguish between the effects and forces produced by gravity and those produced by acceleration. You might think: What has gravity has to do with acceleration? Well, in special relativity, Einstein says that a person sitting in an absolutely smooth train car, could not determine by any possible way (except for looking out of the curtains!), whether he was at rest or moving in uniform motion. In general relativity, Einstein stated that if the train car has speeded up or slowed down or driven around a curve, the passenger couldn't tell whether the forces produced on his body were due to gravitation or whether they were acceleration forces brought into play by placing pressure on the train accelerator or on the brake or by turning the train sharply right or left!

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