GRAVITATIONAL REDSHIFT
 

1.1 A brief history of gravity

The first philosopher who ever wondered about the nature of gravity was Aristotle (384-322 BC). He thought that the natural state of all the objects on Earth, believed at center of the Universe, was at rest, and therefore all the moving objects will always come to a halt. The heavens, however, were believed to move naturally and endlessly in a complex circular motion, and for this reason, he thought that they had to be made of a different substance unknown to Earth - aither. Aristotle believed that everything on the Earth was made up of four elements: earth, air, fire and water. Therefore, aither had to be the fifth element that distinguished the heavens from Earth; a superior element incapable of any change other than the circular motion. His, was also the idea that heavier bodies fall faster than lighter ones when their shapes are the same, a mistaken view that was accepted until Galileo conducted his experiment with weights dropped from the Leaning Tower of Pisa more than 1800 years later. 
Galileo (1564-1642) , with the German astronomer Johannes Kepler, initiated the scientific revolution that flowered in the later work of Sir Isaac Newton. Like Kepler, he believed that all the planets including the Earth orbited the Sun, which at the time was against the belief of the Church. For this reason, more than any other person, Galileo deserves to stand as a symbol of the battle against the Church authority for freedom of inquiry. During his teaching career, he observed how Aristotle had mistaken in believing that the speed of fall was proportional to the weight, by dropping objects from the Leaning Tower. By careful measurement he discovered the law of falling bodies, the parabolic path of projectiles and the harmonic motion of pendulums, turning physics from speculative to exact experimental science. At the beginning of the seventeenth century, Galileo, after hearing of lenses invented in Holland, built the first telescope with which he first discovered lunar mountains and craters, the sunspots, four satellites of Jupiter, the phases of Venus and confirmed his preference for the Copernican system. Despite the numerous discoveries in astronomy and intuition about the nature of gravity, Galileo, missed the key idea that unites both fields embracing and all bodies in the Universe.
Fifty years later, Newton (1643-1727)  published his book Principia in which he describes the three laws of motion, still largely used today, and marking the beginning of, what today is called, Newtonian mechanics with his law of gravitation. In his book, Newton marries the laws of motion, experimented on Earth, with the planets orbiting the Sun, helped by his incredible vision that all planets are simply ever falling objects. However, although the effects of gravitational forces had been completely discovered, the actual cause and nature still remain unveiled; Newton himself, attributed the origin of these forces to the same mysterious intrinsic property of matter. This idea was maintained for the next three hundred years; some remarkable comment was made by James Clerk Maxwell (1831-1879), the interpreter of the electromagnetism, in which he inquired how could two bodies know of the presence of each other without any action made on the surrounding medium.
At the beginning of the twentieth century, Albert Einstein (1879-1955) was working on his Special theory of Relativity when he had, what he called, the happiest thought of his life, namely that an observer in free fall would experience no gravitational pull. As a consequence he proposed the Equivalence Principles, which states the equivalence of a gravitational field with an uniformly accelerated frame, and therefore, he extended his special theory of relativity to accelerated frames in his General theory of Relativity in which, he also included his gravitational field equation. With his Equivalence Principle, Einstein eliminated completely the problem of a gravitational force acting between two bodies, and attributed gravity to the distortion of space and time in the vicinity of the two bodies. During the late years of his life, Einstein tried to understand the nature of the interactions between matter, electromagnetic forces and spacetime in his last effort, the unified field theory, which still remain unfinished today.
Being Gravity, one of the first queries that confronted men, and still being one of the problems that the greatest scientists are trying to solve, it certainly deserves the recognition of the longest unsolved problem that human history has ever encountered.