Einstein's Relativity

The notion of relativity is not as revolutionary as many believe. In fact, spatial relativity is part of our everyday experience. Spatial relativity, also called Galilean relativity in honour of Galileo who first formulated the concept of relative motion, is often confused with Einstein's theories. Galileo simply described the fact that an observer in motion sees things differently from a stationary observer, because he has a different spatial coordinate system, or "reference frame" in Relativity speak. It might sound more complicated than it actually is. Consider the following example:

Galilean relativity: the train example (courtesy of Stephen Hawking).

Two people riding on a train from New York to San Francisco play a game of ping-pong in the sport compartment of the train. Lets say, the train moves at 100 km per hour (= 27.8 m/s) and the two players hit the ball at a speed of two meters per second. In the reference frame of the players, the ball moves back and forth at this particular speed. For a stationary observer standing beside the railroad, however, things look quite different. In his reference frame the ball moves at 29.8 m/s when it is played forward in the direction where the train is heading, while it moves at 25.8 m/s in the same direction when it is played backwards. Thus he doesn't see the ball moving backward at all, but always moving towards San Francisco. For an observer in outer space, things look again totally different because of the Earth's rotation, which is opposite to the train's movement; therefore the outer space observer always sees the ball moving East.

Einstein's new concept of relativity.

Einstein's Relativity differs from classical relativity, because of the way he looked at time. Before Einstein, people thought time to be absolute,

Isaac Newton

"Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space. Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another"

which is to say that one big clock measures the time for the entire universe. Consequently one hour on Earth would be one hour on Mars, or one hour in another galaxy. However, there was a problem with this concept. In an absolute time frame the speed of light cannot be constant. Roemer found that the speed of light is finite and has a certain, quantifiable velocity (usually abbreviated with "c"), which at first implies Galilean relativity. This would mean that while the Earth rotates at a velocity of v, light emitted in the direction of the Earth rotation must be c + v, while light emitted in the opposite direction would travel at c - v, relative to an outside observer.

In 1881, A. Michelson conducted an experiment which proved that this is not the case. With the help of an apparatus that allowed measuring minute differences in the speed of light by changes in the resulting interference patterns, Michelson observed that the speed of light is always the same. No changes whatsoever. The experiment has been repeated later with greater precision by Michelson and E.W. Morley.

Special Relativity published in 1905.

Numerous attempts were made at reconciling these discrepancies, yet they were all unsuccessful, until Einstein solved the dilemma with his famous paper On the Electrodynamics of Moving Bodies in 1905, in which he developed his Special Relativity Theory. Special Relativity is an extremely elegant construct that deals with things moving near or at the speed of light. Surprisingly, the new concept of space and time that arises from Relativity is based only on two simple postulates: 1. The laws of physics are the same in all inertial (=non-accelerating) reference frames, and 2. The speed of light in free space is constant.

It is a matter of common experience that one can describe the position of a point in space by three numbers, or coordinates. For the purpose of explaining the relativistic model, Einstein added time as a fourth component to the coordinate system, and the resulting construct is called spacetime. Just as there is an infinite number of 3-D reference frames in Galilean relativity, there is an infinite number of 4-D spacetime reference frames in Einstein's theory. This is to say that Einstein put an end to absolute time. The revolutionary insight lies in the conclusion that the flow of time in the universe does indeed differ depending on one's reference frame

In his usual humble way, Einstein explained how he reinvented physics: "I sometimes ask myself how it came about that I was the one to develop the theory of Relativity. The reason, I think, is that a normal adult stops to think about problems of space and time. These are things which he has thought about as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up." On Relativity, he said: "Relativity teaches us the connection between the different descriptions of one and the same reality."

This view of Relativity, that there are different realities, has been picked up unanimously by the public, and hence, has taken on a far greater meaning than that of the original scientific theory, the focus of which was -strictly speaking- on mechanics and electrodynamics. This astonishing success was at least in part due to Einstein's personality. He understood himself as a philosopher as much as a scientist, and he was ready to discuss philosophical issues at any time, particularly matters involving Relativity. The philosophical aspect of Relativity forced people to think differently about the universe. Suddenly, the cosmos was not a God-created clockwork anymore, but a totality of disparate realities with the same basic natural laws.

An outstanding feature of Special Relativity is its mass-energy relation, which is expressed in the well-known formula: E=mc².

Einstein derived this relation in an attempt to reconcile Maxwell's electromagnetic theory with the conservation of energy and momentum. Maxwell said that light carries a momentum, which is to say that a wave carries an amount of energy. Due to the principle of conservation of momentum, if a body emits energy in the form of radiation, the body loses an equivalent amount of mass that is given by E/c². This describes the relation between energy and mass.

According to the conservation principle, in a closed system the sum of mass and its energy equivalent is always the same. The mass-energy relation tells us that any change in the energy level of an object necessarily involves a change in the object's mass and vice-versa. The most dramatic consequences of this law are observed in nature, for example in nuclear fission and fusion processes, in which stars like the Sun emit energy and lose mass. The same law also applies to the forces set free in the detonation of an atomic bomb.

General Relativity published in 1916.

Eleven years after On the Electrodynamics of Moving Bodies, Einstein published his second groundbreaking work on General Relativity, which continues and expands the original theory. A preeminent feature of General Relativity is its view of gravitation. Einstein held that the forces of acceleration and gravity are equivalent. Again, the single premise that General Relativity is based on is surprisingly simple. It states that all physical laws can be formulated so as to be valid for any observer, regardless of the observer's motion. Consequently, due to the equivalence of acceleration and gravitation, in an accelerated reference frame, observations are equivalent to those in a uniform gravitational field.

This led Einstein to redefine the concept of space itself. In contrast to the Euclidean space in which Newton’s laws apply, he proposed that space itself might be curved. The curvature of space, or better spacetime, is due to massive objects in it, such as the sun, which warp space around their gravitational centre. In such a space, the motion of objects can be described in terms of geometry rather than in terms of external forces. For example, a planet orbiting the Sun can be thought of as moving along a "straight" trajectory in a curved space that is bent around the Sun.

excerpt taken from http://www.thebigview.com/spacetime/relativity.html