# Special Relativity

Calculus

## Inertial Relativity

Galileo and Newton had extensively dealt with relativity. Both of them were aware of what we now call "The Relativity Principle". This principle states that the basic laws of physics are exactly the same in all inertial reference frames. Inertial reference frames are those observing points where Newton's first law, the law of inertia is applied. Since velocity is relative to what it is comparing, inertial reference frames are points from which momentum (hence, velocity) is measured. Newton's first law states that the movement of any object remains constant until an external force interferes with it. Galileo was the one who formulated the very first rule of classical relativity are all probably familiar with it: when two particles are moving in the same direction, the speed of one relative to the other is the difference between their velocities. When two particles are traveling in opposite directions, the relative speed is the sum of their velocities. Galilean-Newtonian relativity involves certain assumptions that make sense from everyday experience. It is assumed that the lengths of objects are the same in all reference frames regardless of their motion. Also, it assumes that time passes at the same rate in different reference frames. In Classical Mechanics sense, space and time are absolute. This means that space and time in one reference frame are exactly the same as any other reference frame. Maxwell's newly developed theory of electromagnetism conflicted with this.

## Speed of Light

James C. Maxwell had formulated the laws of electromagnetism in the eighteen hundreds. His work was based on experimental research conducted earlier by the renowned experimental physicist Michael Faraday (who, hating math, avoided it, much like many modern school students). When Maxwell, however, formulated Faraday's laws in a more mathematical, and theoretical way, deep conflict arose. This conflict resulted from what classical mechanics predicted (the laws formulated by Galileo and Newton) and what Maxwell's equations of electromagnetism did.

Maxwell's equations predicted that the speed of light is constant; it predicted that the velocity of light, c, would be 3.0 * 10^8 m/s, and this what was exactly measured within experimental error. Classical mechanics posed a difficult question to answer: In what reference frame would the speed of light have a value similar to the value indicated by Maxwell and experiments? Remember that it was assumed prior to Maxwell's theory of electromagnetism that light would have different speeds in different frames of reference. For example, if one was traveling in a rocket ship with a speed of 1.0 x 10^8m/s in the same direction as a light beam was traveling, classical theory predicted that when the observers measure the velocity of the light's beam, they would find it to have a value of 3.0 * 10^8 - 1.0 x 10^8 m/s or 2.0 x 10^8 m/s. If the rocket was traveling in the light's beam opposite direction, then the velocities would add up. Maxwell's equations, however, disagreed strongly with this Galilean-Newtonian relativity. This seemed to imply, at that time, that there must be a certain reference frame in which c would have this value.

Nineteenth century physicists viewed the material world from a highly mechanical point of view. Central to classical theory, is the idea of a medium in which objects or particles can travel in and be exchanged with each other. For example, waves travel on water and along ropes or strings, and sound waves travel in air and other materials. Therefore, why shouldn't light travel in a medium also? Nineteenth century physicists thought. Physicists gave this medium the showy name of "lumineforous ether" (which is now used in crude physics jokes!). They theorized that the ether was everywhere and filled all space. It was, therefore, assumed that the velocity of light given by Maxwell's equations must be in respect with the ether. The idea of the ether experienced a big nail in its coffin after the famous experiment known as the "Michelson-Morley" Experiment was conducted. In fact, the lumineforous ether failed.