Introduction to Relativity 

 Published by Albert Einstein in 1905, special relativity is a theory about the fundamental nature of space and time based on two postulates. The first is that the laws of physics are the same for an observer in any inertial reference. No frame is preferred. The concept was not unfamiliar at the time, expanding on Galileo's and Newton's theories to include all laws of physics, including optics and magnetism, rather than just the laws of mechanics. The second postulate was entirely original: the speed of light in vacuum is a constant, in all directions and in all inertial frames of reference. That the speed of light cannot be exceeded implies that time can dilate, and the length of an object can contract.

     The problem with this is a simple one image a person in a train and a person outside of the train observing the same event, a beam of light starting from the floor of the train travels up to the ceiling then bounces off a mirror on the roof and comes back down. 

     The two observers see two completely different things

  • Inside the train is a "light clock" which consists of two mirrors separated by a distance d with a light beam bouncing back and forth. Every time the photon hits a mirror, we get a "tick" of the clock. To a person inside the train, the time between ticks is: t0 = d / c.
                
  • To the person outside the train, the distance between the mirrors will have changed! If t is the time between ticks as seen by the person outside, then the mirror will have moved forward a distance vt Then the distance traveled is d'2 = d2 + (vt)2 → (ct)2 = (ct0)2 + (vt)2.
             

So here is the problem- light inside the train travels a short distance then the light appears to travel from outside the train.  But light travels at the same speed no matter what speed you are traveling, so how do resolve this problem?

To the person outside, the train clock appears to run slower! Everything slows down, including a Rolex watch, a CD player, his heart beat (!), etc. In other words, events in a moving system take longer to occur from the perspective of a system at rest.

Article and graphics provided by  Professor Kyung Soo Park

Relativity of Simultaneity 

    In physics, the relativity of simultaneity is the concept that simultaneity—whether two events occur at the same time—is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space. Where an event occurs in a single place—for example, a car crash—all observers will agree that both cars arrived at the point of impact at the same time. But where the events are separated in space, such as one car crash in London and another in New Delhi, the question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in others (in a different state of motion relative to the events) the crash in London may occur first, and in still others the New Delhi crash may occur first.

Definition Provided by Wikipedia