Special Relativity

Special relativity refers to a theory that concerns uniform motion.  This theory can also explain experiments with light.  Special relativity encompasses a principle called the weak equivalence principle and addresses how people perceive/measure objects.  As you near extreme velocities (near the speed of light), space begins to shrink to the point that if you were to ride on a photon of light, all space would collapse and the ride from one point to the other would seem instantaneous.  Einstein derived the following two formula’s to account form this phenomenon. 

Trest = Tmove / (1 - (v/c)2)1/2  

In English, this would read : The Time measured by someone at rest relative to the moving object, is equal to the Time measured by a person on the moving object divided by (one minus (the speed of the object as a percentage of the speed of light (e.g. 0.8 / 1))) all rooted.

 Lrest = Lmove / [ 1 - (v/c)2 ]1/2

This same formula can be applied to length as well as time.  This formula is the same as the above, except the times measured are replaced with the distances measured.

As the car moves, it is traveling both in space, and time.  As its speed increase, the amount of time it takes to travel the same distance decreases.  As the car approaches the speed of light, the driver will see the distance decrease, until finally, when the car reaches the speed of light, the distance will appear, to the driver, to be effectively 0.  

Example:

Consider Peter (P) who is standing on a train station platform and Tom (T) who is on a train. The train is a high-speed train that travels at speed equal to 80% that of light. It is also an express train that does not stop at Peter's station.

According to Peter, the platform is 60 meters long and he notices that the front and back of the train line up exactly with the ends of the platform at the same time. What is the length of the train, as measured by Peter? How long, by Peter's watch, does it take the train to pass him?

Peter measures the platform at 60 meters.  The train travels past the platform at 0.8 times the speed of light.  Peter notices that the front and back of the train line up with the ends of the platform at the same time, therefore, the train as measured by Peter is 60 meters long.  Thus, by Peter’s watch it takes the train 2.5 X 10-7 seconds (t = d/v)

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