Time Dilation

Look at the image carefully what does this say....

What is time dilation? What is the time dilation equation in special relativity? Read to know all about this special relativistic phenomenon.
time is not constant everywhere it varies...

The premier theories that dominate classical as well as gravitational mechanics are the special and general theories of relativity. Both were formulated by Albert Einstein in 1905 and 1915 respectively. The special theory deals with motion with respect to inertial frames of reference, while the latter deals with accelerated frames. One phenomenon that is described by both theories is time dilation or the slowing down of time. In this article I'll present an explanation of time dilation for dummies or laymen interested in physics. The equation presented here will only deal with the one related to inertial reference frames.

What is Time Dilation?

Let me first state the principle of time dilation that arises from an analysis of the motion of an object moving at a constant velocity, with respect to an inertial reference frame. Here it is. When an object moves at a constant velocity with respect to any inertial reference frame, a clock attached with the object will move slower than a clock which is fixed to the reference frame. The faster an object moves, slower will be its clock with respect to the reference frame clock. By clock attached to an object, I do not mean an actual clock. The change in the time variable associated with the object itself slows down! This is indeed one of the most astounding relativistic phenomena, besides Lorentz contraction, which you will study in advanced physics.

The Time Dilation Equation

This phenomenon can be described quantitatively by the following time dilation equation. Consider a spaceship moving at a high but constant speed with respect to a stationary reference frame. Let Δt' be the time associated with the spaceship travel, v its velocity and let Δt be the interval of time variable change related to the reference frame. Then the equation states that:

Δt' = Δt / √(1 - v2 / c2)

Here c is the velocity of light (3 x 108 meters per second). Work out the proof of the equation to know it in more detail. If you observe the above equation carefully, you will see that higher the velocity (v) is, longer will be the time interval (Δt')! So effectively, time has slowed down for every one on the spaceship, with respect to the inertial reference frame. However, the inhabitants on the spaceship will see time changing at its usual rate.

Gravitational Time Dilation

A phenomenon similar to special relativity time dilation occurs when an object is in a gravitational potential. The closer an object is to a gravitation potential, greater is the hold of gravity, and slower its clocks will be! So a clock kept at the sea level, will move slower compared to a clock placed on Mount Everest! It is not possible to discuss the equation for time dilation here, as it is different for every spacetime geometry. This phenomenon has been experimentally verified by physicists using the Mössbauer spectrometer.

The phenomenon of time dilation arises due to the very nature of spacetime and as a consequence of the basic postulates of special theory of relativity. The phenomenon of muon decay where it lives longer due to its high speed motion is conclusive evidence for time dilation. The phenomenon in its most crude form can be explained as 'Faster an object moves, slower does its clock move!'. Similarly, the closer you get to the surface of earth, slower is your clock running and the higher you go, faster is the clock going to move. Of course, the change in time is too small to be felt but it does exist. All this is a result of the 'local' nature of time.