Relativity is about the nature of space and time. It is not difficult mathematically; it makes us reexamine our ideas of space and time. Relativity is based upon two postulates. Accepting these postulates makes one examine their consequences and their agreement with experiments.
Einstein's special theory of relativity deals with how we observe events, particularly how we observe events from different frames of references.
Inertial Frame of Reference Reference frames in which the law of inertia is valid. In other words, an object is either at rest or in motion in a straight line at constant speed relative to a frame of reference. There is no acceleration.
Postulates of relativity:
Event A physical happening that occurs at a certain place and time. You can assign three space coordinants and one time coordinant to an event
Simultaneous Events
One of the important consequences of the theory of relativity is that time can no longer be regarded as an absolute quantity. The time interval between two events depends upon the observer's reference frame. If two events occur at widely separated places, it is difficult to determine if they are simultaneous. One must take into account the time it takes for the light from the two events to reach the observer. Two events which are simultaneous to one observer are not necessarily simultaneous to another observer.
Time Dilation
Einstein's theory of relativity predicts that time passes differently in one frame of reference than in another. If different observers measure the time interval between a pair of events, they will not agree about how long the time interval for the event was. The time dilation effect states that clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest). In other words, time is dilated (or stretched) for a moving object.
An applet that will help you visualize space and time in special relativity. Special Relativity
The twin paradox applet: Twin Paradox
Relativity of Length
If you want to accurately measure the length of a moving object, you must simultaneously measure both of its ends. The length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest. In other words, the length of a moving object is always contracted, or shorter than its proper length (length contraction only occurs in the direction of motion).
Momentum and mass
We must redefine momentum as:
The mass of an object increases as its speed increases.
A New Look at Energy
When a steady force is applied to an object of rest mass, the object increases its speed. Work is done and its kinetic energy changes. As the speed of the object approaches c, the mass of the object increases. The work done on the object not only increases its speed but also its mass. Relativity thus predicts that mass is a form of energy. Einstein predicted that the kinetic energy of a particle is given by
We now have Einstein's famous formula
Relativistic Addition of Velocities
Einstein showed that since length and time are different in differnt reference frames, the old addition of velocities is no longer valid. For motion along a straight line,
Impact of Special Relativity
Many experiments have been done to test the validity of relativity. No contradictions have been found. It is accepted as an accurate description of nature. At speeds much less than c, Newtonian physics is valid.