H2 - Concepts of Special Relativity

Inertial frame of reference is one which is moving at constant speed where Newton's Laws of motion apply. Accelerating frames of reference, like circular motion is a non inertial frame of reference ( there is acceleration towards the centre). Acceleration must be 0 for a frame of reference to be inertial.
Special Relativity: The two postulates for special relativity are

1. The speed of light is constant for all observers in an inertial frame of reference
2. The laws of physics are the same for all inertial observers.

Simultaneity: If two events happen together, they are said to be happening simultaneously.
 Consider

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To a person inside the train moving at constant speed, if both the pulses of light are sent out at the same then the time taken for both beams to hit mirrors on either end and reach back to him is the same. The light pulses return simultaneously. 

But consider a stationary observer on the platform observing this event:

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When the train moves forward, the light travelling towards the left has a shorter distance to travel as the back of the train has moved forward towards the pulse of light. Similarly, the light travelling towards the right has a longer distance to travel as the front of the train is moving forward away from the pulse of light. Speed of light is constant in all inertial frames of reference irrespective of the speed of the frame of reference of the observer. Therefore, to an observer on the platform, the light pulse on the right reaches the mirror after the one on the left.

This event is not simultaneous to an observer on the platform. Two events occurring at different points in space cannot be simultaneous for two different frames of references.

From: http://www.youtube.com/watch?v=AZ6N85lNgHY