# Special relativity

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## Explanation

Special relativity is a special case of the principle of relativity that deals with the physical consequences of uniform motion relative to inertial frames of reference. According to the principle of relativity, all laws of physics should be valid in all Inertial frames of reference. Experimental observations also prove that the speed at which an electromagnetic wave like light propagates in a vacuum is always the same, which is c = 299792458 ms-1, independent of the reference frames from which it is measured. This nature of light along with the relativity principle is what gives rise to the two counter-intuitive consequences that are observed when objects move relative a reference frame. The following thought experiment will help you understand special relativity.

Consider two humans. One on a train, sitting exactly at its midpoint, and the other on a platform far away ready to observe the train's velocity as it passes through him. The train is fitted with two powerful light bulbs on both ends A and B and the train moves in the direction of B at speed closer to the light's speed. For now, the bulbs are turned OFF. The train passes the stationary observer on the platform at a constant velocity v. The observer, as usual, records the speed of the train as v relative to his frame of reference F1. But from the train traveller's point of view, it appears that the stationary observer and the entire world is moving at the velocity v and he along with the train is the one at rest. Now that is his frame of reference F2.

Now let's repeat the same scenario. The bulbs are programmed that it turns ON exactly when the two humans align with each other. So when the train moves and reaches a point where both the humans (F1 and F2) align each other the light turns ON and as usual, the human on the platform records (from F1) the velocity of the train as v. He also observes that the light bulbs A and B turned ON simultaneously. Now, from the traveller's frame of reference F2, he would have observed the lights at A and B simultaneously. But for the person on the tracks, he would observe that the light from B reaches the traveller's eye quicker than the light from A. As the train is travelling towards the direction of B, it is only a logical observation to the stationary observer, as for him, the traveller is in motion and is travelling towards the direction of B.

Now in the same sense, the traveller decides to conduct another experiment inside his carriage, and the train is all set to pass the stationary observer once again. The experiment is to use a mirror and a bulb and observe the way light is propagated inside the train between the mirror and the traveller's eyes, which is F2 frame of reference. When the train moves past the stationary observer, just when the two humans align, the bulb turns ON, and both the observers record the light propagation. For the traveller, the light would follow a straight line from the bulb to the mirror and then back to his eyes. But for the stationary observer, the light would take a diagonal path because it propagates from the bulb to the mirror and back to the traveller's eye while the train is in motion. For the observer, it appears that the light takes a longer distance to travel and hence takes a longer time to reach the traveller's eyes. In a sense, it means that the traveller's time appears slow (as the speed of light cannot change, it's the time that has to change to compensate for the observed distance) to the stationary observer. This is known as time dilation.

If the stationary observer happens to measure the total distance of the train as it moves past him, then it would appear to be shorter (in the direction of motion) than the length measured when the train is stationary or the length measured by the traveller. This is the other consequence of relative motion called as length contraction.