Special Relativity Made Easy

Does the word “special relativity” strike fear in your heart? It might seem tough at first glance but it is very easy to understand. 

Postulates

Special theory of relativity is a theory regarding space and time, given by Albert einstein. The main postulates of this theory are: 

1]The Principle of Relativity : The laws of physics are the same in every inertial frame of reference. 

2]The Principle of Invariant Light Speed :The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the light source.

Now, let us understand these two postulates. The first postulate basically means that physical laws, for example, Newton’s laws of motion and laws of electromagnetism, are independent from the choice of inertial systems.  If the laws differed, that difference could distinguish one inertial frame from the others or make one frame somehow more “correct” than another. However, all frames of reference are correct in their own way. Suppose you watch two children playing catch with a ball while the three of you are aboard a train moving with constant velocity. Your observations of the motion of the ball, no matter how carefully done, can’t tell you how fast (or whether) the train is moving. If seen from outside, all three appear to be moving with the train at constant velocity.  This is because Newton’s laws of motion are the same in every inertial frame.

Let’s think about what the second postulate means. Suppose two observers measure the speed of light in vacuum. One is at rest with respect to the light source, and the other is moving away from it. Both are in inertial frames of reference. According to the principle of relativity, the two observers must obtain the same result, despite the fact that one is moving with respect to the other. Now suppose a spacecraft moving with constant velocity turns on a searchlight. An observer on the spacecraft measures the speed of light emitted by the searchlight and obtains the value. According to Einstein’s second postulate, the motion of the light after it has left the source cannot depend on the motion of the source. So the observer on earth who measures the speed of this same light must also obtain the same value. This result contradicts our elementary notion of relative velocities, and it may not appear to agree with common sense. But “common sense” is intuition based on everyday experience, and this does not usually include measurements of the speed of light. 

Speed of light as a constant

Einstein’s second postulate immediately implies the following result: It is impossible for an inertial observer to travel at c, the speed of light in vacuum. We can prove this by showing that travel at c implies a logical contradiction. Suppose that the spacecraft is moving at the speed of light relative to an observer on the earth, so that If the spacecraft turns on a headlight, the second postulate now asserts that the earth observer measures the headlight beam to be also moving at c. Thus this observer measures that the headlight beam and the spacecraft move together and are always at the same point in space. But Einstein’s second postulate also asserts that the headlight beam moves at a speed relative to the spacecraft, so they cannot be at the same point in space. This contradictory result can be avoided only if it is impossible for an inertial observer, such as a passenger on the spacecraft, to move at.

Hopefully, now you can brag that you know the special theory of relativity.

https://cosmo.nyu.edu/hogg/sr/sr.pdf
https://en.wikipedia.org/wiki/Special_relativity