What is the theory of relativity?
Let us start with a simple example. Abhi and Rama decide to meet at a candy store. Abhi approaches the candy store from one end and Rama approaches the candy store from the other end of the straight road. Abhi says the candy store is to his left and Rama says it is to his right. Who is correct? Both.
From the above example, it is clear that we need to define something called an ‘observer’. Abhi and Rama here were our two observers. Each of them was right from his own perspective. They do not agree with each other about ‘left’ and ‘right’ but both would agree that it is a candy store!
Observer along with a measuring stick to measure lengths and clock to measure time constitutes a frame of reference.
Law of addition of velocities
Consider three observers A, B and C. A is riding a motorcycle, B is sitting inside a train and C is standing on a footpath. As a simple case let us take this to be a 1-D problem. Velocity of A cannot be specified unless you mention the observer who is measuring the velocity of A. Let us say velocity of A with respect to C= v and velocity of B with respect to C=u. Then the law of addition of velocities says that =-.
means velocity of A with respect to B or velocity of A as seen from B.
This law of addition holds for accelerations as well.
Inertial frames of reference in the theory of relativity:
Newton’s first law states that a body continues to be in its state of rest or of uniform motion unless an external force acts on it. This is valid only in the case of inertial observers or other word for it, inertial frames.
In a moving train, sometimes you notice trees on the ground moving backwards. If the train is moving with constant velocity ‘v’ with respect to the ground then the trees appear to move with a constant velocity v backwards. No external force acts on the trees backwards, hence they will continue to move with same velocity v backwards as seen from the train. Hence this does not violate Newton’s first law.
However let us say the train is accelerating forward, then as seen from the train the tree appears to accelerate backward. No external force acts on the tree in opposite direction, yet it appears to accelerate (not uniform motion). This implies that Newton’s laws hold good only in inertial frames or frames which move with constant velocity.
The train observer in the first case was inertial while in the second case was non-inertial.
Abhi and Rama are playing tennis on stationary ground. Now if they play tennis on a ship moving smoothly (i.e. with constant velocity) then they will not be able to tell whether the ship is moving or it is stationary on condition that they are not looking outside the ship.
This can be commonly seen in train journeys. When all the windows are closed, we can hardly make out sitting in the train whether the train is at rest or it is moving. (moving with constant velocity).
However, if the train or ship accelerates or takes a turn we can feel it without having to look outside, like we feel extra pressure on the seat etc.
Principle of relativity as stated by Galileo states that all inertial frames are equivalent and Laws of mechanics hold good equally in all inertial frames.
In Galilean relativity mass, length and time are invariant from one frame to another. Velocities, accelerations etc. depend on frames of reference.
Einstein’s theory of relativity
Einstein observed that principle or the theory of relativity could be extended to laws of electromagnetism.
Speed of light ‘c’ in vacuum is a fundamental constant which depends on properties of vacuum space and not on any velocity. Speed of any wave (light or sound) does not depend on the speed of source of the observer, it only depends on the medium.
Combining these two facts and the principle of relativity as extended by Einstein, we can say that speed of light in vacuum is constant with respect to any inertial frame of reference.
In Einstein’s framework length, mass, time also change depending on the observer.