Equivalence Principle

One of the most important principles of Einstein's general relativity is the equivalence principle. It says that: all objects, regardless of their mass and composition, would accelerate in the same manner in the same gravitational field when no external forces act upon them. Confused? Let me put it in simple words. Suppose you simultaneously drop a feather and a stone towards the ground from the same height in a perfectly resistance-less environment. Which one, according to you, will touch the ground first? One may think that as a stone is more massive than a fragile feather, it should experience more gravitational force, and hit the ground first. But that's not the case because as per the principle of equivalence, both objects should fall simultaneously on the ground. In other words, one can say that the inertial and gravitational mass of a body is proportional to each other, which makes the acceleration independent of the physical nature of the body. Now, what is the difference between inertial mass and gravitational mass? The mass that appears in Newton's Second Law of Motion is termed inertial mass. It simply describes how difficult it is to accelerate an object. On the other hand, the mass that appears in Newton's Universal Law of Gravitation is the gravitational mass. It depicts the strength with which gravity acts on a body. So although a stone has more gravitational mass than a feather, the force of gravity acting on it is greater. At the same time, its inertial mass is also greater, which makes it difficult to accelerate. So the two effects cancel out, and it falls with the same acceleration as that of the feather which is precisely the value of acceleration due to gravity in free fall. No matter how small, if there's any violation in the proportionality between inertial and gravitational mass, Einstein's entire system breaks down.