Equivalence Principle

The equivalence principle exists in several versions. The weak equivalence principle states that the trajectory of a point mass in a gravitational field depends only on its initial position and velocity, not on its composition. This is the modern version of Galileo’s observation that all objects fall at the same rate. The Einstein equivalence principle extends this, stating that the outcome of any local non-gravitational experiment in a freely falling reference frame is independent of the velocity and location of the frame in spacetime. Finally, the strong equivalence principle includes gravitational experiments themselves, positing that the gravitational motion of a small test body depends only on its initial position and velocity, not its constitution.

This principle was Einstein’s crucial insight that bridged special and general relativity. It allowed him to generalize the principle of relativity to include accelerating reference frames, which he then equated with gravitational fields. The famous thought experiment of an observer in an elevator illustrates this: if the elevator is accelerating upwards in empty space, the observer feels a downward force identical to gravity. Conversely, if the elevator is in free-fall, everything inside is weightless. This equivalence implies that gravity is not a force propagating through space, but a manifestation of the curvature of spacetime. The paths objects follow under gravity are not due to a force but are the straightest possible paths (geodesics) through a curved spacetime, a radical departure from the Newtonian concept.