Updated October 2, 2024

*Image description: In parabolic flights, during the descent phase, passengers cannot distinguish between the absence of gravity (as in space) and being in free fall. This directly reflects Einstein's equivalence principle, where an observer in a freely falling reference frame cannot perceive the effects of gravity. Image credit NOVESPACE. *

The **equivalence principle** is a key concept of *general relativity*, linking two fundamental notions: **gravitational mass** and **inertial mass**. Although these two types of mass describe different phenomena, they are equivalent.

Albert Einstein (1879-1955) envisioned a hypothetical situation where a person is in a completely closed elevator cabin, unable to see outside. This cabin can either be in free fall in a gravitational field or in an accelerating reference frame in space. He formulated this idea to show that the person could not distinguish whether they feel a gravitational force or an inertial force due to acceleration.

*Gravitational mass* is the mass that determines the force with which an object is attracted in a gravitational field. In contrast, *inertial mass* measures a body's resistance to any change in its motion. Formally, these two concepts are defined by:

**Gravitational mass**: $F_{grav} = m_g \cdot g$, where $m_g$ is the gravitational mass and $g$ is the gravitational acceleration.**Inertial mass**: $F = m_i \cdot a$, where $m_i$ is the inertial mass and $a$ is the acceleration.

According to the *equivalence principle*, these two masses are equal: $m_g = m_i$. This equivalence has been experimentally verified with high precision.

The equivalence principle states that the effects of a gravitational field are indistinguishable from those of an acceleration in a non-inertial reference frame (amusement park ride, car turning, Earth rotating around its axis, etc.). This leads to a remarkable consequence: all objects, regardless of their mass or composition, fall with the same acceleration in a gravitational field in the absence of air resistance.

In **general relativity**, gravitation is no longer considered a classical force, but rather a manifestation of the curvature of space-time. The equivalence principle helps explain why an object in free fall does not feel a gravitational force, as it follows a geodesic in curved space-time.

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