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Principle of Equivalence

### 14.21: Principle of Equivalence

According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for example, diving towards the Earth from an airplane, they would feel completely weightless. Similarly, a person descending in a lift may feel partially weightless. Broadly speaking, it is assumed that an object in a uniform gravitational field and an object undergoing constant acceleration in the absence of gravity are under the same experimental conditions (i.e., no experiment can differentiate between the two scenarios). This statement is called the principle of equivalence.

The principle addresses a fundamental assumption of Newton's law of gravitation: The masses that determine the gravitational force of attraction between two objects are assumed to be the same masses that determine their reaction to the forces via Newton's laws of motion. However, these two masses, sometimes called the gravitational mass and the inertial mass, can be different in practice. The consequences of assuming them to be the same, and so the results of combining Newton's law of gravitation with Newton's laws of motion, agree with the experiments. In other words, the assumption turns out to be experimentally valid. However, the reason for this consequence is not understood.

According to the principle of equivalence, this is not a coincidence. Fundamentally, uniform acceleration and gravitation are the same.

By relating uniform acceleration with gravitation, Einstein proposed that gravitation is not a force between two objects. Instead, it is an effect of the two objects on the space-time around them, which in turn determines their dynamics. He made these ideas mathematical in his general theory of relativity in 1915.

This text is adapted from Openstax, University Physics Volume 1, Section 13.7: Einstein's Theory of Gravity.

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