Equivalence Principle
The equivalence principle states that gravitational mass and inertial mass are identical. These sound like different things:
- Inertial mass measures resistance to acceleration — how hard it is to change an object's motion. (F = ma; a large m means you need a large F to produce the same a.)
- Gravitational mass measures the strength of an object's gravitational attraction — how hard the Earth's gravity pulls it.
There is no a priori reason these should be equal. Yet they are, to extraordinary precision. The Eötvös experiment (1889, refined by Robert Dicke in the 1960s) confirmed the equality to 1 part in 10⁹ using different materials — gold versus aluminum, for example. If inertial and gravitational mass differed even slightly, different materials would fall at different rates. They don't.
Galileo's Discovery, Einstein's Foundation
Galileo noticed the observational consequence — all objects fall at the same rate — without understanding its deep significance. Einstein took it as the foundation of general relativity. His insight: if you're in a sealed box with no windows, you cannot tell the difference between being on Earth's surface (gravitational field pulling you down) and being in a rocket accelerating at g (inertial force pushing you against the floor). The two situations are locally indistinguishable.
This indistinguishability is not a coincidence or a measurement limitation — it reflects something fundamental about the nature of gravity. Gravity is not a force like electromagnetism, which affects charges but not neutral objects. Gravity is a feature of the geometry of spacetime that affects all objects equally, regardless of composition, because it acts on the mass property that is also inertia.
Experimental Precision
The Eötvös-to-Dicke precision (1 in 10⁹) is remarkable because it comes from a pendulum-like torsion balance comparing how different materials are attracted toward the sun. If gravitational and inertial mass differed between materials, objects of different compositions hanging at the same distance from the sun would experience different accelerations — a detectable twist in the balance. No such twist has ever been found.
More recent tests push this to 1 part in 10¹³ or better.
Connections
- galilean-inertia — the experimental discovery (all things fall equally) that the principle formalizes
- general-relativity-gravity — Einstein built general relativity on the equivalence principle; it's the physical content behind spacetime curvature
- universal-gravitation — Newton's theory assumed the equality but did not explain it; Einstein's does