Spacetime & the Equivalence Principle: Structures & Vocabulary

The equivalence principle links acceleration and gravity by stating that sufficiently local experiments in a freely falling laboratory cannot distinguish free fall in a gravitational field from inertial motion without gravity. This insight motivated Einstein's description of gravity as spacetime geometry rather than an ordinary force acting through fixed space.

In a small freely falling elevator, objects float together because they share the same gravitational acceleration; locally gravity can be transformed away. Over larger regions, tidal effects remain because gravitational acceleration varies from place to place, revealing curvature that no single accelerating frame can eliminate.

Gravitational redshift, light deflection, orbital precession, clock-rate differences, and gravitational waves all follow from curved-spacetime physics. Precision experiments compare clocks at different heights and confirm that gravitational potential affects elapsed time.

Spacetime geometry replaces a universal gravitational force field in the general-relativistic picture. Freely falling bodies follow geodesics; an accelerometer carried by a freely falling observer can read zero despite strong gravity.