Equivalence principle

The equivalence principle exists in several forms, each with increasing strength. The weak equivalence principle (WEP) states that the trajectory of a freely falling test body is independent of its composition and internal structure, meaning all bodies fall with the same acceleration in a gravitational field.¹ The Einstein equivalence principle (EEP) extends this to all local, non-gravitational experiments: in a freely falling laboratory, the laws of physics are those of special relativity, and no local experiment can detect the presence of a gravitational field.² The strong equivalence principle (SEP) applies to all experiments, including those involving gravitational self-energy, and is a cornerstone of general relativity but is violated by many alternative theories.

The equivalence of gravitational and inertial mass was first tested by Galileo's alleged experiments from the Leaning Tower of Pisa, though the first precise experiments were conducted by Isaac Newton with pendulums.³ In the late 19th century, Loránd Eötvös used a torsion balance to compare the gravitational and inertial masses of different materials, achieving a precision of about 1 part in 10^9, later improved to 10^13.⁴ Albert Einstein, in 1907, elevated this empirical fact to a fundamental principle, which he called the "happiest thought of my life," leading to the development of general relativity.⁵

In general relativity, the equivalence principle is realized through the concept of geodesics: freely falling bodies follow the straightest possible paths in curved spacetime. The principle implies that gravity is not a force but a manifestation of spacetime curvature.² It also leads to gravitational time dilation and the gravitational redshift, both of which have been confirmed experimentally.⁶ The strong equivalence principle is essential for the interpretation of gravitational waves and black hole physics, where the self-gravity of the system plays a role.

Modern tests of the weak equivalence principle use torsion balances, lunar laser ranging, and satellite experiments. The MICROSCOPE satellite, launched in 2016, tested the WEP to a precision of 10^-15, the most stringent to date, finding no violation.⁷ The Einstein equivalence principle is tested through gravitational redshift measurements, such as the Pound-Rebka experiment and the Gravity Probe A mission.⁶ The strong equivalence principle is tested via lunar laser ranging, which constrains the Nordtvedt effect, a possible violation of SEP due to the Moon's gravitational self-energy.⁸

Beyond the standard tests, the equivalence principle has subtle implications. For instance, it predicts that a clock in a stronger gravitational field runs slower, a fact crucial for the Global Positioning System (GPS) satellites.⁹ The principle also underlies the concept of "Einstein's elevator," a thought experiment that illustrates the local equivalence between gravity and acceleration. A less-known consequence is that the equivalence principle implies that light is deflected by gravity, as confirmed by Arthur Eddington's 1919 solar eclipse expedition.⁵ Furthermore, the principle is violated in some quantum gravity models, such as those involving spacetime foam or certain string theory scenarios, leading to ongoing searches for violations in quantum systems.¹⁰

Weak equivalence principle

The statement that all bodies fall with the same acceleration in a gravitational field, independent of their mass or composition.

Einstein equivalence principle

The principle that in any freely falling laboratory, the laws of physics are those of special relativity, and no local experiment can detect the gravitational field.

Strong equivalence principle

The extension of the equivalence principle to all experiments, including those involving gravitational self-energy; it is a key feature of general relativity.

Torsion balance

A sensitive instrument used to measure tiny forces, historically used by Eötvös to test the equivalence of gravitational and inertial mass.

Gravitational redshift

The phenomenon where light or other electromagnetic radiation loses energy when escaping a gravitational field, a prediction of the equivalence principle.