principle

equivalence principle

The equivalence principle posits that inertial and gravitational mass are indistinguishable in a gravitational field.
72 related articles · 2 formulas · 2 who worked here

Description

Being in an elevator falling in a vacuum is no different from free flight in weightlessness. You will not feel your own weight in both cases. The equivalence principle says: locally, gravity and acceleration are indistinguishable — that very 'happiest moment' in Einstein's life.

History

Galileo Galilei in the early 17th century showed that all bodies fall with the same acceleration (ignoring air resistance). Isaac Newton in 1687 noted the proportionality of gravitational force to acceleration through the introduction of two types of mass, but considered it a coincidence. Albert Einstein in 1907, reflecting on a man falling from a roof, realized that free fall locally eliminates weight, and formulated the equivalence principle as a basis for extending relativity to gravity. This led him to general relativity (1915). Later, the principle was repeatedly tested: from Eötvös experiments with torsion balances to the MICROSCOPE satellite.

How it works

The equivalence principle explains phenomena such as gravitational redshift, the bending of starlight near the Sun, and time dilation in a gravitational field. It is essential for the operation of satellite navigation systems (GPS, GLONASS), where relativistic corrections to clock rates are taken into account. Applicability is strictly local: in sufficiently large regions of spacetime, tidal forces appear, revealing the non-uniformity of the gravitational field.

Fun fact

Aircraft for training cosmonauts fly along a ballistic trajectory and allow passengers inside to experience 20–30 seconds of real weightlessness — this is a direct consequence of the equivalence principle.

Concept graph →

Formulas

$$\Xi = \frac{k_e Q^2}{G M^2}$$
Compares electrostatic to gravitational force strength.
What is in the formula
QvariableElectric charge of the body — electric charge coulomb
MvariableMass of the body — mass kilogram
k_econstantElectrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\xi=\frac{k_eq^2}{gm^2} · 2605.10587v1
$$M_J \propto \frac{T^{3/2}}{\rho^{1/2}}$$
Minimum mass for gravitational collapse overcoming thermal pressure.
What is in the formula
M_JvariableJeans mass, minimum mass for collapse — mass kilogram
TvariableTemperature of the gas — temperature kelvin
ρvariableMass density of the gas — mass density kilogram per cubic metre
m_j\propto\frac{t^{3/2}}{ρ^{1/2}} · 2607.04942v1

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