# Equivalence principle

principle of general relativity stating that inertial and gravitational masses are equivalent

In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

## Quotes

• A little reflection will show that law of the inert and the gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, is
(Inert mass) . (Acceleration) = (Intensity of the gravitational field) . (Gravitational mass).
It is only when there is numerical equality between the inert and gravitational mass that the acceleration is independent of the nature of the body.
• Albert Einstein, The Meaning of Relativity. 1996. p. 57.  (1st edition, 1922, published by Methuen and Company in the UK and by Princeton University Press in the USA; based on the Stafford Little Lectures of Princeton University, delivered by Einstein in May 1922)
• We postulate: It shall be impossible, by any experiment whatsoever performed inside such a box, to detect a difference between an acceleration relative to the nebulae and gravity. That is, an accelerating box in some gravitational field is indistinguishable from a stationary box in some different gravitational field. How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911—what a brilliant, marvelous man Einstein was!
• Richard Feynman, 1962-63, in Feynman Lectures on Gravitation (1995), Lecture 7
• In fact, how could you tell inside a space ship whether you are sitting on the earth or are accelerating in free space? According to Einstein’s equivalence principle there is no way to tell if you only make measurements of what happens to things inside!
• Richard Feynman, in The Feynman Lectures on Physics, Vol. II (1964), 42-5 Gravity and the principle of equivalence
• [T]he gravitational force allows us to declare that all observers—regardless of their state of motion—are on absolutely equal footing. Even those whom we would normally think of as accelerating may claim to be at rest, since they can attribute the force they feel to their being emersed in a gravitational field. In this sense gravity enforces the symmetry: it ensures the equal validity of all possible observational points of view, all possible frames of reference.
• Brian Greene, The Elegant Universe (1999/2003) Ch. 5 The Need for a New Theory: General Relativity vs. Quantum Mechanics.
• Are any of nature's fundamental parameters truly constant? ... Extensions of Albert Einstein’s theory of general relativity can realize variations in Newton’s constant. In the simplest such extension, one adds a scalar field ... The predictions of the extended theory may be described in terms of two so-called post-Einstein parameters β and γ, whose values are exactly 1 in general relativity. A recent experiment ... has determined that (γ – 1) = (2.1 ± 2.3) × 10–5, a constraint that represents an order-of-magnitude improvement over previous results. Modifications of general relativity typically lead to violations of the equivalence principle. Tests of the principle, in turn, can be used to set model-dependent constraints on the variations of fundamental couplings.
• ... what is the motivation for the special gauge invariant Lagrangians that we use in the standard model and general relativity? One possible answer is that quantum theories of mass zero, spin one particles violate Lorentz invariance unless the fields are coupled in a gauge invariant way, while quantum theories of mass zero, spin two particles violate Lorentz invariance unless the fields are coupled in a way that satisfies the equivalence principle.