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The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times.
In mathematics, a weak equivalence is a notion from homotopy theory that in some sense identifies objects that have the same "shape". This notion is formalized in the axiomatic definition of a model category. A model category is a category with classes of morphisms called weak equivalences, fibrations, and cofibrations, satisfying several axioms.
In general relativity, the equivalence principle is the equivalence of gravitational and inertial mass. At the core of this assertion is Albert Einstein's idea that the gravitational force as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non- inertial (i ...
Because "local Lorentz invariance" (LLI) also holds in freely falling frames, experiments concerning the weak Equivalence principle belong to this class of tests as well. The outcomes are analyzed by test theories (as mentioned above) like RMS or, more importantly, by SME. [3]
The mass–energy equivalence in special relativity refers to the inertial mass. However, already in the context of Newtonian gravity, the weak equivalence principle is postulated: the gravitational and the inertial mass of every object are the same. Thus, the mass–energy equivalence, combined with the weak equivalence principle, results in ...
An alternative expression of the equivalence principle is to note that in Newton's universal law of gravitation, F = GMm g /r 2 = m g g and in Newton's second law, F = m i a, there is no a priori reason why the gravitational mass m g should be equal to the inertial mass m i. The equivalence principle states that these two masses are identical ...
The Eötvös experiment was a physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with the same accuracy.
In other projects Wikidata item; ... In mathematics, weak equivalence may refer to: Weak equivalence of categories; ... Weak equivalence principle