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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.
Weak equivalence principle This page was last edited on 27 May 2024, at 02:43 (UTC). Text is available under the Creative Commons Attribution ...
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.
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]
[p 4] The measurement of gravitational redshift and blueshift by this experiment validated the prediction of the equivalence principle that clocks should be measured as running at different rates in different places of a gravitational field. It is considered to be the experiment that ushered in an era of precision tests of general relativity.
For example, the category of (reasonable) topological spaces has a structure of a model category where a weak equivalence is a weak homotopy equivalence, a cofibration a certain retract and a fibration a Serre fibration. [20] Another example is the category of non-negatively graded chain complexes over a fixed base ring. [21
The weak equivalence principle plays a prominent role in relativity theory and the Eötvös experiment was cited by Albert Einstein in his 1916 paper The Foundation of the General Theory of Relativity. Measurements of the gravitational gradient are important in applied geophysics, such as the location of petroleum deposits.
The above definition can be succinctly phrased by the following equivalent definition: a model category is a category C and three classes of (so-called) weak equivalences W, fibrations F and cofibrations C so that