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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, weak equivalence may refer to: Weak equivalence of categories; ... See also. Weak equivalence principle This page was last edited on 27 May ...
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]
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
An earlier definition, used especially for chemical elements, holds that an equivalent is the amount of a substance that will react with 1 g (0.035 oz) of hydrogen, 8 g (0.28 oz) of oxygen, or 35.5 g (1.25 oz) of chlorine—or that will displace any of the three.
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The equivalence point is marked in red. In chemistry, neutralization or neutralisation (see spelling differences) is a chemical reaction in which acid and a base react with an equivalent quantity of each other. In a reaction in water, neutralization results in there being no excess of hydrogen or hydroxide ions present in the solution.