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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.
Weak equivalence principle This page was last edited on 27 May 2024, at 02:43 (UTC). Text is available under the Creative Commons Attribution ...
According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors (see Eötvös experiment), there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free ...
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 ...
A homotopy equivalence class of spaces is then called a homotopy type. There is a weaker notion: a map : is said to be a weak homotopy equivalence if : () is an isomorphism for each and each choice of a base point. A homotopy equivalence is a weak homotopy equivalence but the converse need not be true.
The particular equivalence often referred to as the "Galilean equivalence principle" or the "weak equivalence principle" has the most important consequence for freely falling objects. Suppose an object has inertial and gravitational masses m and M , respectively.
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.