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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.
Constraints on this, and on the existence of a composition-dependent fifth force or gravitational Yukawa interaction are very strong, and are discussed under fifth force and weak equivalence principle. A version of the equivalence principle, called the strong equivalence principle, asserts that self-gravitation falling bodies, such as stars ...
In a weak field approximation, clocks tick at a rate of t' = t (1 + Φ / c 2) where Φ is the difference in gravitational potential. In this case, Φ = gh where g is the acceleration of the traveling observer during turnaround and h is the distance to the stay-at-home twin.
Typically, this map is not a weak equivalence. For example, the homotopy pushout encountered above always maps to the ordinary pushout. This map is not typically a weak equivalence, for example the join is not weakly equivalent to the pushout of , which is a point.
The CPT theorem implies that the difference between the properties of a matter particle and those of its antimatter counterpart is completely described by C-inversion. Since this C-inversion does not affect gravitational mass, the CPT theorem predicts that the gravitational mass of antimatter is the same as that of ordinary matter. [5]
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