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A College Course on Relativity and Cosmology$
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Ta-Pei Cheng

Print publication date: 2015

Print ISBN-13: 9780199693405

Published to Oxford Scholarship Online: August 2015

DOI: 10.1093/acprof:oso/9780199693405.001.0001

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Equivalence of Gravitation and Inertia

Equivalence of Gravitation and Inertia

4 Equivalence of Gravitation and Inertia
A College Course on Relativity and Cosmology

Ta-Pei Cheng

Oxford University Press

After a review of the Newtonian theory of gravitation in terms of its potential function, this chapter starts the study of general relativity (GR) with the introduction of the equivalence principle (EP). The weak EP (equality of gravitational and inertial masses) was extended by Einstein to the strong EP (equivalence between inertia and gravitation for all interactions). This implies the existence of “local inertial frames” at every spacetime point. In a sufficiently small region, a “local inertial observer” will not sense any gravitational effect. The equivalence of acceleration and gravity means that GR (with physics laws valid in all coordinate systems, including accelerating frames) must necessarily be a theory of gravitation. The strong EP is used to deduce results for gravitational redshift and time dilation, as well as gravitational bending of a light ray. The operation of GPS is shown to depend crucially on relativistic time dilation effects.

Keywords:   Newtonian theory of gravitation, equivalence principle, gravitational mass, inertial mass, gravitational redshift, gravitational time dilation, bending of light ray, GPS

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