General relativity, 2

Authors

David Peak, Utah State UniversityFollow

Document Type

Course

Journal/Book Title/Conference

Physics 3710 – Intermediate Modern Physics, Spring 2018

Publication Date

1-8-2018

First Page

1

Last Page

3

Abstract

Newton’s law of gravitostatics is incompatible with special relativity. To see this, suppose at time t in frame O m₁ is at x₁(t) and m₂ is at x₂(t). Newton’s gravitational force law says F_{1on 2}(t) = Gm₁m₂ / [x₂(t) − x₁(t)]² and relativistic dynamics says dp₂ /dt = F_{1on 2}. Transforming to another frame Oʹ moving relative to O leads to dp′₂/dt′ = F′_{1on 2}. But what is F′_{1on 2} ? If x₁(t) and x₂(t) are the simultaneous positions of m₁ and m₂ in O, the transformed positions x′₁ and x′₂ are not simultaneous in Oʹ. Obviously, Newtonian gravity has to be modified to make it relativistically correct. The same is true for the electrostatic Coulomb force. But, for electric charges there’s also magnetism, and that helps save the day. Clearly, what’s needed for gravity is an analog of magnetism. To create such an analog, Einstein appealed to geometry.

Recommended Citation

Peak, David, "General relativity, 2" (2018). General Relativity. Paper 2.
https://digitalcommons.usu.edu/intermediate_modernphysics_general/2