At any given event gravity accelerates all particles equally—yet gravity is very strong in some places and very weak in others. In this chapter, we learn a powerful thinking tool to help us deal with these variations: the gravitational potential. The potential takes the concept of “acceleration times height” that, we previously found, determines the march of time and generalizes it to cases where the gravitational acceleration varies with position. The potential encodes global relationships, such as the gravitational redshift of light emitted from one point and received by a distant observer, as well as the local acceleration at each point.We also showhow the spacetime metric is affected by the potential. Incorporating the potential into themetric neatly unites gravity with relativity and eliminates any need for a theory of gravity involving forces.
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