2 - The Einstein Equivalence Principle and the Foundations of Gravitation Theory

Summary

The Principle of Equivalence has played an important role in the development of gravitation theory. Newton regarded this principle as such a cornerstone of mechanics that he devoted the opening paragraphs of the Principia to a detailed discussion of it (Figure 2.1). He also reported there the results of pendulum experiments he performed to verify the principle. To Newton, the Principle of Equivalence demanded that the “mass” of any body, namely that property of a body (inertia) that regulates its response to an applied force, be equal to its “weight,” that property that regulates its response to gravitation. Bondi (1957) coined the terms “inertial mass” m₁ and “passive gravitational mass” m_p, to refer to these quantities, so that Newton's second law and the law of gravitation take the forms

F = m₁a, F = m_Pg

where g is the gravitational field. The Principle of Equivalence can then be stated succinctly: for any body m_P = m₁

An alternative statement of this principle is that all bodies fall in a gravitational field with the same acceleration regardless of their mass or internal structure. Newton's equivalence principle is now generally referred to as the “Weak Equivalence Principle” (WEP).

It was Einstein who added the key element to WEP that revealed the path to general relativity.