The strong principle of equivalence is usually formulated as an assertion that in a sufficiently small, freely falling laboratory the gravitational fields surrounding the laboratory cannot be detected. We show that this is false by presenting several simple examples of phenomena which may be used to detect the gravitational field through its tidal effects; we show that these effects are, in fact, local (observable in an arbitrarily small region). Alternative formulations of the strong principle are discussed and a new formulation of strong equivalence (the ’’Einstein principle’’) as an assertion about the field equations of physics, rather than an assertion about all laws or all experiments, is proposed. We also discuss the weak principle of equivalence and its two complementary aspects: the uniqueness of free fall of test particles in arbitrary gravitational fields (’’Galileo principle’’) and the uniqueness of free fall of arbitrary systems in weak gravitational fields (’’Newton principle’’).

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