# On Einstein's equivalence principles

There are two foundative Equivalence Principles in General relativity:

Weak Equivalence Principle (WEP): the dynamics of a test particle in a gravitational field is independent of its mass and internal composition. (WEP is equivalent to say that the ratio between the gravitational mass $m_g$ and the inertial mass $m_i$ has a universal value $k$. This value can be considered as the scalar $1$).

Einstein equivalence principle (EEP): A frame linearly accelerated relative to an inertial frame in special relativity is LOCALLY identical to a frame at rest in a gravitational field.

Most textbooks say that "obviously" (EEP) implies (WEP) but the converse is not true.

I don't understand why the implication (EEP) $\Rightarrow$ (WEP) is true, and moreover I'd like a counterexample showing that (WEP) $\not\Rightarrow$ (EEP).

EEP has something more than what WEP has. WEP states that in a small reign of space-time,there is no difference for a particle to free fall (to move in a gravitational field) or to move in a box with acceleration $g$ in the inverse direction.