  It is a general belief that all fundamental interactions need to be
quantized. However, all attempts to develop a quantum theory of gravity
presented various problems, leading to a recent active debate about how to
probe its quantum nature. In the present work we provide a proof for the
necessity of quantizing fundamental interactions demonstrating that a quantum
version is needed for any non trivial conservative interaction whose strength
is a function of the relative distance between two objects. Our proof is based
on a consistency argument that in the presence of a classical field two
interacting objects in a separable state could not develop entanglement. This
requirement can be cast in the form of a holonomic constraint that cannot be
satisfied by generic interparticle potentials. Extending this picture of local
holonomic constraints, we design a protocol that allows to measure the terms of
a multipole expansion of the interaction of two composite bodies. The results
presented in this work can pave the way for a study of fundamental interactions
based on the analysis of entanglement properties.
