Abstract
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 depends on 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.
Highlights
More than a century after its birth, quantum mechanics is considered one of the physical theories that received the greatest experimental confirmation
We provide a general result that proves that any conservative interaction must have a quantized version, under the hypothesis that the effective interparticle potential depends on the relative distance between two objects but not on the derivative of any order of such a distance with respect to time
In this work we proved that every non-trivial conservative potential will generate entanglement between two physical objects
Summary
More than a century after its birth, quantum mechanics is considered one of the physical theories that received the greatest experimental confirmation. We provide a general result that proves that any conservative interaction must have a quantized version, under the hypothesis that the effective interparticle potential depends on the relative distance between two objects but not on the derivative of any order of such a distance with respect to time. Starting from this assumption we show that the request that it does not create entanglement is equivalent to impose a holonomic constraint that cannot be satisfied for a generic setup. More general implementations of potentials depending on the internal states will be considered below
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