Entanglement, holonomic constraints, and the quantization of fundamental interactions

TL;DR

This paper argues that all non-trivial conservative interactions, including gravity, must be quantized, using a proof based on entanglement and holonomic constraints, and proposes a protocol to measure interaction multipoles.

Contribution

It provides a novel proof that quantization is necessary for fundamental interactions based on entanglement constraints and introduces a measurement protocol for interaction multipoles.

Findings

Classical fields cannot generate entanglement between objects.

Quantum interactions are required for entanglement to develop in non-trivial cases.

A protocol for measuring multipole expansion terms of interactions is proposed.

Abstract

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.