# Attraction Induced by Mutual Quantum Measurements of Velocity

## TL;DR

This paper proposes that mutual quantum measurements of velocity between macroscopic objects can produce an effective force resembling gravity, potentially explaining mass equivalence and suggesting corrections to Newtonian gravity.

## Contribution

It introduces a novel mechanism where quantum measurement-induced velocity diffusion leads to gravitational-like forces, linking quantum measurement theory with classical gravity.

## Key findings

- Mutual quantum measurements induce asymmetric velocity diffusion.
- The emergent force can replicate Newton's law of gravitation.
- Possible corrections to Newtonian gravity for broader measurement classes.

## Abstract

We define the notion of mutual quantum measurements of two macroscopic objects and investigate the effect of these measurements on the velocities of the objects. We show that multiple mutual quantum measurements can lead to an effective force emerging as a consequence of asymmetric diffusion in the velocity space. We further show that, under a certain set of assumptions involving the measurements of mutual Doppler shifts, the above force can reproduce Newton's law of gravitation. Such a mechanism would explain the equivalence between the gravitational and the inertial masses. For a broader class of measurements, the emergent force can also lead to corrections to Newton's gravitation.