Center of mass in special and general relativity and its role in an effective description of spacetime

TL;DR

This paper proposes a physically motivated approach to defining geometric concepts in spacetime using quantum matter, emphasizing the role of extended particles and noncommutative coordinates influenced by particle spin.

Contribution

It introduces a novel perspective that links spacetime geometry to quantum matter operations, challenging traditional idealizations and incorporating spin-dependent noncommutativity.

Findings

Spacetime coordinates can be effectively described by noncommuting variables influenced by particle spin.

Physical probes are extended particles, not idealized points, affecting the geometric interpretation.

The approach aims to refine the effective description of spacetime by integrating quantum and geometric concepts.

Abstract

In this contribution, we suggest the approach that geometric concepts ought to be defined in terms of physical operations involving quantum matter. In this way it is expected that some (presumably nocive) idealizations lying deep within the roots of the notion of spacetime might be excluded. In particular, we consider that spacetime can be probed only with physical (and therefore extended) particles, which can be effectively described by coordinates that fail to commute by a term proportional to the spin of the particles.