# Extracting Geometry from Quantum Spacetime: Obstacles down the road

## TL;DR

This paper discusses fundamental obstacles in deriving classical spacetime geometry from quantum gravity theories, highlighting issues with defining trajectories and the feasibility of linking geometry to matter behavior.

## Contribution

It identifies core conceptual challenges in extracting classical geometry from quantum gravity, questioning the overall feasibility of this approach.

## Key findings

- Trajectories of localized objects cannot be defined in quantum theory.
- Linking spacetime geometry to matter behavior faces fundamental difficulties.
- The analysis suggests reconsidering the goals of quantum gravity research.

## Abstract

Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We consider some difficulties that would be confronted in attempting such an enterprise. The problems we uncover seem to go beyond the technical level to the point of questioning the overall feasibility of the project. The main issue is related to the fact that, in the quantum theory, it is impossible to assign a trajectory to a physical object, and, on the other hand, according to the basic tenets of the geometrization of gravity, it is precisely the trajectories of free localized objects that define the spacetime geometry. The insights gained in this analysis should be relevant to those interested in the quest for a quantum theory of gravity and might help refocus some of its goals.