# Proper time is stochastic time in 2d quantum gravity

## TL;DR

This paper demonstrates that in 2D quantum gravity, proper time aligns with stochastic time from stochastic quantization, especially clear within the causal dynamical triangulations framework, revealing a fundamental connection between these concepts.

## Contribution

It establishes a direct equivalence between proper time and stochastic time in 2D quantum gravity, clarifying the relation within the CDT approach.

## Key findings

- Proper time equals stochastic time in 2D quantum gravity.
- The relation is clearer in the CDT formulation.
- Supports earlier ideas by Kawai and collaborators.

## Abstract

We show that proper time, when defined in the quantum theory of 2d gravity, becomes identical to the stochastic time associated with the stochastic quantization of space. This observation was first made by Kawai and collaborators in the context of 2d Euclidean quantum gravity, but the relation is even simpler and more transparent in he context of 2d gravity formulated in the framework of CDT (causal dynamical triangulations).