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An Upper Bound for the Mass of Microscopic Clocks

Bruno Arderucio Costa, Yafet E. Sanchez Sanchez

Abstract

According to general relativity, clocks are the basic measuring devices needed to probe spacetime geometry. However, it is generally accepted that the mass of clocks capable of measuring small time intervals must be bounded from below. In this article, we consider two gravitationally induced phenomena: first, the extent to which such a mass disturbs the geometry that the clocks intended to probe; second, the magnitude of the gravitational self-interaction. We adopt the semiclassical coupling between gravity and quantum matter in the non-relativistic regime to obtain upper bounds on the mass of the clocks for a given time resolution and running time.

An Upper Bound for the Mass of Microscopic Clocks

Abstract

According to general relativity, clocks are the basic measuring devices needed to probe spacetime geometry. However, it is generally accepted that the mass of clocks capable of measuring small time intervals must be bounded from below. In this article, we consider two gravitationally induced phenomena: first, the extent to which such a mass disturbs the geometry that the clocks intended to probe; second, the magnitude of the gravitational self-interaction. We adopt the semiclassical coupling between gravity and quantum matter in the non-relativistic regime to obtain upper bounds on the mass of the clocks for a given time resolution and running time.
Paper Structure (5 sections, 26 equations, 1 figure)

This paper contains 5 sections, 26 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Clock
  3. Semiclassical coupling
  4. An Upper Bound for the Mass of the Clock
  5. Discussion

Figures (1)

  • Figure 1: The variance $\tau$ for the distribution \ref{['update']} behaves approximately as the same power law \ref{['nparticletau']} for large $\mathcal{N}$ for three ratios $n/\mathcal{N}$: 10% (left), 50% (center), and 90% (right). The calculated points (for $50\leq\mathcal{N}\leq200$) are in red, and the fitted curve is in blue. The fitted values of $\gamma$ were 0.490, 0.495, and 0.491, respectively. The largest difference in the value of $\gamma$ for a pair of ratios $n/\mathcal{N}$ is around 1%. Fits for larger values of $\mathcal{N}$ bring $\gamma$ closer to ½.