Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals

TL;DR

This paper introduces a novel method to measure the mass density along the line of sight by analyzing variations in the arrival times of electromagnetic signals, which are influenced by gravitational effects and geometric delays.

Contribution

The method allows direct determination of mass density moments along the line of sight using TOA variations, independent of angular positions and off-line masses.

Findings

Two scalar quantities can be derived from TOA data to quantify spacetime curvature effects.

The method is robust against off-line masses and positional uncertainties.

Requires extremely precise timing measurements for effective application.

Abstract

We present a new method of measuring the mass density along the line of sight, based on precise measurements of the variations of the times of arrival (TOA's) of electromagnetic signals propagating between two distant regions of spacetime. The TOA variations are measured between a number of slightly displaced pairs of points from the two regions. These variations are due to the nonrelativistic geometric effects (Roemer delays and finite distance effects) as well as the gravitational effects in the light propagation (gravitational ray bending and Shapiro delays). We show that from a sufficiently broad sample of TOA measurements we can determine two scalars quantifying the impact of the spacetime curvature on the light propagation, directly related to the first two moments of the mass density distribution along the line of sight. The values of the scalars are independent of the angular positions or the states of motion of the two clock ensembles we use for the measurement and free from any influence of masses off the line of sight. These properties can make the mass density measurements very robust. The downside of the method is the need for extremely precise signal timing.