Exploring Direct Detection of Massive Particles Using Wave Propagation from Gravitational Coupling with a Wire Under Tension

TL;DR

This paper explores the potential for detecting massive particles passing near a tensioned wire via gravitational and electrostatic interactions, analyzing wave-induced displacements and their detectability with current sensors.

Contribution

It introduces a novel method to detect massive particles through wave propagation on a wire caused by gravitational coupling, providing detailed displacement estimates and feasibility analysis.

Findings

Planck-scale dark matter would produce undetectable displacements.

Detection of particles with mass > 4×10^7 kg is theoretically possible with current sensors.

Charged particles could produce detectable electrostatic displacements.

Abstract

We investigate the feasibility of detecting galactic orbit dark matter passing through Earth by measuring its gravitational coupling with a wire under tension. We do so by exploring the transverse and longitudinal waves induced on the wire to detect a massive particle passing within $\sim 1$ m of the wire. The particle's $r^{-2}$ interaction with the wire provides an initial momentum which develops into a propagating wave carrying a distinctive time dependent displacement. Most interestingly, we find that both transverse and longitudinal waves develop with unique profiles, allowing for a full, three dimensional reconstruction of the particle's trajectory and its mass over velocity ratio. We find that, at interaction distances of 0.1 to 100 mm with a 90 micron diameter copper beryllium wire, Planck scale dark matter with mass $\sim 10^{19}$ GeV/$c^2$ would create immeasurable displacements on the scale of $10^{-24}$ to $10^{-26}$ m. In order to create displacements detectable by modern, commercially available, displacement sensors on the nanometer scale we require dark matter with a particle mass greater than $4 \times 10^7$ kg ($\sim 2 \times 10^{32}$ GeV/$c^2$). This is outside the upper limit of the Planck scale by 13 orders of magnitude and would also have such a low particle flux that a detection event would be implausible. Finally, we perform a similar analysis for a charged wire and an elementary charged particle with their electrostatic interaction, finding that a sufficiently slow charged particle would produce a transverse displacement comparable to the sensitivity of currently available sensors.