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A purely mechanical system realizing a Coulomb-like interaction
Abstract
We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, V∝ 1/r, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a 1/r3 force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.
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BibTeX
@misc{ee2026purely,
title = {{A purely mechanical system realizing a Coulomb-like interaction}},
author = {June-Haak Ee and U-Rae Kim and Jungil Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06917},
eprint = {2609.06917},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06917},
}
RIS
TY - UNPB
TI - A purely mechanical system realizing a Coulomb-like interaction
AU - June-Haak Ee
AU - U-Rae Kim
AU - Jungil Lee
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06917
UR - https://arxiv.org/abs/2609.06917
AB - We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, V∝ 1/r, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a 1/r^3 force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.
ER -