Year: 2026
Type: preprint
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, $V\propto 1/r$, 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.
Source: arXiv (Cornell University)
Authors: Ee, June-Haak, Kim, U-Rae, Lee, Jungil
Institution: Korea University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G6337415494, G7825001157
OpenAlex ID: W7212050356