Relativistic Mechanics and a Special Role for the Coulomb Potential
| dc.creator | Boyer, Timothy H. | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:07:07Z | |
| dc.date.available | 2026-07-07T10:07:07Z | |
| dc.description | It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz transformation through order v^2/c^2. However, this invariance requires the introduction of velocity-dependent and acceleration-dependent forces between particles. The textbook treatments of "relativistic mechanics" can be misleading; the discussions usually deal with only one particle experiencing prescribed forces and so make no mention of these additional velocity- and acceleration-dependent forces. A simple example for a situation analogous to a parallel-plate capacitor is analyzed for all the conservation laws of Galilean invariance or Lorentz invariance. For this system, Galilean invariance requires that the mechanical momentum is given by pmech=mv but places no restriction on the position-dependent potential function. On the other hand, Lorentz invariance requires that the mechanical momentum is given by pmech=mv/(1-v^2/c^2)^1/2, and in addition requires that the potential function is exactly the Coulomb potential V(|r1-r2|)=k/|r1-r2|. It is also noted that the transmission of the interparticle-force signal at the speed of light again suggests a special role for the Coulomb potential. A nonrelativistic particle system interacting through the Coulomb potential becomes the Darwin Lagrangian when extended to a system relativistic through order v^2/c^2, and then allows extension to classical electrodynamics as a fully Lorentz-invariant theory of interacting particles. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/0810.0434 | |
| dc.identifier | http://arxiv.org/abs/0810.0434 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170521 | |
| dc.subject | Classical Physics | |
| dc.title | Relativistic Mechanics and a Special Role for the Coulomb Potential | |
| dc.type | text |