2012/12/12 by Yaakov Friedman, Tzvi Scarr · 1 citation
Physics and Astronomy · #physics.gen-ph
paper · pdf · doi:10.1088/0031-8949/86/06/065008
published as Physica Scripta, 86 (2012) 065008 · 16 pages. arXiv admin note: substantial text overlap with arXiv:1105.0492
arxiv created 2012/12/12 · arxiv updated 2015/06/12
We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation F=(dp)/(dt), where F is the 3D force and p=m0γv is the 3D relativistic momentum. The standard 4D equation F=(dp)/(dτ) is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion.