2010/05/11 by Jens Madsen Houlrik, Houlrik, Jens Madsen, Germain Rousseaux +1
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #General Physics (physics.gen-ph) #physics.class-ph #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1005.1762
4 pages.
arxiv created 2010/05/11 · arxiv updated 2010/05/31
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the SIdefinition of length based on the universal constant c has profound consequences at low velocities. Galilean physics, exact in the limit c → ∞, is mirrored by a dual so-called Carrollian superluminal kinematics [4-6] exact in the limit c → 0. Several new results follow. The Galilean limit explains mass conservation in Newtonian mechanics, while the dual limit is a kinematical prerequisite for wavelike tachyonic motion [8, 9]. As an example, the Landé paradox [19, 20] of waveparticle duality has a natural resolution within special relativity in terms of superluminal, particlelike waves. It is emphasized that internal particle energy mc2 can not be ignored, while kinetic energy leads to an extended Galilei group. We also demonstrate that Maxwell's equations have magnetic and electric limits covariant under Galilean and Carrollian symmetry.