Pré-Publication, Document De Travail Année : 2010

“Nonrelativistic” kinematics: Particles or waves?

Résumé

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 mc^2 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.

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hal-00482388 , version 1 (10-05-2010)

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Jens Madsen Houlrik, Germain Rousseaux. “Nonrelativistic” kinematics: Particles or waves?. 2010. ⟨hal-00482388⟩
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