http://popups.lib.uliege.be/1373-5411/index.php?id=591 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=2810 In the wave-particle duality, a free particle can be considered as a wave packet. Is there a wave property that corresponds to the rest mass of the particle? We suggest that this problem can be approached by treating the rest mass on the same footing as energy and momentum. Here we demonstrate that, by assuming that the matter wave of a particle is an excitation of a real physical field in the vacuum, one could derive the mass-energy relation from the solution of a simplified wave equation describing a free particle. This solution suggests that the rest mass of a particle is associated with a "transverse wave number", which characterizes the radial variation of the wave function in the transverse plane. This model has several appealing features. For example, it predicts that a massless particle must travel at the constant speed of light. Tue, 03 Sep 2024 14:56:05 +0200 Thu, 10 Oct 2024 09:55:30 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2810 http://popups.lib.uliege.be/1373-5411/index.php?id=587 A computational derivation of the Klein-Gordon quantum relativist equation and the Schrôdinger quantum equation with forward and backward space-time shifts was developed in Dubois (1999, 2000). The forward-backward space λ and time t shifts are related to a phase velocity u = λ/t. The ratio v/u, where v is a group velocity, is related to the mass of paticles: for v < u, particles have a real mass and for v = u, there is no mass, as for photons. In this paper, it is shown that this formalism gives rise to a quantum interpretation of the mass in relation with plane waves. Moreover there is a third case for mass of particle: when for v > u, particles have an imaginary mass, as for tachyons. From these considerations, we look at the possibility to develop a dual relativity including these three types of mass. Fri, 28 Jun 2024 12:11:02 +0200 Tue, 08 Oct 2024 13:32:07 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=587