Planck-Einstein-de Broglie relations for wave packet: the acoustic world

TL;DR

This paper explores the analogy between quantum relations and acoustic wave packets, proposing an 'acoustic world' where wave properties mimic relativistic effects, revealing new insights into wave-particle duality and relativistic transformations in a medium.

Contribution

It introduces a model of wave packets in an acoustic medium that exhibits relativistic properties and parallels quantum relations, extending the concept of wave-particle duality to an acoustic context.

Findings

Wave packets in an acoustic medium obey Lorentz-like transformations.

Energy, mass, and momentum of wave packets undergo relativistic changes.

Existence of energy and action limits for disturbances in the medium.

Abstract

In this paper we study the relations of Planck-Einstein-de Broglie type for the wave packets. We assume that the wave packet is a possible model of particle . When studying the behaviour of the wave packet for standing waves, in relation to an accelerated observer (i.e. Rindler observer), there can be demonstrated that the equivalent mass of the packet is the inertial mass. In our scenario, the waves and of the wave packets are depicted by the strain induced/produced in the medium. The properties of the waves, of the wave packet and, generally, of the perturbations in a material medium suggest the existence of an acoustic world. The acoustic world has mechanical and thermodynamical properties. The perturbations that are generated and propagated in the medium are correlated by means of acoustic waves with maximum speed. The observers of this world of disturbances (namely the acoustic world) have senses that are based on the perception of mechanical waves (disturbance of any kind) and apparatus for detecting and acquiring information by means of the same type of wave. Time and length measurements (and other parameters) are correlated by Lorentz type transformations, where the maximum speed is the speed of the sound waves. By applying these transformations to the packet of standing waves, there results that the energy, mass, linear momentum and the action variable/variable action undergo relativistic changes. We highlight the fact that the dynamic relativist relationship between energy and momentum is a consequence of the wave packet model for a particle. We have also emphasized the existence of certain limits for the energy of the disturbance and the corresponding action variable.