A Classical Model for Wave-Particle Duality

Leonid I. Manevitch

Chen Yang, S. Olutunde Oyadiji

Abstract Wave-particle duality is the fundamental phenomenon of particles and fields in quantum mechanics. In the past, the trajectory-like (particle-like) behaviour and wave-like behaviour has been considered separately. In this article, a superimposed model is derived to characterise wave-particle duality of classical particles. The superimposed model reflects an invariant mathematical structure (analogous variables and differential equations) from classical mechanics, classical field theories and quantum mechanics. Its analytical solution carries trajectory-like property (phase-independent) and wave-like property (phase-dependent) of particles that is consistent with to Schrodinger’s picture. Subsequently, the presented model is applied to model duality of classical waves in electromagnetism, acoustics and elasticity. The analysis implies the existence of quantum effects of classical waves at macroscopic scale. It predicts quantum picture on energy and momentum exchange between classical particles and waves. As seen in the model, wave-particle duality reflects inherent and indispensable characteristics of classical objects.

Bruce R. Wheaton

Rutger Ockhorst, Freek Pols

Abstract Wave-particle duality is included in many secondary school and university physics curricula as a concept central to quantum physics. The very term wave-particle duality suggests that a firm grasp of the individual classical concepts of wave and particle is crucial to studying quantum mechanics successfully. This raises the question whether students’ mental models of these concepts are sufficiently addressed and developed prior to the teaching of wave-particle duality. We explored Dutch upper secondary school students’ mental models of waves and particles using a short questionnaire. It was administered to a total of 147 students from two different groups. One group consisted of secondary school students prior to receiving formal education in introductory quantum mechanics while students from the other group had recently completed the Dutch national curriculum for pre-university education, which includes wave-particle duality. Our findings support the notion that students model classical particles and waves as mutually exclusive phenomena. Mental models of wave-particle duality, which require mixing the two classical models, appear to be only superficially developed. Our findings open avenues for future research on students’ mental models of waves and particles as basis for wave-particle duality.

Bruce R. Wheaton

Marcelo Janovitch, Brunelli, Matteo, Patrick P. Potts

According to the wave-particle duality (WPD), quantum systems show both particle- and wave-like behavior, and cannot be described using only one of these classical concepts. Identifying quantum features that cannot be reproduced by any classical means is key for quantum technology. This task is often pursued by comparing the quantum system of interest to a suitable classical counterpart. However, the WPD implies that a comparison to a single classical model is generally insufficient; at least one wave and one particle model should be considered. Here we exploit this insight and contrast a bosonic quantum heat engine with two classical counterparts, one based on waves and one based on particles. While both classical models reproduce the average output power of the quantum engine, neither reproduces its fluctuations. The wave model fails to capture the vacuum fluctuations while the particle model cannot reproduce bunching to its full extent. We find regimes where wave and particle descriptions agree with the quantum one, as well as a regime where neither classical model is adequate, revealing the role of the WPD in non-equilibrium bosonic transport.