Assuming that the allowed quantum states of a particle are under continued stochastic hopping, we find that the wave-particle duality emerges naturally in such a process. Introducing small randomness leads to wave-packet evolution, similar to what we get in non-relativistic quantum mechanics. This provides an intuitive mechanism for the emergence of quantum behavior from a fundamentally discrete process.
Assuming that the allowed quantum states of a particle are under continued stochastic hopping, we find that the wave-particle duality emerges naturally in such a process. Introducing small randomness leads to wave-packet evolution, similar to what we get in non-relativistic quantum mechanics. This provides an intuitive mechanism for the emergence of quantum behavior from a fundamentally discrete process.
Stunning progress in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry, and biology, whether the fundamental quantum nature may condition the dynamical and functional system properties on mesoscopic if not macroscopic scales. However, which are the distinctive signatures of quantum properties in complex systems, notably when modulated by environmental stochasticity and dynamical instabilities? It appears that, to settle this question across the above communities, a shared understanding is needed of the central feature of quantum mechanics: wave-particle duality. In this Perspective, we elaborate how randomness induced by this very quantum property can be discerned from the stochasticity ubiquitous in complex systems already on the classical level. We argue that in the study of increasingly complex systems, such distinction requires the analysis of single incidents of quantum dynamical processes.
Wave-particle duality remains one of the most striking and conceptually unresolved features of quantum mechanics. Here I present a dynamical mechanism for wave-particle duality based on spontaneous stochastic mass-energy interconversion at subatomic scales. By promoting particle mass to a fluctuating quantity consistent with Einstein’s mass-energy equivalence, I derive a Schrödinger equation with an additional stochastic kinetic-phase term. Applied to the canonical double-slit experiment, the framework shows that quantum interference arises from coherent, path-dependent phase accumulation driven by mass-energy fluctuations, while particle-like localization emerges naturally at detection. The formalism yields closed-form expressions for interference visibility, predicts a momentum- and mass-dependent decoherence rate, admits a path-integral interpretation, and enables direct experimental bounds using neutron, electron, and atom interferometry. The results provide a physically grounded account of wave-particle duality without modifying the axioms of quantum mechanics.
We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.
In quantum mechanics, the probabilistic interpretation, the complementarity principle (wave-particle duality), and the uncertainty principle form the foundation of the orthodox Copenhagen interpretation. However, this interpretation occasionally produces results that conflict with physical reasoning and intuition, leading to a long-standing debate that has persisted for nearly a century. Based on the conditions of action quantization and determinacy relations, this study reveals that the trajectory of an elementary particle forms a virtual line. At discrete points along this line, the particle exhibits particle-like properties, whereas in the regions between these points, the particle's existence cannot be detected. The most fundamental form of matter is the matter field. Its motion is wave-like and is described by a continuous wave equation and wave function over the entire spacetime domain. At specific spacetime points defined by xn =nh px and tn = nh E⁄ for n=1,2,3,…, the quantized matter field gives rise to the excitation and annihilation of elementary particles, indicating their discontinuous nature. This creation–annihilation process constitutes the wave motion of the matter field. The time and spatial scales associated with this process correspond to one period and one wavelength of the matter field wave, respectively. The Schrödinger equation, in this context, is understood as the non-relativistic equation of motion for a low-speed matter field. The eigenfunction of an elementary particle is, in essence, a wave function that describes the dynamic behavior of the matter field, encompassing the processes of its motion, as well as the generation and annihilation of the particle.
This conceptual paper presents a unified reinterpretation of wave-particle duality within the Scalar Drag Emergence Framework (SDEF). Instead of treating systems as having dual natures (wave and particle), all behavior is described as arising from a single process: the continuous handoff of structured information across successive reconstructions. A "packet" is not an object moving through space but a temporally extended structure maintained through repeated handoffs. Each handoff involves retention (core), acquisition (leading edge), and loss (trailing edge). Persistence requires that retention compensates for unavoidable loss, guided by ancestry (A) and loop integrity (L). Key distinction: Observation always yields discrete, localized detection events. Wave-like behavior is not directly observed but inferred from the statistical distribution of many events. Duality reinterpretation: Particle-like observation occurs when the handoff is nearly complete — the packet appears localized and coherent. Wave-like observation occurs during redistribution — the packet appears distributed. The difference lies in when the process is sampled, not in what exists. No dual nature is required. This work is strictly conceptual. It does not modify experimental predictions but provides a unified mechanistic interpretation that removes the need for dual ontologies.
A satisfactory explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view, a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than an actuality, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be reasonably comprehended. The necessity of acquiring the wave function in its entirety for detection, as evinced by the appearance of collapse of the wave function, supports the paradigm of reality of the wave function described here. Quanta 2016; 5: 93–100.