The wave particle duality is one of the less intuitive properties of Quantum Mechanics.Under some particular experimental circumstances, when corpuscular systems can follow two alternative paths which later on rejoin and superpose, some wave like interference happens.If one of the paths is blocked the wave like behaviour disappears.As the particle arrives to the final position we can infer it has followed the free path, and therefore it is always spatially separated of the blocking system and there is not local interaction between them.The simplest hypothesis is that a third element, a physical wave, allows an indirect interaction between particle and blocking system, a de Broglie wave.A simple mathematical model, extension of General Relativity, shows how this indirect interaction can happen, mediated by gravity.
The wave particle duality is one of the less intuitive properties of Quantum Mechanics.Under some particular experimental circumstances, when corpuscular systems can follow two alternative paths which later on rejoin and superpose, some wave like interference happens.If one of the paths is blocked the wave like behaviour disappears.As the particle arrives to the final position we can infer it has followed the free path, and therefore it is always spatially separated of the blocking system and there is not local interaction between them.The simplest hypothesis is that a third element, a physical wave, allows an indirect interaction between particle and blocking system, a de Broglie wave.A simple mathematical model, extension of General Relativity, shows how this indirect interaction can happen, mediated by gravity.
Louis de Broglie put forward the idea of wave-particle duality in 1923-24, less than two years before the advent of Quantum Mechanics. This last theory assumes that duality, but in a more abstract and counter-intuitive manner than de Broglie did. In this article the wave behavior of matter is presented in a didactic way following de Broglie´s ideas. This kind of presentation may (hopefully) be helpful to better understand the quantum features in a more intuitive way. It is shown that this wave mechanics, in the framework of the theory of relativity, is compatible with Planck´s quantum and explains as well the particle´s dynamics, provided the uncertainty relations are properly incorporated. The main difficulty with this view lies in its interpreting the wave as a non-local entity
The wave-particle duality of photons, as hypothesized by Einstein, was well accepted by the early 1920's. De Broglie's bold hypothesis in 1924, that all matter likewise has a wave-particle duality added further fuel to the fire in the development of Quantum Mechanics. It seared into the minds of physicists the wave-particle duality of Nature. Needless to say, this counter intuitive and bold assertion mystified the World beyond any sensible comprehension by common sense. The question often asked by ordinary people is what is the matter with de Broglie waves? We provide just this answer and demystify this 'matter' in this short paper.
A very simple (therefore strong) argument, grounded in the action reaction principle, predicts the existence of isolated quantum, de Broglie waves.In this article I propose an experimental set up able to detect these quantum waves.As far as quantum waves are associated to any kind of elementary particles, massive or massless, charged or neutral, etc., its character is probably gravitational, i.e., they are micro-gravitational waves.The quantum wave is isolated when a particle can follow two (or more) alternative paths which later on can rejoin and interfere.We know that the corpuscular particle follows one path while the wave follows both.This wave could perturb a laser beam, and this perturbation could be detected in a Mach-Zehnder interferometer.
There are many evidences in Quantum Mechanics about the existence of de Broglie waves: the two-slit experiment, self interference when a particle can follow two or more paths that converge, etc.There is not direct evidence of its existence because we use exclusively particle detectors.This paper presents a new evidence of the existence of de Broglie waves grounded in the action reaction principle.The action reaction principle is a fundamental ingredient of Physics: when two systems interact both change of state (i.e., they depart from the free, isolated evolution path in the phase space).A simple experiment using a Mach-Zehnder interferometer is analysed.A representation of the evolution in the phase space for different cases (isolated system and interaction with a detector) is shown.By applying the action reaction principle we show that some subsystem, different from the corpuscular photon, must follow one arm of the interferometer when we can infer that the photon follows the other arm.There cannot be interaction between the photodetector in one arm and the photon following the other arm.This new subsystem would be a distributed de Broglie wave.
Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.