De Broglie waves connect GR with quantum mechanics

James Murray Hill

Michael H. Brill

P. Weinberger

De Broglie's contribution in the Philosophical Magazine from 1924 is fascinating from many standpoints: for its moderate use of mathematics, the close connection to Einstein's special theory of relativity, and of course for the proposal of matter waves. We revisit this mostly speculative publication, which contributed crucially to the birth of quantum mechanics.

Carson L. Tang

Philipp I. Vysikaylo, N. V. Samsonenko, M V Semin

Abstract Properties of de Broglie waves and their differences from any other waves, for example, electromagnetic, are discussed. Their little-known properties are given: 1) the propagation velocity is greater than the speed of light V > c ; 2) dispersion even in vacuum (waves of different frequencies propagate at different speeds, which results in the spreading of any wave packets associated with the particles); 3) the connection of the de Broglie wave with another physical wave moving with a speed v less than the speed of light, but so always v · V = c 2, and for the photons v = V = c. According to later views of de Broglie, this second wave is not the group wave. Possible mechanisms of generating the de Broglie waves based on spherical and cylindrical hollow quantum resonators, which can be specially created in matter using specific nanostructures are considered. Perhaps their nature itself realizes them for any micro-objects, regardless of their electrical, magnetic and gravitational properties. That is, this phenomenon is universal. Applications and realizations of this idea are discussed in the part II of our article.

Peyman Parsa

The physical origin of the de Broglie wavelength remains one of the central interpretive questions in quantum mechanics. This work is developed within the Zero-field framework, a phenomenological model in which space is treated as a continuous medium containing localized regions of inward energy flow toward particle-centered Zero-fields. Within this framework, moving particles generate rotation-induced guiding structures referred to as Frontal Waves. These waves are proposed to accompany particle motion and provide a geometric interpretation of the de Broglie wavelength and wave–particle duality. The proposed Frontal Wave wavelength reproduces the standard de Broglie relation and is interpreted as the physical guiding structure associated with matter-wave behavior. The framework is applied to the Double Slit Experiment and the Mach–Zehnder interferometer, where Frontal Waves propagate through multiple paths and form interference structures that guide particle trajectories toward regions of constructive interference. Connections with Bohmian mechanics are discussed, emphasizing that the model serves as a phenomenological interpretation rather than a modification of the mathematical formalism of quantum mechanics. The Frontal Wave concept provides a geometric picture of matter-wave behavior and offers a unified interpretation of particle guidance, interference phenomena, and the de Broglie wavelength within the broader Zero-field framework.