It is shown that the experiments on interference and diffraction of single particles allow to set indirectly the phase velocity of de Broglie waves. The author considers the possible start and end times of the interference pattern during the passage of a single particle through one of the slits of a device for observing the particle interference. It is found that if the phase velocity is less than the velocity of the particle, the particle will come to the detector before the interference occurs, so its location is not subject to the distribution of the probability density which will be available later. At the same time, if the phase velocity is greater than the velocity of the particle, the particle will come to the detector when the interference pattern is over, so the location of the particle will not obey the distribution of the probability density which no longer exists. As a result, it is found that the phase velocity of de Broglie waves is equal to the speed of the particle.
It is shown that the experiments on interference and diffraction of single particles allow to set indirectly the phase velocity of de Broglie waves. The author considers the possible start and end times of the interference pattern during the passage of a single particle through one of the slits of a device for observing the particle interference. It is found that if the phase velocity is less than the velocity of the particle, the particle will come to the detector before the interference occurs, so its location is not subject to the distribution of the probability density which will be available later. At the same time, if the phase velocity is greater than the velocity of the particle, the particle will come to the detector when the interference pattern is over, so the location of the particle will not obey the distribution of the probability density which no longer exists. As a result, it is found that the phase velocity of de Broglie waves is equal to the speed of the particle.
In a recent paper, titled “Explanation for the observed wave-particle-duality of Light” (Tank, H.K. http://vixra.org/abs/1402.0153, 2014) it was explained that: “Since at very high frequencies, narrowband filtering and generation of purely monochromatic light of one Hertz bandwidth is not yet technically possible, there has been quite a wide bandwidth of waves involved, in the double slit experiments and photoelectric experiments performed so far. And since this wide ‘band’ of waves coherently add only at discrete points in space and time, we get ‘particles’ at the detectors.” Now, to further confirm the validity of this explanation, a new kind of experiment is proposed here, in which protons and electrons are accelerated at appropriate velocities vp ve , such that their de Broglie wavelengths are equal; i.e. ( h / mp vp )= ( h / me ve ) and let them pass through closely spaced slits so that they can interfere with each other. Similarly, in another experiment, their wave-functions: A exp i ( kp X - ωp t ) = A exp i ( ke X - ωe t ) , and let them pass through closely spaced slits, and see how the two matter-waves interfere.
Abstract In 1925, de Broglie hypothesized that any material particle has an associated wave with /h p . Electron diffraction seems to support that Hypothesis. But then, the electron at rest will have infinite wavelength, and infinite wave phase velocity. This says that for a material particle, the de Broglie relation does not hold. Failed attempts to save the postulate, kept the flawed relation, and modified the waves into train waves, pilot waves, probability waves, … to name a few. We keep the de Broglie waves unchanged, and modify the relation. First, we observe that the Planck energy E h used by de Broglie defines virtual electromagnetic waves. Consequently, for any particle, the virtual electromagnetic wavelength is / /c h mc , and / /h m c . Refinement of de Broglie argument, indicates that /h mmay be x , Heisenberg’s uncertainty in the particle location. de Broglie’s later analysis supports this interpretation, and we offer an explanation to particle diffraction as a consequence of Heisenberg’s uncertainty. We apply / /h m c to obtain the dispersion relations for the de Broglie virtual waves.
The de Broglie wavelength λ= h/mv of simple particles (photon, electron, neutron) atoms (helium, neon) and molecules (fullerene, fluorous porphyrin) deduced from the de Broglie (dB) relation and those measured by double slits interferometry are compared.The de Broglie relation is verified in very large domains of velocity v and mass m of the particles, respectively 8 and 13 orders of magnitude.In this paper one analyses the interference spectra of photons and electrons and give the Intensity Relations IR(II-DI) between the interference intensity (II) by two slits and the diffracted intensity (DI) by one slit.The double slits interference in the de Broglie-Bohm interpretation is an interference of particle and pilot waves, internal and external waves each passing by a different slit.The velocities of these waves are discussed.From the universal de Broglie relation and the relation vp = vw between the particle and pilot waves one shows that only in the domain of the maximum of the light spectrum (λm~ 550 µm) the dB relation leads to the Plank-Einstein (PE) relation hν=mc 2 .A measure of the mass of the photon m* = 4 10 -36 Kg is deduced.The de Broglie relation for different wave lengths shows that the PE relation must be modified, the velocity of light is not constant as shown by various experiments: Global Positioning Systems GPS, red shift in astronomy etc.This has been discussed by Marmet in years 2000.The same conclusion was given by Sato in 2010 for electromagnetic waves.The trajectories of electrons observed by Jönsson by double slits interferometry and then calculated by Gondran according to the de Broglie-Bohm interpretation are then analyzed in detail.The correlations observed between the properties of these trajectories at short and long distances from the slits permit to give the general equation of the trajectories.The origin of these properties is discussed in the framework model of De Broglie and Bohm, assuming that at any point the intensity of the two waves (particle and pilot wave) passing by the 2 slits are deceasing functions of the distance to the slits.The changes of direction of the trajectories are explained.
Within the framework of the ‘Pairwise Interference Model’ of light–matter interaction, it is postulated that light particles follow definite trajectories, and thus, for example, in the double-slit experiment, a particle can pass through only one of the two slits. On this premise, the interference of two photons is examined in greater detail. It is hypothesized that the interference of a photon pair requires the involvement of matter and, initially, that both molecular excitations and photons oscillate at the same frequency and that the continuity of the oscillation is not disrupted by absorption and emission. The molecular excitations in the light source are supposed to oscillate synchronously. Both photons arrive at the same point on the detector but may travel along different paths and therefore arrive at different times. Under these conditions, their phase difference, φ(2) – φ(1), is always zero. Consequently, no interference pattern can form on the detector screen and therefore the assumptions made are incorrect. Alternatively, one may assume that only the photon oscillates, whereas the excitation stores the phase, φ, possessed by the photon at the instant of absorption. In this case, φ(2) – φ(1) corresponds to the difference in travel times modulo the oscillation period, and an interference pattern can form. However, this assumption is problematic for some reasons: the nature of the matter-based memory remains unclear; according to the special theory of relativity, no time elapses for a particle travelling at the speed of light, meaning that it cannot oscillate; and the assumption contradicts Bohr’s correspondence principle. In a classical wave, the phase information propagates away from the source at the wave velocity without changing. This leads to the alternative possibility that the excitations oscillate, whereas the photons do not. Instead, the photons transport information about the phase of the excitation at the instant of emission. As can be shown, in this case, φ(2) – φ(1) likewise corresponds to the difference in travel times modulo the oscillation period. However, this hypothesis contradicts the de Broglie postulate, according to which all particles exhibit wave properties, and the relation ε = hν must therefore be interpreted differently. It also raises the question of how the dimensions of a laser, specifically the mirror separation, can influence the wavelength of the amplified light if a photon has no wavelength. Using replicator dynamics and the ‘Pairwise Interference Model’ of light–matter interaction, a simulation demonstrates that, in a simplified laser model, assuming that photons do not oscillate whereas excitations do, self-organisation gives rise to a phase pattern in the sequence of photons within the emitted light beam that corresponds to the pattern obtained by discretising a classical wave. Thus, coherent light can exhibit wave properties even if photons themselves do not. Finally, the possibility of how incoherent light acquires wave properties is briefly discussed.
This paper develops a phase-first reconstruction of quantum interference within standard quantum mechanics and wave optics. Its central idea is that interference patterns become conceptually clearer when the complex phase is treated as the organizing structure and probability or intensity density is treated as the visible statistical expression of that structure. The guiding principle is: the phase structures the pattern; the density renders it visible. The paper shows how this principle applies to single-slit diffraction, double-slit interference, Airy patterns, Fourier optics, Fresnel propagation, probability current, the Madelung representation, which-way marking, reduced coherence, and quantum eraser experiments. In each case, the observed density pattern is interpreted as the visible result of coherent phase relations among amplitudes. The reconstruction is strictly conservative. It does not modify quantum mechanics, the Born rule, unitary dynamics, or standard wave optics. It introduces no new postulates and makes no new empirical prediction. Its purpose is conceptual and pedagogical: to clarify the architecture of quantum interference by placing relative phase at the center of the analysis. This work is Part I of the series The Geometry of Phase. It establishes the phase-geometric foundation for later parts of the series, where the same perspective is extended to de Broglie matter waves, proper-time phase, relativistic action, and possible curvature-coupled phase extensions.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.