The standard single-slit diffraction formula Δy ≈ λL/a contains three variables: de Broglie wavelength λ, screen distance L, and slit width a. Slit-material mass density ρ does not appear. As a result, density has never been systematically varied as an independent experimental parameter in matter-wave interferometry — not because it was tested and found irrelevant, but because the standard formalism provided no reason to test it. This paper identifies slit-material density as an untested variable and addresses three questions: (1) Why has this variable remained untested for a hundred years despite requiring no new apparatus? (2) Why do two systems — electrons and fullerenes C₆₀ — spanning six orders of magnitude in mass constitute a sufficient experimental programme? (3) What do the two possible outcomes — density dependence observed, or not observed — establish for physics? The paper demonstrates that the experimental absence reflects a structural feature of the standard formalism rather than a technical limitation, that the electron–fullerene pair provides the strongest available two-point inductive test because the systems are maximally independent, and that either outcome produces a definitive scientific conclusion.
The standard single-slit diffraction formula Δy ≈ λL/a contains three variables: de Broglie wavelength λ, screen distance L, and slit width a. Slit-material mass density ρ does not appear. As a result, density has never been systematically varied as an independent experimental parameter in matter-wave interferometry — not because it was tested and found irrelevant, but because the standard formalism provided no reason to test it. This paper identifies slit-material density as an untested variable and addresses three questions: (1) Why has this variable remained untested for a hundred years despite requiring no new apparatus? (2) Why do two systems — electrons and fullerenes C₆₀ — spanning six orders of magnitude in mass constitute a sufficient experimental programme? (3) What do the two possible outcomes — density dependence observed, or not observed — establish for physics? The paper demonstrates that the experimental absence reflects a structural feature of the standard formalism rather than a technical limitation, that the electron–fullerene pair provides the strongest available two-point inductive test because the systems are maximally independent, and that either outcome produces a definitive scientific conclusion.
This volume presents three companion papers forming a unified theoretical and experimental programme for a wave-mechanical account of gravitational motion. Paper 29 develops the theoretical framework in which gravitational motion emerges from constructive-interference maximum migration of de Broglie matter waves in a density-dependent refractive-index field. The gravitational field is expressed as an effective refractive-index field n(r) derived from the Schwarzschild metric. Feynman’s path-integral formalism establishes that all non-stationary paths are eliminated by oscillatory phase cancellation, and that the surviving constructive-interference maximum shifts toward regions of higher mass density. The argument proceeds through four interconnected stages — the gravitational refractive-index field, asymmetric phase accumulation, probability-density redistribution, and physical-motion identification — completed by two theorems and one derived result. The framework recovers GR geodesics in the geometric-optics limit, requires no hidden variables, and generates five classes of experimentally discriminating predictions. Paper 77 identifies slit-material mass density as an untested variable in matter-wave interferometry. The standard single-slit formula Δy ≈ λL/a contains no density term; as a result, density has never been systematically varied as an independent parameter in a century of matter-wave experiments. This paper explains the historical absence through the structural logic of theory-determined observation and the Copenhagen prohibition on mechanism questions, establishes that electrons and fullerene C₆₀ constitute a sufficient two-point experimental programme spanning six orders of magnitude in mass, specifies a three-layer control protocol to exclude slit-width artefacts, and analyses what each possible outcome establishes for the completeness of the standard formalism. Paper 78 develops a three-dimensional experimental matrix introducing slit thickness as a third independently variable parameter alongside particle species and slit-material density. The 5×5×3 design of 75 independent measurements has a random-coincidence probability of approximately 1/1,728,000. The paper derives the quantitative scaling prediction for the thickness dimension (Δx ∝ d, ratio 1:3:6 across three thickness levels), specifies a three-layer thickness control protocol, and analyses the inferential structure of partial as well as full confirmation. The experiment begins with a single laboratory session: electron diffraction through five FIB-fabricated slits of ranked density at 50 nm thickness.
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.
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.
De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.
The 1999 experiment reported by Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller, Gerbrand van der Zouw, and Anton Zeilinger in Nature demonstrated de Broglie matter-wave interference for C60 fullerene molecules, extending experimen- tally observable quantum coherence to an object of unprecedented mass and internal complexity at the time (Arndt et al. 1999). This article develops a complete critical– propositional analysis of that experiment in systematic dialogue with the Theory of Objectivity (TO), as developed by Vidamor Cabannas and Denivaldo Silva. The analysis distinguishes three epistemological levels that must not be conflated: the experimentally established phenomenon of molecular interference; the physical interpretation supplied by quantum mechanics and decoherence theory; and the modal- ontological claims of the TO. This distinction is essential because empirical compatibility with a modal ontology is not equivalent to demonstration of modal necessity. The C60 experiment is especially relevant to the TO in four domains. First, a complex composed object behaves as a coherent quantum unit at the level of its center- of-mass propagation, providing a meaningful point of dialogue with the compositional structure associated with Absolute Truth 6 (VA6). Second, the diffraction grating is not merely a passive geometrical boundary: molecule–surface interactions modify the effective slit width, generating an empirically measurable interface between geometry and dynamics and providing a strong operational bridge to Absolute Truth 4 (VA4). Third, the preservation or destruction of interference depends on correlations between the molecule and its environment, thereby connecting physical distinguishability, infor- mation, and radiation. This creates the most significant point of contact with Absolute Truth 7 (VA7), under which the TO identifies its transcendent element with knowledge or information produced in atomic relations and regards such information as equivalent to atomic radiation. Fourth, the experiment offers possible operational analogues for the TO’s Inducing Effects, although these analogues must not be treated as established identities without independent derivation. The article also examines possible relations to VA1–VA7, the TO phenomenic elements, the Cosmogonic Theorem, and the cosmological Eras. It argues that the C60 experiment provides selective and indirect empirical corroboration for operational projections compatible with VA4, VA6, and VA7, but does not constitute confirmation of the TO as a complete ontology. Later experiments on thermal decoherence strengthen the radiation–information bridge by showing that photon emission can reduce molecular interference when it becomes capable of encoding spatial information (Hackermüller et al. 2004). In dialogue with Heisenberg, Einstein, Bohm, Joos and Zeh, Zurek, Aspect, Planck, LIGO/Virgo, JWST observations, and Petina’s taxonomy of fundamental laws, the paper proposes a research program capable of converting qualitative TO correspondences into quantitative and potentially discriminatory predictions. The central methodological conclusion is that the scientific strength of the TO will not depend on retrospectively redescribing established quantum phenomena in its own vocabulary, but on deriving from its modal architecture measurable relations that either reproduce quantum theory from more fundamental principles or predict deviations in controlled regimes. Keywords: Theory of Objectivity; C60; fullerene; matter waves; wave–particle duality; quantum interference; decoherence; information; boundaries; radiation; modal ontology; empirical corroboration.
This paper proposes that gravity arises from the constructive interference of de Broglie matter waves in a density-dependent refractive medium. The argument proceeds in five steps: (1) greater mass implies greater density; (2) by Snell's law, greater density implies a higher refractive index; (3) a higher refractive index implies a shorter wavelength; (4) when matter waves propagate outward from an object in all directions, the wavelength is shorter on the side facing the larger mass; (5) constructive interference is stronger and more densely packed where the wavelength is shorter, so the object is preferentially redistributed toward the side of greater mass. This shows gravity to be a wave-mechanical phenomenon: matter is not pulled toward mass by some force; it is redistributed toward mass through the constructive interference of its own matter wave. Newton and Einstein described the trajectory and the geometric structure of gravitational motion; this paper proposes the physical mechanism by which that motion occurs. This paper makes three propositions explicit, with carefully distinguished epistemic status: (A) the mass distribution determines the effective refractive medium through which matter waves propagate — an experimentally established fact, confirmed independently by the COW experiment (1975) and by semiconductor heterojunction experiments confirming Snell's law for matter waves at density boundaries; (B) the displacement of the constructed-interference maximum is the physical mechanism of actual gravitational motion — the paper's sole new physical identification, going beyond Born's rule as standardly stated; it is consistent with but not compelled by the COW data, and constitutes the primary target of experimental falsification (Section 6.6d); (C) the COW fringe shift is a direct measurement of the gravitational mechanism — a logical corollary that follows necessarily from (A) and (B), not an independent assumption. Section 6.6d translates these propositions into five differentiating experimental predictions, ordered by experimental accessibility, including an immediately executable reanalysis of existing COW data and a novel slit-material density experiment that provides a clean differential test between the present framework and standard wave optics.