De Broglie Matter Wave Research Articles

Quantization Essence

Ideal Resonance does not fade, and thus, it is, as it were, out of time. So the corresponding Planck QUANTUM, which determines the STATIONARY Allowed States of Energy, is simply a reflection of the Ideal Resonance. which "Quantum Mechanics" used on the example of the Mechanical Harmonic Oscillator. And the fundamental difference of QUANTUMS is only that for frequencies not equal to zero and their minimum energy of the Resonance-Quantum has a finite, non-zero initial value, which also determines the minimum distance between the allowed energy levels. At the same time, the internal structure of the QUANTUM can be not only electromagnetic, like Planck's, and not only acoustic, like Einstein's, but also be determined by the so-called de Broglie matter waves. But, in order to remove any mysticism from QUANTUMS, one must UNDERSTAND that the DUALISM introduced by them is determined by Pontryagin's functional connection of the ELEMENTARY PARTICLE and the Packet of Waves that form it.

Rotational wave velocity of protons

The angular momentum of particles is the result of rotational waves, which are believed not to rotate in a classical sense. Therefore, the rotational wave properties of protons or nucleons, which should be comparable to De Broglie matter waves, have never been attributed to a wavelength, frequency or energy, but solely to their spin, which is a quantized property and probably does not reflect the true angular momentum as the product of radius and rotational impulse of a particle. Using data that originates from the hadron accelerator CERN in Switzerland, the true, not quantized velocity of the rotational wave of protons could be, however, measured. Thereby, its frequency is 2072.18 Hz, hence, it is unexpectedly low. The spike in the polarizability curve of protons at Q^2 = 0.33 GeV^2, published currently in the journal Nature, together with the rotational wave frequency obtained from CERN data, provides reliable evidence that this might be an interference in terms of superposition of the particle wave of the scattered electrons with the rotational wave of the protons at the same energy level, doubling the expected curve value, which, since there are no other possible explanations, proves the determined rotating wave velocity of protons.

The uncertainty property of electromagnetic field in optical thin microcavity

The uncertainty property of electromagnetic field in thin microcavity is exactly derived in this paper. The intensity of the electromagnetic field at the center of thin microcavity is indeterminate while other positions intensity are determinate. The product of the deviation of momentum and the deviation of position at the center of thin microcavity is larger than a certain constant. By introducing the energy quantization condition (E=Nħω), we verify this constant has the same physical dimension as Planck’s constantħ and the value is an integral multiple of Planck’s constant, the integer is the smallest volume element at the center of thin microcavity. Furthermore, the perimeter of the smallest volume element is an integer multiple of the wavelength of the incident electromagnetic wave, which satisfies the assumption of DE Broglie matter wave. Our results are the first to find that the uncertainty property of electromagnetic field in thin microcavity and further derived the quantum uncertainty principle through the quantization of energy.

Piercing the veil of modern physics: part 1 & basics

This article is part 1 in the Piercing the Veil of Modern Physics, which is to lay the foundation for the full text. First, it should be clearly pointed out that a particle moving at the value c of the light speed in vacuum, its static mass can only be equal to 0, but doesn't exist in reality. Therefore, it is vital that how can we correctly make a distinction between the speed of light in vacuum and that in reality. Then, by the aid of the law of conservation of mass-energy, we know that the energy convergence phenomena of high-speed electrons are the result of the binding energy inside them to be lost gradually in the form of electromagnetic radiation. So, according to the related electromagnetic theories and the kinetics formulas of the special relativity theory, the study concluded that the charge of a moving electron will follow along with its static mass to be lost synchronously, and its charge-mass ratio whose value remains unchanged. Since an electron can be further broken down, then there should be a kind of more fundamental particles, the electro-ultimate particles, which can compose electrons and whose charge-mass ratio should be equal to the electronic physical constant. Besides, if nature's background (ether) is also composed of the electro-ultimate particles, Maxwell's electromagnetic theory should be true. A corollary is that all photons radiating from the electrons in a storage ring are composed of the electro-ultimate particles. Then, combining with de Broglie's matter wave formula, it is pointed out that the energy convergence phenomena of high-speed particles are the primary factor causing the spectrum redshift. And through this formula, the average force suffered by a high-speed particle moving along the direction of its wavelength can be obtained. Thus, according to Newton's third law to make a judgment, the ether must exist. Finally, point out the essence of so-called wave-particle duality: No matter where, as long as there is energy, there must be mass. And vice versa. The two as a unity of opposites present in front of us in the form of wave. They must exist at the same time, carry each other, be short of one cannot. In reality, both values can be close to zero, but never equal to zero.

Quantum Curvature: Toward the Unity of Relativity and Quantum Mechanics

Quantum curvature interpretation has greatly promoted the unification of relativity and quantum mechanics in physics thought level. In this paper, we discuss the deep unification of relativity and quantum mechanics according to new research by some scholars. This paper involves the derivition of quantum hypothesis from the relativistic transformation, the relation between Compton's matter wave and De Broglie's matter wave, and the quantum divition mechanism of inertial systems in the superposition principle of quantum states.

Atom sieve for nanometer resolution neutral helium microscopy

Neutral helium microscopy is a new tool for imaging fragile and/or insulating structures as well as structures with large aspect ratios. In one configuration of the microscope, neutral helium atoms are focused as de Broglie matter waves using a Fresnel zone plate. The ultimate resolution is determined by the width of the outermost zone. Due to the low-energy beam (typically less than 0.1 eV), the neutral helium atoms do not penetrate solid materials and the Fresnel zone plate therefore has to be a free-standing structure. This creates particular fabrication challenges. The so-called Fresnel photon sieve structure is especially attractive in this context, as it consists merely of holes. Holes are easier to fabricate than the free-standing rings required in a standard Fresnel zone plate for helium microscopy, and the diameter of the outermost holes can be larger than the width of the zone that they cover. Recently, a photon sieve structure was used for the first time, as an atom sieve, to focus a beam of helium atoms down to a few micrometers. The holes were randomly distributed along the Fresnel zones to suppress higher order foci and side lobes. Here, the authors present a new atom sieve design with holes distributed along the Fresnel zones with a fixed gap. This design gives higher transmission and higher intensity in the first order focus. The authors present an alternative electron beam lithography fabrication procedure that can be used for making high transmission atom sieves with a very high resolution, potentially smaller than 10 nm. The atom sieves were patterned on a 35 nm or a 50 nm thick silicon nitride membrane. The smallest hole is 35 nm, and the largest hole is 376 nm. In a separate experiment, patterning micrometer-scale areas with hole sizes down to 15 nm is demonstrated. The smallest gap between neighboring holes in the atom sieves is 40 nm. They have 47011 holes each and are 23.58 μm in diameter. The opening ratio is 22.60%, and the Fresnel zone coverage of the innermost zones is as high as 0.68. This high-density pattern comes with certain fabrication challenges, which the authors discuss.

The electron spin and spin magnetic moment in dual-4 d space-time Quantum mechanics

In dual-four-dimensional space-time quantum mechanics, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c，and frequency is ν0=E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1=ħ/mc，and frequency is ν1=E1/h. m0 and m is the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.

The Schrödinger Equation, the Zero-Point Electromagnetic Radiation, and the Photoelectric Effect

A Schrodinger type equation for a mathematical probability amplitude Ψ(x,t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V(x). The particle phase space probability density is denoted Q(x,p,t), and the entire system is immersed in the “vacuum” zero-point electromagnetic radiation. We show, in the first part of the paper, that the generalized Liouville equation is reduced to a simpler Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. This leads us to a simpler Liouville equation that will facilitate the calculations in the second part of the paper. Within this second part, we address ourselves to the following task: Since the Schrodinger equation depends on $\hbar $ , and the zero-point electromagnetic spectral distribution, given by $\rho _{0}{(\omega )} = \hbar \omega ^{3}/2 \pi ^{2} c^{3}$ , also depends on $\hbar $ , it is interesting to verify the possible dynamical connection between ρ 0(ω) and the Schrodinger equation. We shall prove that the Planck’s constant, present in the momentum operator of the Schrodinger equation, is deeply related with the ubiquitous zero-point electromagnetic radiation with spectral distribution ρ 0(ω). For simplicity, we do not use the hypothesis of the existence of the L. de Broglie matter-waves. The implications of our study for the standard interpretation of the photoelectric effect are discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunneling phenomenon and the Compton’s effect.

双4维时空量子力学描述中电子自旋、自旋磁矩

双4维时空量子力学描述中，微观客体的自旋是场物质球自身的转动。在自身参考系，场物质球的半径由静态康普顿动量m0c定义：R0=ħ/m0c，转动频率为：E0= hν0；在运动参考系，场物质球的半径由动态康普顿动量mc定义：R1= ħ/mc，转动频率为：E1= hν1。m，m0是微观客体的动、静质量。电子自旋S及自旋磁矩μs都可以通过场物质球模型来计算。若自身参考系就在复数空间，在闵氏4维时空观察转动场物质球的运动，生成双4维复数时空，形成场物质的波动运动，它就是德布罗意物质波。 In dual-four-dimensional quantum mechanism, the spin of micro object is caused by the rotation of field matter sphere itself. In its own frame of reference, the radius is defined as the static Compton momentum R0=ħ/m0c, and frequency is ν0= E0/h. In the Dynamic frame of reference, the radius is defined as the dynamic Compton momentum R1= ħ/mc, and frequency is ν1= E1/h. m0 and m are the static and dynamic mass of a micro matter sphere, respectively. The electron spin s and spin magnetic moment μs both can be calculated by the field matter sphere model. If the frame of reference is in the complex space-time, and we observe the motion in a Minkowshi Space, then there will be a dual four-dimensional complex space-time. The fluctuation motion of field matter is De Broglie matter wave.

Once again about Einstein’s realism: the matter waves and Bell’s inequalities from the point of view of the special theory of relativity

We explore the possibility to give a classical explanation to the specifics and physical sense of de Broglie matter waves when studying the microparticle as an object of non zero size, from the point of view of the special theory of relativity. We show that the particularities of de Broglie matter waves and the results of the experimental verifications of Bell inequalities for the pairs of entangled photons are naturally interpreted as the results of implementation of the conclusions of the special theory of relativity to the microparticles. We conclude that it is appropriate to go back to the search of the new means of realistic description of the nature proposed by Einstein and his realistic worldview that states that the world studied by the science is real and every part of it at any moment of time has objective physical characteristics.

Focusing of a neutral helium beam with a photon-sieve structure

The manipulation of low-energy beams of neutral atoms and molecules via their de Broglie wavelength is a branch of atom optics often referred to as de Broglie matter wave optics. The application areas include fundamental quantum mechanics, atom interferometry, and the development of new microscopy instrumentation. The focusing of de Broglie matter waves with a Fresnel zone plate was used to demonstrate the first neutral helium microscopy imaging. The ultimate resolution of such a microscope is limited by the width of the outermost zone. Because a Fresnel zone plate for atoms cannot be fabricated on a substrate (the low-energy atom beams would not be able to penetrate the substrate material), this gives a fabrication determined limit for the first-order focus of around 30--50 nm. Therefore, it is important to search for alternative optical elements that enable higher resolution. Photon sieves consist of a large number of pinholes, arranged suitably relative to the Fresnel zones. The great advantages are that the width of the pinholes can be larger than the respective Fresnel zones and a free-standing pinhole is much easier to fabricate than a free-standing zone. Thus, with a photon-sieve structure applied for de Broglie matter wave manipulation, the fabrication limit for focusing is reduced to potentially around 3--5 nm. Here we present a realization of such an ``atom sieve,'' which we fabricated out of a silicon nitride (SiN) membrane, using electron-beam lithography and reactive ion etching. Our atom sieve is 178 $\ensuremath{\mu}\mathrm{m}$ in diameter and has 31 991 holes. The diameter of the holes varies from 1840 to 150 nm. Using a beam of neutral, ground-state helium atoms with an average wavelength of 0.055 nm, we demonstrate helium atom focusing down to a spot size of less than 4 $\ensuremath{\mu}\mathrm{m}$. The focus size is limited by the intrinsic velocity spread of the helium beam.

Biasing a coin after the toss: asymmetric delayed choice quantum eraser via Bragg regime cavity QED

Quantum eraser (QE), on the one hand, is treated as the most intriguing phenomenon that puts a conception of the time in classical and quantum physics in contrast whereas, on the other hand, the same phenomenon is considered fallacious and based on the wrong arguments. Here, we propose an asymmetric delayed choice QE based on a Mach–Zandher–Bragg (MZB) atom interferometer that marks the intriguing effects more explicitly through delayed choice, tunable manipulation of the de Broglie matter wave interference. We also plot distinguishability D and fringe visibility V as a function of the atom–field interaction time utilized for the delayed choice eraser to highlight the counter-intuitive nature of the phenomenon. The interferometric scheme is based on Bragg diffraction of neutral two-level atoms through cavity fields. It is shown that the proposal is deterministic in nature and can be demonstrated experimentally with overall good fidelity utilizing the available technical resources.

The Beynon Gabor zone plate: a new tool for de Broglie matter waves and hard X-rays? An off axis and focus intensity investigation

Optical elements based on Fresnel zones are used in a range of applications, from X-ray telescopy to microscopy and recently also in the manipulation of de Broglie matter waves. In 1992 Beynon and co-workers presented a binary Gabor type zone plate (henceforth referred to as the Beynon Gabor zone plate). Because this zone plate has no higher order foci, it is in principle a very attractive candidate for focusing of de Broglie matter waves and in some cases X-rays. So far the Beynon Gabor zone plate investigations presented in the literature have concentrated on the intensity distribution along the optical axis and in the focal plane. Here we present a detailed numerical investigation of the Beynon Gabor zone plate, including an investigation of the off-optical axis, off focal plane intensity distribution for point source illumination. We show that at integer fractions of the focal length, the beam becomes nearly toroidal (doughnut-shaped). This offers potentially interesting new possibilities for de Broglie matter wave and X-ray optics, for example in STED-like applications. We further show that the increased intensity at the focal point predicted in the literature for a particular Beynon Gabor zone plate transmission function configuration is an artifact due to the lack of sampling nodes. We support our calculations with experimental measurements in the visible light range, using a Beynon Gabor zone plate fabricated with electron beam lithography.

De Broglie-wave lens

A simple focusing device is proposed for de Broglie matter waves—a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two coaxial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone, which creates a very intense, spatially localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are as follows. The spot diameter is ~0.1 µm, the ratio of focal and incident intensities is ~15, the focal length of the diffractive lens is in the range ~0.13 to 6 cm, the focusing depth is in the range ~15 to 30 cm, and the energy transmitting efficiency is ~30 %. For the relatively large diameters of the pinholes, 5.0 µm, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.

Diffractive multifocal focusing of de Broglie matter waves

Diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel zone). The focusing, defocusing and refocusing phenomenon results from periodic phase changes at singular points, which are observed for the even Fresnel numbers, where the intensity is zero and the phase is undefined. As an on-axis observation point passes through a singular point, the nature of the wave in the neighborhood of the axis changes from that of a diverging wave to that of a converging wave, i.e., the wave refocuses. The amplitudes of the oscillations in the intensity and phase of the de Broglie wave depend on the ratio of the radii of the two apertures in the system. This effect of diffractive multifocal focusing of de Broglie waves can be used for designing a diffractive lens for matter-wave beams.

Some Comments on the Matter Wave-light Wave Hypothesis

From the de Broglie matter wave hypothesis and Planck’s energy quantization law, and assuming conservation of energy in the absorption of a photon and its consequent conversion to kinetic energy of motion by a material particle initially at rest, one can deduce a simple mathematical relationship between the wavelength λ (or frequency ν), of the photon absorbed by the particle at rest, and the resulting de Broglie matter wave length, λD, of the particle with kinetic energy of motion of mv2/2. The relationship so deduced, λD∝√λ, suggests that visible wavelengths of light, from about 4000 A, in the violet, to beyond about 7000 A, in the red, on absorption by an electron at rest, lead to material electron wavelengths, λD, of the order of the size of the electron transfer proteins seen in the photosynthetic reaction centers of photosynthesizing organisms, at about a size of 50–100 A. In addition to understanding the mechanism of photosynthesis as a material wave mediated phenomenon, further areas of importance of the relations pointed out in this paper are in the design of experiments to gain a deeper understanding of the basic tenets of wave mechanics, and in the use of tunable lasers to probe various properties of material waves, and to precisely control their properties for applications including lithography.

De Broglie Matter Waves from the Linearized Einstein Field Equations

We suggest a connection between matter waves and gravitational waves. We find solutions of the linearized Einstein field equations in the form of de Broglie waves. These therefore acquire a new geometrical meaning.

The mechanical and the wave-theoretical aspects of momentum considering discrete action

The mechanical aspect of momentum, basically its role as a tangent vector of the trajectory of the particle, is related to properties of the momentum found in the contexts of Hamilton's optico-mechanical analogy, de Broglie's matter waves, and quantum mechanics. These properties are treated in a systematic way by considering an approximation of the particle mechanical action of the particle by a step function. A special method of discretizing partial differential equations is shown to be required. Using this method, a discrete dynamics is developed. It is shown that particle dynamics can be regarded as the limit case of the discrete dynamics as the step functions tend to the continuous ones. The equation of motion of a free particle in an arbitrary reference system is deduced in two ways: (i) in continuous dynamics by making use of the invariance of action within changes of reference systems, and (ii) by taking the mentioned limit in discrete dynamics of an equation which expresses that the mechanical and wave-theoretical aspects of the momentum are interrelated in specific way.