Particle Duality Research Articles

Role of Fourier transform in quantum mechanics: applications and implications

The Fourier transform, as a fundamental mathematical tool, plays a pivotal role in quantum mechanics. Its significance extends to wave function analysis, solving the Schrdinger equation, and elucidating the relationship between position and momentum. In this review article, the primary objective is to summarize the diverse applications of the Fourier transform in quantum mechanics. This paper will delve into key applications, highlighting the uncertainty principle, the Planck-Einstein relation, and the Fourier transform solution of the Schrdinger equation. These theorems and relationships not only facilitate the mathematical manipulation of quantum states but also lay the theoretical foundation of quantum mechanics. By exploring these critical aspects, the author aims to provide a comprehensive understanding of how the Fourier transform underpins the core principles of quantum theory, offering valuable insights into the wave particle duality and the probabilistic nature of quantum systems. This discussion will emphasize the essential nature of the Fourier transform in both theoretical development and practical problem-solving within quantum mechanics

A hydrodynamic approach to reproduce multiple spinning vortices in horizontally rotating three-dimensional liquid helium-4

This paper reports a three-dimensional (3D) simulation of a rotating liquid helium-4, using a two-fluid model with spin-angular momentum conservation. Our model was derived from the particle approximation of an inviscid fluid with residual viscosity. Despite the fully classical mechanical picture, the resulting system equations were consistent with those of the conventional two-fluid model. We consider bulk liquid helium-4 to be an inviscid fluid, assuming that the viscous fluid component remains at finite temperatures. As the temperature decreased, the amount of the viscous fluid component decreased, ultimately becoming a fully inviscid fluid at absolute zero. Weak compressibility is assumed to express the volume change because some helium atoms do not render fluid owing to Bose–Einstein condensations or change states because of local thermal excitation. One can solve the governing equations for an incompressible fluid using explicit smoothed-particle hydrodynamics, simultaneously reproducing density fluctuations and describing the fluid in a many-particle system. We assume the following fluid–particle duality: a hydrodynamic interfacial tension between the inviscid and viscous components or a local interaction force between two types of fluid particles. The former can be induced in the horizontal direction when non-negligible non-uniformity of the particles occurs during forced two-dimensional rotation, and the latter is non-negligible when the former is negligible. We performed a large-scale simulation of 3D liquid helium forced to rotate horizontally using 32 graphics processing units. Compared with the low-resolution calculation using 2.4 × 106 particles, the high-resolution calculation using 19.6 × 106 particles showed spinning vortices close to those of the theoretical solution. We obtained a promising venue to establish a practical simulation method for bulk liquid helium-4.

A revised double-slit experiment to explore the mechanism of photon wavefunction collapse by numerical design

The double-slit experiment has long been pivotal in understanding matter’s wave–particle duality. A central question revolves around Born’s interpretation of wavefunction whether a single photon demonstrates a 50% probability of passing through each slit individually as particles or simultaneously traverses both as waves. Experimentally, once the photon’s path is detected, the observer effect causes its wavefunction to collapse, rendering the results inconclusive. Designing an experiment to minimize instrumental involvement during the wavefunction collapse of photons, while aiming to gain insight into its collapse mechanism, becomes necessary. We propose a revised experiment that replaces the traditional setup with two Au nanoparticles acting as observers, triggering photon collapse before spectrum collection. In single-photon scenarios, we consider two assumptions: first, the photon wavefunctions collapse into a particle and transfer energy to one of the nanoparticles exclusively, and second, the photon acts as a wave, splitting and transferring its energy to two nanoparticles simultaneously, which does not align well with Born’s interpretation of wavefunction as spatial probabilities. These two assumptions would generate distinctly different spectra. Conversely, in high-intensity experiments, both nanoparticles collectively undergo excitation, regardless of the collapse mechanism. A comparative analysis of scattering spectra under the two conditions reveals crucial insights into the genuine nature of photon collapse. We also proposed using two molecules attached to a metal nanoparticle as an alternative design. Whether affirming or refuting the observer effect, this research holds promise for resolving the theoretical debate surrounding the collapse of wavefunctions and advancing quantum computing and communication fields.

Dissipation-Induced Photon Blockade in the Anti-Jaynes–Cummings Model

Due to the fundamental differences between the quantum world and the classical world, some phenomena, such as entanglement and wave–particle duality, only exist in the quantum realm. These peculiar phenomena cannot be demonstrated by classical means: Quantum networks, quantum cryptography, and quantum precision measurements all require quantum sources. Photons are particularly well-suited as quantum sources owing to their minimal interaction with the environment, high flight speed, and ease of interaction with current typical quantum systems. Single-photon sources include pulsed excitation of quantum dots, spontaneous parametric down-conversion, and photon blockade. Herein, we propose that the anti-Jaynes–Cummings model can induce a pronounced photon antibunching effect when subjected to intense cavity dissipation. Similar to the photon blockade caused by strong photon–photon interaction, this antibunching effect is referred to as ’dissipation-induced blockade’. Our findings indicate that the minimum decay rate of a qubit, coupled with a high decay rate for photons, is conducive to achieving strong antibunching within the system. Notably, g(2)(0)<g(2)(τ), a characteristic of photon antibunching, is only valid under the optimal condition Δ=0. Conversely, g(2)(0)<1 is satisfied across all parameters, indicating that g(2)(0)<1 is not a prerequisite for antibunching in the anti-Jaynes–Cummings model. Moreover, under the optimal conditions of the antibunching effect, the average photon number attains its peak value. Consequently, the current anti-Jaynes–Cummings model is promising for developing single-photon sources characterized by excellent purity and average photon number.

Energy-Space-Time Plateau-Rayleigh Instability, Quantum Phenomenon & the Fundamental Interactions

In general, fluids in motion or at rest tend to minimize their surface area due to their surface tension. It is shown that kinetic energy flow through space-time experience the same Plateau-Rayleigh instability observed in fluid dynamics. Energy, space-time act like fluids, and the space-time reaction to the energy action is the equivalent of an interface tension between energy and space-time. Energy cannot continuously flow through space-time due to an energy-space-time Plateau-Rayleigh instability, space-time compression (contraction) on kinetic energy direction of motion induces an energy wave like motion (a space-time compression wave acting as kinetic energy waveguide), the particle or energy packet must follow when moving through space-time, the reason for the observed wave - particle duality. Quantum phenomenon is simply a consequence of the space-time compression on kinetic energy direction of motion. Kinetic energy and space-time are fluids and energy quanta can reach a critical point when energy quanta can change from linear to circular motion and assume a spherically symmetrical shape (the minimum surface area possible to minimize the tension at the space-time energy interface) and so it condensates as mass energy. It is shown that energy quanta to mass transformation occurs via Plateau–Rayleigh energyspace-time instability and it is governed by an energy-space-time Young-Laplace equation. Electric field lines are described as space contraction energy shock waves induced by a dynamic space-time phase transition at maximum kinetic energy space- time interface tension which is the “charge”. Space-time always reacts to the presence of energy and that reaction is the interface tension at the energy-space-time boundary: gravitational & electric energy fields are consequences of energyspace-time interface tension (at either rest or kinetic energy boundary) also governed by an energy-space-time instability Young-Laplace equation. Gravitational constant G and the fine structure constant ∝ are respectively, the energy interface field’s interaction constants. The Strong force is a consequence of a direct contact between the nucleon's energy-space-time interface tension fields and has no interaction constant. The range and variation in the strength of the Strong force is due to Heisenberg’s uncertainty principle

General-relativistic wave–particle duality with torsion

We propose that the four-velocity of a Dirac particle is related to its relativistic wave function by ui=ψˉγiψ/ψˉψ . This relativistic wave–particle duality relation is demonstrated for a free particle related to a plane wave in a flat spacetime. For a curved spacetime with torsion, the momentum four-vector of a spinor is related to a generator of translation, given by a covariant derivative. The spin angular momentum four-tensor of a spinor is related to a generator of rotation in the Lorentz group. We use the covariant conservation laws for the spin and energy–momentum tensors for a spinor field in the presence of the Einstein–Cartan torsion to show that if the wave satisfies the curved Dirac equation, then the four-velocity, four-momentum, and spin satisfy the classical Mathisson–Papapetrou equations of motion. We show that these equations reduce to the geodesic equation. Consequently, the motion of a particle guided by the four-velocity in the pilot-wave quantum mechanics coincides with the geodesic motion determined by spacetime. We also show how the duality and the operator form of the Mathisson–Papapetrou equations arise from the covariant Heisenberg equation of motion in the presence of torsion.

De Broglie, General Covariance and a Geometric Background to Quantum Mechanics

What is striking about de Broglie’s foundational work on wave–particle dualism is the role played by pseudo-Riemannian geometry in his early thinking. While exploring a fully covariant description of the Klein–Gordon equation, he was led to the revolutionary idea that a variable rest mass was essential. DeWitt later explained that in order to obtain a covariant quantum Hamiltonian, one must supplement the classical Hamiltonian with an additional energy ℏ2Q from which the quantum potential emerges, a potential that Berry has recently shown also arises in classical wave optics. In this paper, we show how these ideas emerge from an essentially geometric structure in which the information normally carried by the wave function is contained within the algebraic description of the geometry itself, within an element of a minimal left ideal. We establish the fundamental importance of conformal symmetry, in which rescaling of the rest mass plays a vital role. Thus, we have the basis for a radically new theory of quantum phenomena based on the process of mass-energy flow.

Wave Particle Duality: De Broglie Waves in Indirect Quantum Measurements

Wave Particle Duality: De Broglie Waves in Indirect Quantum Measurements

Whence Nonlocality? Removing Spooky Action-at-a-Distance from the de Broglie Bohm Pilot-Wave Theory Using a Time-Symmetric Version of the de Broglie Double Solution

In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry.

Robustness of Wave-Particle Duality under Unruh Effect.

By considering a uniformly accelerated two-level system in an initial superposition state of a qubit, we investigate the loss of coherence induced by the acceleration. In addition, we investigate the impact of acceleration on the complementarity relation in a quantum interferometric circuit or quantum scattering circuit. We present an alternative approach to exploring acceleration effects through examination of quantum coherence decay and degradation in the interference pattern. Our investigations help to provide understanding of the consequences of decoherence induced by the Unruh effect on the wave-particle duality of a uniformly accelerated qubit.

Sub-Diffraction Photon Trapping: The Possible Optical Energy Eigenstates within a Tiny Circular Aperture with a Finite Depth

One of the challenging riddles that is set by light is: do photons have wavefunctions like other elementary particles do? Wave–particle duality has been a prevailing fact since the beginning of quantum theory thought; in electromagnetism, light is already a kind of undulation, so what about the waves of probability then? Well, Quantum Field Theory (QFT) has a rigorous explanation and supports the idea when they are considered as fields of particles via second quantization; they do have wavefunctions of probability, and it does not have anything to do with the regular oscillations. They can be related to the energy and momentum signatures of harmonic oscillations, resembling an imitation of the behavior of a classical harmonic oscillator, which then has a wavefunction to solve the corresponding time-independent Schrödinger equation. For the last half century, electrical engineering has owned the best out of these implications of Quantum Electrodynamics (QED) and QFT by engineering better semiconductor techniques with finely miniaturized transistors and composite devices for digital electronics and optoelectronics fields. More importantly, these engineering applications have also greatly evolved into combined fields like quantum computing that have introduced a completely new and extraordinary world to electronics applications. The study takes advantage of the power of QFT to mathematically reveal the bosonic modes (Laguerre–Gaussian) that appear in a sub-diffraction cylindrical aperture. In this way, this may lead to the construction of the techniques and characteristics of room-temperature photonic quantum gates which can isolate photon modes under a diffraction limit.

Study on the Diffraction-like and Interference-like Mechanisms of Particle Flow

This paper demonstrates that the light and dark fringe in Young's double-slit experiment is not actually the diffraction and interference pattern of light wave. We investigate the scattering phenomenon after the particle flow passes through the gaps and find that the scattering type and scattering degrees of freedom of the particle flow depend on the physical parameters of the particles and the gaps. When the particle flow undergoes uniform scattering, a uniform "yes" and "no" interspersed discrete distribution pattern will form on the receiving screen. Based on the diffraction-like and interference-like mechanism of particle flow, this paper explains the electron diffraction and interference experiment, as well as the Young's double-slit interference experiment and the diffraction of light through circular holes and plates. This article provides an in-depth discussion on Einstein's concept of wave particle duality and de Broglie's matter wave hypothesis, as well as an analysis of Feynman's experimental idea of electron double slit interference. Our research shows that the matter wave hypothesis is not valid, which has shaken the foundation of modern quantum mechanics and has significant scientific significance. In addition, this study has important application value for the development of technology for detecting and analyzing particles or gaps.

Application of Virtual Reality in Learning Quantum Mechanics

Quantum mechanics is a physical theory that describes the behavior of microscopic matter. According to quantum theory, a microscopic particle may be described as either a particle or a wave, called wave–particle duality. Many students in high school or college (BC level) find it difficult to imagine that microscopic particles have both particle and wave properties. This is mainly caused by the scale of the world they see since quantum mechanics deals with things that are too small, while the wave and particle phenomena at the microscopic scale are difficult to understand, measure, or verify in the real world. In this study, virtual reality technology was used to develop teaching modules on quantum mechanics, allowing learners to see the particles and wave phenomena of electrons and photons in the microscopic world through interactive operation in virtual experiments. A teaching experiment was conducted by recruiting 60 high school students as research subjects. The control group (30 students) used physics textbooks, and the experimental group (30 students) used the virtual teaching modules for learning quantum mechanics. The analysis results show that the experimental group’s learning effectiveness is higher than the control group. The questionnaire results show that students were satisfied with the learning experience using virtual teaching modules with high learning motivation and low cognitive load because virtual reality can visualize the abstract concepts of wave–particle duality and help them understand quantum mechanics.

A construction method of the wave–particle entanglement state of the particle system

Entanglement of the wave–particle duality of particles has attracted enormous attention as one of fundamental feature of quantum mechanics. Herein, we systematically studied the wave–particle entanglement of the particle system composed of N particles. The results indicate that the particle system has the wave–particle entanglement after the interaction, when the wave function of any one of the system can be obtained by using same basis vectors before the interaction. Moreover, a construction method of the wave–particle entanglement state is found for the particle system. Finally, the photons can show the wave–particle entanglement in the previous experimental work, which was further confirmed by the construction method. The results provide a new understanding for the entanglement of the wave–particle duality.

Thinking about the Wave-Particle Duality with Plasma Theory and Explaining it based on the Oscillator and Qseudo-Oscillator Models

It is the first time for us to observe the quantum world with the plasma theory. Mean-while, many new concepts, such as the discrete quantum, precise quantum and the non-linear quantum, etc., and new horizons, i.e., cutting off the connection of interaction, or equivalently introducing destructive disturbance, are supposed into the quantum mechanics at the first. The normal and pseudo-oscillator models are introduced and used to explain the wave and particle duality of quantum field. By adding such new content, it is hoped that people can understand the physics behind the quantum mechanics, rather than recognizing it with the pure mathematic knowledge. It is suggested that the quantum world is better to consider the influence of outside environment, and then the quantum mechanics is turned into the quantum dynamics. The establishment of quantum dynamics is helpful for people better understand and hence utilize the quantum mechanics, such as the quantum optics, quantum communication and quantum computer, etc.

Revisiting wave–particle duality in Bohr–Einstein debate

The notion of wave–particle duality remains one of the most debated subjects in the history of quantum physics. The most famous debate on the subject occurred between Bohr and Einstein. In this work, we revisit the wave–particle duality in the Bohr–Einstein debate from the viewpoint of the recently established duality-entanglement relation. We show that the duality-entanglement relation can provide a valuable framework for quantitative analysis of the Einstein's gedanken double-slit experiment and clarify some of its fundamental aspects.

News Article

Book, “X-Ray Spectroscopy for Chemical State Analysis” (Jun Kawai, Springer, 2023) Professor Jun Kawai (Kyoto University, Japan) has published an interesting and useful book on materials characterization methods using X-ray emission, absorption, and photoelectron spectroscopies. Readers will be able to learn about basic X-ray physics topics such as “Particle and Wave Duality of X-rays” (Chapter 1), “Profile Change of X-Ray Spectra” (Chapter 2), and “Chemical Effects of Multiply Ionized Satellites” (Chapter 3). They can also gain some practical knowledge on instrumentation, including “Pyroelectric X-Ray Emission” (Chapter 4), “Small-Size and Low-Power X-Ray Instruments” (Chapter 5), “Synchrotron Radiation Experiments” (Chapter 6), and “Quantitative Analysis Using XRF and SEM” (Chapter 7). The book includes some interesting historical episodes, such as Professor Yoneda's discovery of enhanced diffuse scattering at the total reflection critical angle (now often called the Yoneda peak or Yoneda wing in grazing-incidence small angle X-ray scattering) and TXRF. The author also describes his own experience - how he has achieved novel experiments. The book consists of 243 pages. Overall, this book seems to provide a good overview of X-ray spectroscopy methods and their applications. The inclusion of historical context and the author's experiences helps to give readers insight into how these techniques were developed and applied in practice. For further information of the book, see the following page, https://doi.org/10.1007/978-981-19-7361-1

Topological gauge fields and the composite particle duality

We unveil a duality that extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond ($2+1$)D. Thus, a quantum system in arbitrary dimensions can experience a modification of its statistical properties if coupled to a certain gauge field. For instance, a bosonic quantum fluid can feature composite fermionic (or anyonic) excitations when coupled to a statistical gauge field. We compute the explicit form of the aforementioned synthetic gauge fields in $\text{D}\ensuremath{\le}3+1$. We introduce a bosonic liquid and its composite dual in ($1+1$)D as proof of principle. We recover well-known results, resolve old controversies, and suggest a microscopic mechanism for the emergence of such a gauge field. We also outline potential directions for experimental realizations in ultracold atom platforms.

Particle-continuum duality of skyrmions

Topological solitons are crucial to many branches of physics, such as models of fundamental particles in quantum field theory, information carriers in nonlinear optics, and elementary entities in quantum and classical computations. Chiral magnetic materials are a fertile ground for studying solitons. In the past a few years, a huge number of all kinds of topologically protected localized magnetic solitons have been found. The number is so large, and a proper organization and classification is necessary for their future developments. Here we show that many topological magnetic solitons can be understood from the duality of particle and elastic continuum-medium nature of skyrmions. In contrast to the common belief that a skyrmion is an elementary particle that is indivisible, skyrmions behave like both particle and continuum media that can be tore apart to bury other objects, reminiscing particle-wave duality in quantum mechanics. Skyrmions, like indivisible particles, can be building blocks for cascade skyrmion bags and target skyrmions. They can also act as bags and glues to hold one or more skyrmions together. The principles and rules for stable composite skyrmions are explained and presented, revealing their rich and interesting physics.

Delayed-choice quantum erasure with nonlocal temporal double-slit interference

Wave–particle duality is a counterintuitive nature of quantum physics that challenges many common-sense assumptions, and Young’s double-slit interference is a prototypical example. While most quantum erasure experiments emphasized the choice of erasing or marking the which-path information of one quantum system, we use frequency entanglement to report a nonlocal temporal double-slit interferometer such that the which-time information determines the wave-like or particle-like behaviors. Since frequency-entangled photons are created simultaneously by using spontaneous parametric down conversion, the mark of temporal distinguishability is readily prepared by delaying one of the entangled photons, and its quantum eraser is implemented by using spectrally resolved detection with a tunable delayed choice. These results may provide an alternative aspect and insight into the role of the temporal degree in quantum-light complementarity and photon interference.