Wave-Particle Duality: Particle Always Remains Particle and Its Wave Function Always Remains Wave

On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.

The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization?

The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.

Storm-Time Evolution of Energetic Electron Pitch Angle Distributions by Wave-Particle Interaction

The quasi-pure pitch-angle scattering of energetic electrons driven by field-aligned propagating whistler mode waves during the 9～15 October 1990 magnetic storm at L≈ 3 ～ 4 is studied, and numerical calculations for energetic electrons in gyroresonance with a band of frequency of whistler mode waves distributed over a standard Gaussian spectrum is performed. It is found that the whistler mode waves can efficiently drive energetic electrons from the larger pitchangles into the loss cone, and lead to a flat-top distribution during the main phase of geomagnetic storms. This result perhaps presents a feasible interpretation for observation of time evolution of the quasi-isotropic pitch-angle distribution by Combined Release and Radiation Effects Satellite （CRRES） spacecraft at L ≈ 3 ～ 4.

KELEA (Kinetic Energy Limiting Electrostatic Attraction) Offers an Alternative Explanation to Existing Concepts Regarding Wave-Particle Duality, Cold Fusion and Superconductivity

Existing explanations for several major phenomena in physics may need to be reconsidered in light of the description of a natural force termed KELEA (kinetic energy limiting electrostatic attraction). Three examples are selected for discussion in this paper: i) The proposed wave-particle duality of electrons;ii) cold fusion;and iii) superconductivity. The current interpretations of these enigmatic concepts are incomplete and not fully validated by scientific methods. The observations underlying these processes are seemingly consistent with KELEA acting as a repelling force between opposite electrical charges. Relatively simple experiments can be designed to either confirm or exclude KELEA in these and in various other currently perplexing physical phenomena.

Wave-particle duality relation with a quantum N-path beamsplitter

The wave-particle duality relation derived by Englert sets an upper bound of the extractable information from wave and particle properties in a two-path interferometer.Surprisingly,previous studies demonstrated that the introduction of a quantum beamsplitter in the interferometer could break the limitation of this upper bound,due to interference between wave and particle states.Along the other line,a lot of efforts have been made to generalize this relation from the two-path setup to the N-path case.Thus,it is an interesting question that whether a quantum N-path beamsplitter can break the limitation as well.This paper systemically studies the model of a quantum N-path beamsplitter,and finds that the generalized wave-particle duality relation between interference visibility and path distinguishability is also broken in certain situations.We further study the maximal extractable information's reliance on the interference between wave and particle properties,and derive a quantitative description.We then propose an experimental methodology to verify the break of the limitation.Our work reflects the effect of quantum superposition on wave-particle duality,and exhibits a new aspect of the relation between visibility and path distinguishability in N-path interference.Moreover,it implies the observer's influence on wave-particle duality.

Simultaneous Measurement of Fringe Visibility and Path Predictability of Wave-Particle Duality

An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young＇s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters.

Study on the Physical Basis of Wave-Particle Duality: Modelling the Vacuum as a Continuous Mechanical Medium

One great surprise discovered in modern physics is that all elementary particles exhibit the property of wave-particle duality. We investigated this problem recently and found a simple way to explain this puzzle. We proposed that all particles, including massless particles such as photon and massive particles such as electron, can be treated as excitation waves in the vacuum, which behaves like a physical medium. Using such a model, the phenomenon of wave-particle duality can be explained naturally. The key question now is to find out what kind of physical properties this vacuum medium may have. In this paper, we investigate if the vacuum can be modeled as an elastic solid or a dielectric medium as envisioned in the Maxwell theory of electricity and magnetism. We show that a similar form of wave equation can be derived in three cases: (1) By modelling the vacuum medium as an elastic solid;(2) By constructing a simple Lagrangian density that is a 3-D extension of a stretched string or a vibrating membrane;(3) By assuming that the vacuum is a dielectric medium, from which the wave equation can be derived directly from Maxwell’s equations. Similarity between results of these three systems suggests that the vacuum can be modelled as a mechanical continuum, and the excitation wave in the vacuum behaves like some of the excitation waves in a physical medium.

Quantum Interference without Wave-Particle Duality

Interference of light and material particles is described with a unified model which does not need to assume the wave-particle duality. A moving particle is associated with a region of spatial correlated points named coherence cone. Its geometry depends on photon or particle momentum and on the parameters of the experimental setup. The final interference pattern is explained as a spatial distribution of particles caused by the coherence cone geometry. In the present context, the wave front superposition principle, wave-particle duality and wave-collapse lose their meaning. Fits of observed single electron and single molecule interference patterns together with the simulation of expected near-field molecule interference (Talbot carpet) demonstrate the model validity.

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

From wave-particle duality to wave-particle-mixedness triality:an uncertainty approach

The wave-particle duality,as a manifestation of Bohr’s complementarity,is usually quantified in terms of path predictability and interference visibility.Various characterizations of the wave-particle duality have been proposed from an operational perspective,most of them are in forms of inequalities,and some of them are expressed in forms of equalities by incorporating entanglement or coherence.In this work,we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer,with uncertainty as a unified theme.More specifically,by employing the simple yet fundamental concept of variance,we establish a resolution of unity,which can be interpreted as a complementarity relation among wave feature,particle feature,and mixedness of a quantum state.This refines or reinterprets some conventional approaches to wave-particle duality,and highlights informational aspects of the issue.The key idea of our approach lies in that a quantum state,as a Hermitian operator,can also be naturally regarded as an observable,with measurement uncertainty(in a state)and state uncertainty(in a measurement)being exploited to quantify particle feature and wave feature of a quantum state,respectively.These two kinds of uncertainties,although both are defined via variance,have fundamentally different properties and capture different features of a state.Together with the mixedness,which is a kind of uncertainty intrinsic to a quantum state,they add up to unity,and thus lead to a characterization of the waveparticle-mixedness complementarity.This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.

Unified Gas-Kinetic Wave-Particle Methods VI:Disperse Dilute Gas-Particle Multiphase Flow

A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is proposed.In the two-phaseflow,the gas phase is always in the hydrodynamic regime and is fol-lowed by GKS for the Navier-Stokes solution.The particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interac-tion with the variation of particle’s Knudsen number.In the intensive particle colli-sion regime,the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phaseflow reduces to the two-fluid Eulerian-Eulerian(EE)model.In the rarefied regime,the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian(EL)formulation.In the tran-sition regime for the solid particle,the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods seamlessly.The GKS-UGKWP method will be tested in allflow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase interaction.It is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phaseflow.

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Problem: The Fresnel equations describe the proportions of reflected and transmitted light from a surface, and are conventionally derived from wave theory continuum mechanics. Particle-based derivations of the Fresnel equations appear not to exist. Approach: The objective of this work was to derive the basic optical laws from first principles from a particle basis. The particle model used was the Cordus theory, a type of non-local hidden-variable (NLHV) theory that predicts specific substructures to the photon and other particles. Findings: The theory explains the origin of the orthogonal electrostatic and magnetic fields, and re-derives the refraction and reflection laws including Snell’s law and critical angle, and the Fresnel equations for s and p-polarisation. These formulations are identical to those produced by electromagnetic wave theory. Contribution: The work provides a comprehensive derivation and physical explanation of the basic optical laws, which appears not to have previously been shown from a particle basis. Implications: The primary implications are for suggesting routes for the theoretical advancement of fundamental physics. The Cordus NLHV particle theory explains optical phenomena, yet it also explains other physical phenomena including some otherwise only accessible through quantum mechanics (such as the electron spin g-factor) and general relativity (including the Lorentz and relativistic Doppler). It also provides solutions for phenomena of unknown causation, such as asymmetrical baryogenesis, unification of the interactions, and reasons for nuclide stability/instability. Consequently, the implication is that NLHV theories have the potential to represent a deeper physics that may underpin and unify quantum mechanics, general relativity, and wave theory.

Dynamics of the inner electron radiation belt:A review

The Van Allen radiation belts are an extraordinary science discovery in the Earth magnetosphere and consist of two electron belts.The inner Van Allen belt contains electrons of 10s to 100s keV;the outer belt consists mainly of 0.1-10 MeV electrons.Their dynamics have been analyzed for decades.The newly-launched Van Allen Probes provide unprecedented opportunities to investigate the inner belt more thoroughly.Data from this advanced mission have allowed scientists to demonstrate that the inner belt was formed not only through inward transport of outer belt electrons but Cosmic Ray Albedo Neutron Decay(CRAND)has also played an important role.In addition,the inner belt electrons show energy-dependent variations and present“zebra stripe”structures in the energy spectrum.At the same time,scientists have further confirmed that the electrons in the inner radiation belt get lost through coulomb collision and wave-particle interaction.Despite these advances,important questions remain unanswered and require further investigation.The launch of Macao Science Satellite-1 mission,with its low inclination angle and low altitude orbit,will provide advanced radiation belt data for better understanding of the structure and dynamics of the inner electron radiation belt.

Hybrid simulation of q=1 high-order harmonics driven by passing energetic particles in tokamak plasmas

High-order harmonics q(ψ_(s))=1 energetic particle modes(EPMs)have been observed in toroidal plasmas experiments with neutral beam injection.To investigate these phenomena,linear properties and nonlinear dynamics of these EPMs driven by passing energetic particles(EPs)are studied via the global hybrid kinetic-magnetohydrodynamic code M3D-K.Simulation results demonstrate that passing EPs'effects on high mode-number harmonics(q(ψ_(s))=m/n=2/2,3/3,4/4)instability are more obvious than the q(ψ_(s))=1/1 mode,especially when q-profile is sufficiently flat in the core region.Furthermore,the effects of the pitch angleΛ_0 and beam ion pressure P_(hot)/P_(total)on the features of high n components are also analyzed specifically.It is found that there exists only one resonant condition for these EPMs.In the nonlinear phase,these high mode-number harmonics can induce significant energetic ions redistribution and chirping up phenomena,which differs from the classical fishbone excited by passing EPs.These discoveries are conducive to better apprehend the underlying physical mechanisms of the highorder harmonics driven by passing EPs.

Soliton Wave for the Magnetic Electron

A century ago, de Broglie discovered the wave associated to the motion of the electron. We present here the soliton solutions of a nonlinear relativistic wave equation. Two such solitons exist, corresponding to the two possible states of a particle with spin j = 1/2. The mystery of wave-particle dualism is solved: the electron is both a particle, a point which is a singularity, and a wave extended throughout the whole space.

On the loss mechanisms of radiation belt electron dropouts during the 12 September 2014 geomagnetic storm

Radiation belt electron dropouts indicate electron flux decay to the background level during geomagnetic storms,which is commonly attributed to the effects of wave-induced pitch angle scattering and magnetopause shadowing.To investigate the loss mechanisms of radiation belt electron dropouts triggered by a solar wind dynamic pressure pulse event on 12 September 2014,we comprehensively analyzed the particle and wave measurements from Van Allen Probes.The dropout event was divided into three periods:before the storm,the initial phase of the storm,and the main phase of the storm.The electron pitch angle distributions(PADs)and electron flux dropouts during the initial and main phases of this storm were investigated,and the evolution of the radial profile of electron phase space density(PSD)and the(μ,K)dependence of electron PSD dropouts(whereμ,K,and L^*are the three adiabatic invariants)were analyzed.The energy-independent decay of electrons at L>4.5 was accompanied by butterfly PADs,suggesting that the magnetopause shadowing process may be the major loss mechanism during the initial phase of the storm at L>4.5.The features of electron dropouts and 90°-peaked PADs were observed only for>1 MeV electrons at L<4,indicating that the wave-induced scattering effect may dominate the electron loss processes at the lower L-shell during the main phase of the storm.Evaluations of the(μ,K)dependence of electron PSD drops and calculations of the minimum electron resonant energies of H+-band electromagnetic ion cyclotron(EMIC)waves support the scenario that the observed PSD drop peaks around L^*=3.9 may be caused mainly by the scattering of EMIC waves,whereas the drop peaks around L^*=4.6 may result from a combination of EMIC wave scattering and outward radial diffusion.

Elementary analysis of interferometers for wave particle duality test and the prospect of going beyond the complementarity principle

A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young＇s two-slit interferometer and the Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern （wave nature） and the which-way information （particle nature） of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave-particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.

Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas

Nonlinear evolution of multiple toroidal Alfvén eigenmodes(TAEs)driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas.To clearly identify the effect of nonlinear coupling on the beam ion loss,simulations over single-n modes are also carried out and compared with those over multiple-n modes,and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail.It is found that in the multiple-n case,the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case.Moreover,increasing fast ion betaβh can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases.For example,the loss level in the multiple-n case forβh=6.0%can even reach 13%of the beam ions and is 44%higher than the sum loss level calculated from all individual single-n modes in the single-n case.On the other hand,when the closely spaced resonance overlap occurs in the multiple-n case,the release of mode energy is increased so that the widely spaced resonances can also take place.In addition,phase space characterization is obtained in both single-n and multiple-n cases.

Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis

According to the orthodox interpretation of quantum physics, wave-particle duality(WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers(AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg’s position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer(WM-AI) and compare them with the historical schemes of strongmeasurement atom interferometer(SM-AI), such as Einstein’s recoiling slit and Feynman’s light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector(WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic centerof-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schr¨odinger’s equation for the composite atom-electron-photon system in these WM-AIs. We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg’s uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.

Evolutions of equatorial ring current ions during a magnetic storm

In this paper, we present evolutions of the phase space density(PSD) spectra of ring current(RC) ions based on observations made by Van Allen Probe B during a geomagnetic storm on 23–24 August 2016. By analyzing PSD spectra ratios from the initial phase to the main phase of the storm, we find that during the main phase, RC ions with low magnetic moment μ values can penetrate deeper into the magnetosphere than can those with high μ values, and that the μ range of PSD enhancement meets the relationship: S(O^+) >S(He^+)>S(H^+). Based on simultaneously observed ULF waves, theoretical calculation suggests that the radial transport of RC ions into the deep inner magnetosphere is caused by drift-bounce resonance interactions, and the efficiency of these resonance interactions satisfies the relationship: η(O^+) > η(He^+) > η(H^+), leading to the differences in μ range of PSD enhancement for different RC ions. In the recovery phase,the observed decay rates for different RC ions meet the relationship: R(O^+) > R(He^+) > R(H^+), in accordance with previous theoretical calculations, i.e., the charge exchange lifetime of O^+ is shorter than those of H^+ and He^+.