Point Particles Research Articles

The Proton and Occam’s Razor

Otto Stern’s 1933 measurement of the unexpectedly large proton magnetic moment indicated to most physicists that the proton is not a point particle. At that time, many physicists modeled elementary particles as point particles, and therefore Stern’s discovery initiated the speculation that the proton might be a composite particle. In this work, we show that despite being an elementary particle, the proton is an extended particle. Our work is motivated by the experimental data, which we review in section 1.By applying Occam’s Razor principle, we identify a simple proton structure that explains the origin of its principal parameters. Our model uses only relativistic and electromagnetic concepts, highlighting the primary role of the electromagnetic potentials and of the magnetic flux quantum Φ M = h/e. Unlike prior proton models, our methodology does not violate Maxwell’s equation, Noether’s theorem, or the Pauli exclusion principle.Considering that the proton has an anapole (toroidal) magnetic moment, we propose that the proton is a spherical shaped charge that moves at the speed of light along a path that encloses a toroidal volume. A magnetic flux quantum Φ M = h/e stabilizes the proton’s charge trajectory. The two curvatures of the toroidal and poloidal current loops are determined by the magnetic forces associated with Φ M . We compare our calculations against experimental data.

Foundations for QED, Feynman operator calculus, Dyson conjectures, and Einstein’s dual theory

This paper reviews research on the foundations of quantum electrodynamics (QED). We show that there are three definitions of the proper time that follow from Einstein’s theory. The first definition is used to prove that the universe has a unique clock (Newton-Horwitz-Fanchi time) available to all observers. This clock is used to briefly discuss the mathematical foundations for Feynman’s time ordered operator calculus. We use this calculus to solve the first and second conjectures of Dyson for QED: that the renormalized perturbation series is asymptotic and, that the ultra-violet divergence is caused by a violation of the time-energy uncertainly relationship. The second definition gives Minkowski’s version of Einstein’s theory and its problems are briefly reviewed. The third definition gives the dual Newton, dual Maxwell and dual quantum theories. The theory is dual in that, for a set of n particles, every observer has two unique sets of global variables (X, t) and (X, τ) to study the system, where X is the canonical center of mass. Using (X, t) time is relative with speed c, while in (X, τ), time is unique with relative speed b. The dual Maxwell theory contains a longitudinal (dissipative) term in the E field wave equation, which appears instantaneously with acceleration and we predict that radiation from a cyclotron will not produce photoelectrons. It is shown that this term gives an effective mass for the photon. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein’s theory and without the need for point particles or a self-energy divergency. This means that a second quantized version will not produce a self-energy or infrared divergency. These results along with the proof of Dyson’s second conjecture resolves all the problems with QED. The dual Dirac theory provides a new formula for the anomalous magnetic moment of a charged particle, which can give exact values for the electron, muon and proton g-factors.

Self-consistent Spin, Tidal, and Dynamical Equations of Motion in the REBOUNDx Framework

We introduce self-consistent spin, tidal, and dynamical equations of motion into REBOUNDx, a library of additional effects for the popular N-body integrator REBOUND. The equations of motion used are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems of which the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code’s performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx.

The algebraic origin of the Doppler factor in the Liénard–Wiechert potentials

After reviewing the algebraic derivation of the Doppler factor in the Liénard–Wiechert potentials of an electrically charged point particle, we conclude that the Dirac delta function used in electrodynamics must be the one obeying the weak definition, non-zero in an infinitesimal neighborhood, and not the one obeying the strong definition, non-zero in a point. This conclusion emerges from our analysis of (a) the derivation of an important Dirac delta function identity, which generates the Doppler factor, (b) the linear superposition principle implicitly used by the Green function method, and (c) the two equivalent formulations of the Schwarzschild–Tetrode–Fokker action. As a consequence, in full agreement with our previous discussion of the geometrical origin of the Doppler factor, we conclude that the electromagnetic interaction takes place not between points in Minkowski space, but between corresponding infinitesimal segments along the worldlines of the particles.

Quantum Brownian motion induced by an inhomogeneous tridimensional space and a S1× R3 topological space-time

In this paper we investigate the Quantum Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless scalar field in (3 + 1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet, Neumann, mixed and quasiperiodic). The modes of the field are confined and compactified to a finite length region, which consequently provides a natural measure scale for the system. Useful expressions for the Wightman function have been obtained, which allow us to calculate analytical expressions for the velocity dispersion in all condition cases considered. We also obtain expressions for the velocity dispersion in the short and late time regimes. Finally, we exhibit some graphs in order to show the behavior of the velocity dispersions, discussing important divergencies that are present in our results.

Investigating the magnitude and temporal localization of inertial particle mixing in turbulent channel flows

Mixing of inertial point particles in a turbulent channel flow at Reτ=950 is investigated by means of direct numerical simulations. We consider inertial particles, at varying Stokes number, released from pairs of sources located at different positions inside the channel and analyze the rate at which particles come into close proximity to each other. To do so, we employ a Lagrangian framework, which is suitable for the analysis of trajectories and in general for the study of mixing and dispersion problems. By varying the release position of particles along the wall-normal direction we obtain a thorough description of mixing in an anisotropic turbulent flow. Moreover, we analyze the effects of particle inertia and show that these are not univocal but also depend on the position and alignment of the sources, owing in particular to the dependence of the flow timescales on the distance from the wall.

Semisimple four‐dimensional topological field theories cannot detect exotic smooth structure

AbstractWe prove that semisimple four‐dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth four‐manifolds and homotopy equivalent simply connected closed oriented smooth four‐manifolds. We show that all currently known four‐dimensional field theories are semisimple, including unitary field theories, and once‐extended field theories which assign algebras or linear categories to 2‐manifolds. As an application, we compute the value of a semisimple field theory on a simply connected closed oriented 4‐manifold in terms of its Euler characteristic and signature. Moreover, we show that a semisimple four‐dimensional field theory is invariant under ‐stable diffeomorphisms if and only if the Gluck twist acts trivially. This may be interpreted as the absence of fermions amongst the ‘point particles’ of the field theory. Such fermion‐free field theories cannot distinguish homotopy equivalent 4‐manifolds. Throughout, we illustrate our results with the Crane–Yetter–Kauffman field theory associated to a ribbon fusion category, settling in the negative the question of whether it is sensitive to smooth structure. As a purely algebraic corollary of our results applied to this field theory, we show that a ribbon fusion category contains a fermionic object if and only if its Gauss sums vanish.

Particle entity in the Doi–Peliti and response field formalisms

We introduce a procedure to test a theory for point particle entity, that is, whether said theory takes into account the discrete nature of the constituents of the system. We then identify the mechanism whereby particle entity is enforced in the context of two field-theoretic frameworks designed to incorporate the particle nature of the degrees of freedom, namely the Doi–Peliti field theory and the response field theory that derives from Dean’s equation. While the Doi–Peliti field theory encodes the particle nature at a very fundamental level that is easily revealed, demonstrating the same for Dean’s equation is more involved and results in a number of surprising diagrammatic identities. We derive those and discuss their implications. These results are particularly pertinent in the context of active matter, whose surprising and often counterintuitive phenomenology rests wholly on the particle nature of the agents and their degrees of freedom as particles.

On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane

In this paper, we provide a mathematically and physically consistent minimal prescription for a charged spinless point particle coupled to a constant magnetic field in a 2-dimensional noncommutative plane. It turns out to be a gauge invariant prescription in contrast to the widely and carelessly used naive minimal prescription in the context of 2-dimensional quantum mechanics in a noncommutative plane. Besides, we explore the noncommutative U(1) gauge theoretic structure of the underlying noncommutative system by explicitly computing the 1-parameter family of Seiberg–Witten maps.

Study of the intermediate mass ratio black hole binary merger up to 1000:1 with numerical relativity

We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, , with the small hole starting from rest at a proper distance . We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors.

Drag increase and turbulence augmentation in two-way coupled particle-laden wall-bounded flows

The exact regularized point particle method is used to characterize the turbulence modulation in two-way momentum-coupled direct numerical simulations of a turbulent pipe flow. The turbulence modification is parametrized by the particle Stokes number, the mass loading, and the particle-to-fluid density ratio. The data show that in the wide region of the parameter space addressed in the present paper, the overall friction drag is either increased or unaltered by the particles with respect to the uncoupled case. In the cases where the wall friction is enhanced, the fluid velocity fluctuations show a substantial modification in the viscous sub-layer and in the buffer layer. These effects are associated with a modified turbulent momentum flux toward the wall. The particles suppress the turbulent fluctuations in the buffer region and concurrently provide extra stress in the viscous sub-layer. The sum of the turbulent stress and the extra stress is larger than the Newtonian turbulent stress, thus explaining the drag increase. The non-trivial turbulence/particles interaction turns out in a clear alteration of the near-wall flow structures. The streamwise velocity streaks lose their spatial coherence when two-way coupling effects are predominant. This is associated with a shift of the streamwise vortices toward the center of the pipe and with the concurrent presence of small-scale and relatively more intense vortical structures near the wall.

Solitary wave billiards.

In the present work we explore the concept of solitary wave billiards. That is, instead of a point particle, we examine a solitary wave in an enclosed region and examine its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. Furthermore, the nature of the scattering of the deformable solitary wave particle is elucidated on the basis of a negative Goos-Hänchen effect which, in addition to a trajectory shift, also results in an effective shrinkage of the billiard domain.

Fundamentals of unified physics

This work is based on the following three premises: (1) Equality c = u with u = (‐2u)1/2 as the total escape speed (from all the masses in the universe) and u the total gravitational potential; given a value of the universe mass, as shared by many physicists, u tends to c, hence constant on Earth. Moreover, the above equality implies the massiveness of light, which regards the second premise: (2) Structure of light: Longitudinal/sinusoidal particles, photons, moving along rays, having parameters λ (their length) and frequency ν (their number, of the same ray, flowing in a time unit); now, if photons and electron should have, at their impact, opposite direction, a circling electron could fall into its nucleus, hence the third premise. (3) A structure of the electron where its charge is not uniformly distributed, but it can be considered as a point particle fixed on the electron surface, facing the atom nucleus during the electron orbits; the electron charge corresponds to the photons-electron impact point, where photons are absorbed and released. Due to these structures, the photons-electron impacts will force the involved electron to move, with a radial velocity w, toward wider orbits. On these bases, and according to the classical mechanics laws, we found, but not limited to, these results: The measured speed of light, constant on Earth because of the equality #1, turns out to be also invariant whatever the relative motion observer-source (of light) is: In short, during the interaction photons-electron, due to both the electron radial velocity and its Doppler effect, if the photons frequency decreases, then their length will increase (and vice versa) always inducing the invariant c. [The equality c = u has a cosmological reason: If c > u, all the visible masses, following the photons mass moving toward the infinity, would be dispersed from each other; if c < u all masses would collapse, while, for c = u, the photons mass (as well as neutrinos mass, as shown) will ensure an endless balance between dispersion and collapse.] The gravitational redshift and the claimed time dilation depend, like c, on the variation of the total potential. On H atom, the number of the electron circular orbits turns out to be n = 1, 2…137; the electron orbital speed along its ground-state (g-s) orbit becomes v 1 = c/137, while the electron charge g-s orbital speed is v o = αc with α being the fine-structure constant. As for the claimed fall of circling electrons into their nucleus due to their supposed photons emission, we found that the circling electrons are emitting the previously absorbed photons only during the spiral path from higher toward lower orbits; this emission avoids their fall. Then we show that the compensation velocity (to restore the resonance source-detector located at different heights) has opposite direction with respect to the one predicted by relativity.

Interaction of Two Charged Dielectric Spheres with a Point Charge

We consider the problem of interaction of three charged particles, the size of one of which can be disregarded. The equations for the expansion coefficients of the electric field potential are derived using the method of expansion in spherical harmonics. Expressions are obtained for the Cartesian components of the interaction force and the torque due to this force. It is shown that in spite of the axial symmetry breaking after the addition of the third particle, if the free charge is distributed uniformly over the surface of a spherical particle, all vector components of the torque acting on this particle are equal to zero. By separating the contributions from image charges in explicit form, we have derived the expressions for the surface charge density and the force of interaction of the particles. The conditions for the emergence of attraction between similarly charged spherical particles depending on the position of the point particle are investigated.

Boltzmann’s Entropy During Free Expansion of an Interacting Gas

In this work, we study the evolution of Boltzmann’s entropy in the context of free expansion of a one-dimensional interacting gas inside a box. Our interacting particle model is a gas of hard point particles with alternating masses, a system known to have good ergodicity properties. Boltzmann’s entropy is defined for single microstates and is given by the phase-space volume occupied by microstates with the same value of macrovariables which are coarse-grained physical observables. We demonstrate the idea of typicality in the growth of the Boltzmann’s entropy for two choices of macro-variables—the single particle phase space distribution and the hydrodynamic fields. Due to the presence of interactions, the growth curves for both these entropies are observed to converge to a monotonically increasing limiting curve, on taking the appropriate order of limits, of large system size and small coarse-graining scale. Moreover, we observe that the limiting growth curves for the two choices of entropies are identical as implied by local thermal equilibrium. We also discuss issues related to finite size and finite coarse gaining scale which lead to interesting features such as oscillations in the entropy growth curve. We also discuss shocks observed in the hydrodynamic fields.

Three-body harmonic molecule

In this study, the quantum three-body harmonic system with finite rest length R and zero total angular momentum L = 0 is explored. It governs the near-equilibrium S-states eigenfunctions of three identical point particles interacting by means of any pairwise confining potential that entirely depends on the relative distances between particles. At R = 0, the system admits a complete separation of variables in Jacobi-coordinates, it is (maximally) superintegrable and exactly-solvable. The whole spectra of excited states is degenerate, and to analyze it a detailed comparison between two relevant Lie-algebraic representations of the corresponding reduced Hamiltonian is carried out. At R > 0, the problem is not even integrable nor exactly-solvable and the degeneration is partially removed. In this case, no exact solutions of the Schrödinger equation have been found so far whilst its classical counterpart turns out to be a chaotic system. For R > 0, accurate values for the total energy E of the lowest quantum states are obtained using the Lagrange-mesh method. Concrete explicit results with not less than eleven significant digits for the states are presented in the range a.u. In particular, it is shown that (I) the energy curve develops a global minimum as a function of the rest length R, and it tends asymptotically to a finite value at large R, and (II) the degenerate states split into sub-levels. For the ground state, perturbative (small-R) and two-parametric variational results (arbitrary R) are displayed as well. An extension of the model with applications in molecular physics is briefly discussed.

Arrested coarsening and large density fluctuations in driven particle mixtures in two dimensions

Using molecular dynamics simulations, we study a driven, nonadditive binary mixture of spherical particles confined to move in two dimensions and immersed in an explicit solvent consisting of point particles with purely repulsive interactions. We show that, without a drive, the mixture of spherical particles phase separates and coarsens with kinetics consistent with an Ising-like conserved dynamics. Conversely, when the drive is applied, the coarsening is arrested and the system develops large density fluctuations. We show that the drive creates domains of a characteristic size which decreases with an increasing force. Furthermore, we find that these domains are anisotropic and can be oriented either parallel or perpendicular to the drive direction. Finally, we connect our findings to existing theories of strongly-driven systems, pointing out the importance of introducing the explicit solvent particles to break the Galilean invariance of the system.

SBETHE: Stopping powers of materials for swift charged particles from the corrected Bethe formula

The Fortran program sbethe calculates the stopping power of materials for swift charged particles with small charges (electrons, muons, protons, their antiparticles, and alphas). The electronic stopping power is computed from the corrected Bethe formula, with the shell correction derived from numerical calculations with the plane-wave Born approximation (PWBA) for atoms, which were based on an independent-electron model with the Dirac–Hartree–Fock–Slater self-consistent potential for the ground-state configuration of the target atom. The density effect correction is evaluated from an empirical optical oscillator strength (OOS) model based on atomic subshell contributions obtained from PWBA calculations. For projectiles heavier than the electron, the Barkas correction is evaluated from the OOS model, and the Lindhard–Sørensen correction is estimated from an accurate parameterization of its numerical values. The calculated electronic stopping power is completely determined by a single empirical parameter, the mean excitation energy or I value of the material. The radiative stopping power for electrons, and positrons, is evaluated by means of Seltzer and Berger's cross section tables for bremsstrahlung emission. The program yields reliable stopping powers and particle ranges for arbitrary materials and projectiles with kinetic energy larger than a certain cutoff value Ecut, which is specific of each projectile kind. The program is accompanied by an extensive database that contains tables of relevant energy-dependent atomic quantities for all the elements from hydrogen to einsteinium. sbethe may be used to generate basic information for dosimetry calculations and Monte Carlo simulations of radiation transport, and as a pedagogical tool. Program summaryProgram title:sbetheCPC Library link to program files:https://doi.org/10.17632/7zw25f428t.1Licensing provisions: CC by NC 3.0Programming language: Fortran 90/95Nature of problem: The program calculates the stopping power of arbitrary materials for swift charged projectiles with small charges. The material is characterized by its chemical composition, mass density, and the empirical I value. The considered projectiles are electrons, positrons, negative muons, antimuons, protons, antiprotons, and alphas, which are described as point particles characterized by their mass and charge. If the actual I value of the material is known, the results from the program are expected to be reliable for projectiles with kinetic energy higher than a value Ecut, of the order of 1 keV for electrons and positrons, 150 keV for muons and antimuons, 0.75 MeV for protons and antiprotons, and 5 MeV for alpha particles.Solution method: The electronic stopping power is calculated by means of a corrected Bethe formula [1], which combines the conventional Bethe logarithm with the following corrections,1) the shell correction obtained from calculations based on the plane-wave Born approximation with the self-consistent Dirac–Hartree–Fock–Slater (DHFS) potential of neutral atoms in their ground-state configuration [2],2) the density effect correction, which accounts for the reduction of the stopping power caused by the dielectric polarization of the medium,3) a parameterization of the Lindhard–Sørensen correction, which generalizes the Bloch correction for relativistic projectiles, and4) the Barkas correction, which accounts for differences between the stopping powers of particles and their antiparticles.The density-effect and the Barkas corrections are calculated from a model of the optical oscillator strength (OOS) of the material, which combines the contributions of inner atomic subshells calculated with the DHFS potential, with a classical oscillator model for the contribution of valence electrons,A simple extrapolation formula is used to extend the calculated electronic stopping power to energies less than Ecut to allow the calculation of particle ranges.For electrons and positrons, the radiative stopping power is calculated from numerical tables prepared by Seltzer and Berger [3].Additional comments including restrictions and unusual features: The calculated stopping power is determined by a single parameter, the mean excitation energy or I value. The program assigns to each material a default I value, derived from the recommendations in the ICRU Report 37, which can be changed by the user. The distribution package includes text files with tables of atomic energy-dependent quantities (subshell optical oscillator strengths, shell corrections, scaled cross sections for bremsstrahlung emission) that are used in the calculations.

Local Quantum Theory with Fluids in Space-Time

In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger’s theory is presented, which reproduces all of the standard empirical predictions of conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant “local hidden variable theory” in space-time, whose existence proves definitively that such theories are possible. This does not conflict with Bell’s theorem because it is a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems’ wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given.

A point particle source model for conjugate heat and mass transfer in dispersed two-phase flows by BEM based methods

The paper reports on development of a Boundary Element Method (BEM) based two phase dispersed flow model, that allows an accurate and efficient heat and mass transfer coupling by using a moving point source model to account for particle–fluid interaction. The two-way coupling model highlights the efficient use of the elliptic fundamental solution and the Dirac delta distribution properties to accurately evaluate the heat and mass point particle source impact on the continuous phase, solved by the Boundary Domain Integral Method (BDIM). In addition to the BDIM model of the particle–fluid heat and mass transfer interaction, the two-phase flow case under consideration is extended to the case of porous spherical particle drying with internal moving drying front, which is solved by the Boundary Element Method. As the two-phase flow is considered to be dilute, the particle–fluid momentum exchange is covered by a one-way coupling algorithm, with Lagrangian particle tracking used for determination of particle positions and velocities in the flow. Two computational cases are presented, where 1000 and 10000 particles are dried in a stream of hot air. Comparison between the obtained drying times for the cases of the one-way and the two-way heat and mass transfer coupling results shows, that the developed two-way coupling model accurately captures the effect of moisture accumulation and temperature decrease in the fluid phase, leading to realistic computations of drying rates of particles in the flow.