This document brings a solution for the "4/3 electromagnetic problem" that shows a discrepancy between the overall momentum for the EM field created by a charged sphere shell and its energy. The solution comes by including a term caused by the charge-field interaction over the sphere (j·E) multiplied by the distance to the center of mass (the center of the charged sphere).
The idea of center of mass displacement on interactions can be applied to other electromagnetic problems, as long as there are particles or systems with some extension, and to other fields of physics.
Adding a Shift term to solve the 4/3 problem in classical electrodinamicsSergio Prats
This work shows that for a charged spherical surface moving at slow speed, 푣 ≪ 푐, the 4/3
discrepancy between the electromagnetic (EM) mass calculated from (a) the field’s energy and
(b) the field’s momentum is solved by taking into account the exchange of energy between the
field and the charge on the surface of the sphere, while this interaction does not change the
overall field energy, it shifts the energy in the direction opposed to the sphere velocity. If we
take the electromagnetic mass as the one obtained from the electrostatic energy, this shift
adds a new term to the field velocity that makes it to move with the same velocity than the
charge, hence compensating the excess of momentum in the EM field.
Field energy correction with discrete chargesSergio Prats
This document introduces a correction in the classical electromagnetic field energy density when there are discrete charges instead of a whole density of charge based in the fact that the EM field induces by a particle does not affect itself and does not contribute to the potential in the hamiltonian.
A deeper analysis is done on how to deal with the radiated field energy, the reaction force and its analogy with quan Vacuum
The Harmonic Oscillator/ Why do we need to study harmonic oscillator model?.pptxtsdalmutairi
The harmonic oscillator system is important as a model for molecular vibrations. The vibrational energy levels of a diatomic molecule can be approximated by the levels of a harmonic oscillator
At first, we are going to study harmonic oscillator from a classical mechanical perspective and then will discuss the allowed energy levels and the corresponding wave function of the harmonic oscillator from a quantum mechanical point of view.
Later on we are going to describe the infrared spectrum of a diatomic molecules using the quantum mechanical energies. Also we are going to figure out how to determine molecular force constant.
Finally, we are going to learn selection rules for a harmonic oscillator and the normal coordinates which describe the vibrational motion of polyatomic molecules.
Momentum flux in the electromagnetic fieldSergio Prats
This article shows how to get the flux of momentum in the electromagnetic field from the Maxwell stress tensor in the scope of classical electromagnetism.
Electricity is associated with the presence and motion of electric charge. There are two types of electricity: static electricity and current electricity. Static electricity results from an imbalance of negative and positive charges in an object that can build up until being discharged. Electric charge is measured in coulombs and there are two types: positive and negative.
The electric field is the region of space surrounding an electrically charged object where an electric force can be detected. It is represented by electric field lines. The electric field intensity is the electric force per unit charge and is measured in newtons per coulomb. Coulomb's law describes the electric force between two point charges. Gauss's law relates the electric flux through a closed surface to the net
An apologytodirac'sreactionforcetheorySergio Prats
This work comments and praises Dirac's work on the reaction force theory, it is based on his 1938 'Classical theory of radiating electrons' paper. Some comments from the author are added.
1) The document is an introduction to Supersymmetric Quantum Mechanics (SUSY QM) aimed at undergraduate students with a basic understanding of quantum mechanics.
2) It explains how SUSY QM involves pairs of partner Hamiltonians that are closely related through factorization methods. The energy eigenstates of the Hamiltonians are related, with one Hamiltonian's excited states corresponding to the other's eigenstates.
3) An example using the Morse potential is worked through to demonstrate how SUSY QM allows all energy eigenstates and wavefunctions to be algebraically determined using the "shape invariance" condition.
Fundamental Concepts on Electromagnetic TheoryAL- AMIN
The document summarizes key concepts from a presentation on electromagnetic theory. It discusses different types of fields, including scalar and vector fields. It also covers gradient, divergence, curl, coordinate systems, static electric and magnetic fields, Maxwell's equations, and other fundamental electromagnetic concepts. Multiple students contributed sections on topics including Coulomb's law, Biot-Savart law, Lorentz force, and Maxwell's equations in differential, integral and harmonic forms.
Adding a Shift term to solve the 4/3 problem in classical electrodinamicsSergio Prats
This work shows that for a charged spherical surface moving at slow speed, 푣 ≪ 푐, the 4/3
discrepancy between the electromagnetic (EM) mass calculated from (a) the field’s energy and
(b) the field’s momentum is solved by taking into account the exchange of energy between the
field and the charge on the surface of the sphere, while this interaction does not change the
overall field energy, it shifts the energy in the direction opposed to the sphere velocity. If we
take the electromagnetic mass as the one obtained from the electrostatic energy, this shift
adds a new term to the field velocity that makes it to move with the same velocity than the
charge, hence compensating the excess of momentum in the EM field.
Field energy correction with discrete chargesSergio Prats
This document introduces a correction in the classical electromagnetic field energy density when there are discrete charges instead of a whole density of charge based in the fact that the EM field induces by a particle does not affect itself and does not contribute to the potential in the hamiltonian.
A deeper analysis is done on how to deal with the radiated field energy, the reaction force and its analogy with quan Vacuum
The Harmonic Oscillator/ Why do we need to study harmonic oscillator model?.pptxtsdalmutairi
The harmonic oscillator system is important as a model for molecular vibrations. The vibrational energy levels of a diatomic molecule can be approximated by the levels of a harmonic oscillator
At first, we are going to study harmonic oscillator from a classical mechanical perspective and then will discuss the allowed energy levels and the corresponding wave function of the harmonic oscillator from a quantum mechanical point of view.
Later on we are going to describe the infrared spectrum of a diatomic molecules using the quantum mechanical energies. Also we are going to figure out how to determine molecular force constant.
Finally, we are going to learn selection rules for a harmonic oscillator and the normal coordinates which describe the vibrational motion of polyatomic molecules.
Momentum flux in the electromagnetic fieldSergio Prats
This article shows how to get the flux of momentum in the electromagnetic field from the Maxwell stress tensor in the scope of classical electromagnetism.
Electricity is associated with the presence and motion of electric charge. There are two types of electricity: static electricity and current electricity. Static electricity results from an imbalance of negative and positive charges in an object that can build up until being discharged. Electric charge is measured in coulombs and there are two types: positive and negative.
The electric field is the region of space surrounding an electrically charged object where an electric force can be detected. It is represented by electric field lines. The electric field intensity is the electric force per unit charge and is measured in newtons per coulomb. Coulomb's law describes the electric force between two point charges. Gauss's law relates the electric flux through a closed surface to the net
An apologytodirac'sreactionforcetheorySergio Prats
This work comments and praises Dirac's work on the reaction force theory, it is based on his 1938 'Classical theory of radiating electrons' paper. Some comments from the author are added.
1) The document is an introduction to Supersymmetric Quantum Mechanics (SUSY QM) aimed at undergraduate students with a basic understanding of quantum mechanics.
2) It explains how SUSY QM involves pairs of partner Hamiltonians that are closely related through factorization methods. The energy eigenstates of the Hamiltonians are related, with one Hamiltonian's excited states corresponding to the other's eigenstates.
3) An example using the Morse potential is worked through to demonstrate how SUSY QM allows all energy eigenstates and wavefunctions to be algebraically determined using the "shape invariance" condition.
Fundamental Concepts on Electromagnetic TheoryAL- AMIN
The document summarizes key concepts from a presentation on electromagnetic theory. It discusses different types of fields, including scalar and vector fields. It also covers gradient, divergence, curl, coordinate systems, static electric and magnetic fields, Maxwell's equations, and other fundamental electromagnetic concepts. Multiple students contributed sections on topics including Coulomb's law, Biot-Savart law, Lorentz force, and Maxwell's equations in differential, integral and harmonic forms.
A model is proposed to show that the electron spin may not be purely intrinsic but the result of a loop of current with two different components interacting between them
This document discusses the energy characteristics of interactions between particles and systems. It introduces the concept of a spatial-energy parameter (P-parameter) to describe interactions. The key points are:
1) Interactions along a potential gradient (positive work) calculate the resulting potential energy by adding reciprocals of subsystem energies. Interactions against the gradient (negative work) add subsystem masses and energies algebraically.
2) P-parameter is proposed to quantify the energy of atom valence orbitals based on electron orbital energies and radii. For similar systems, P-parameters are added algebraically.
3) P-parameter is analogous to the quantum mechanical wave function and has wave properties. It provides a way to materialize
This article shows how to use a Green function to calculate the reaction force based in future external forces instead of using the time derivative of the acceleration, which leads to wrong results.
Mass, energy and momentum at cms i2 u2Tom Loughran
The document discusses mass, energy, and momentum at the CMS detector at the LHC. It explains that:
1) At high energies, energy and momentum are practically equivalent according to the equation E2 = p2 + m2, where mass terms become negligible. This allows energy to be calculated from momentum measurements.
2) The mass of a parent particle that decays can be determined by subtracting the momentum term p2 from the total energy term E2 of its decay products, giving m2.
3) At the LHC, initial energies and momenta of collisions are not precisely known, so conservation cannot be used directly, but transverse momentum is assumed to be zero initially and its conservation is used.
Sergey seriy thomas fermi-dirac theorySergey Seriy
This document presents modern ab-initio calculations based on Thomas-Fermi-Dirac theory with quantum, correlation, and multishell corrections. It summarizes extensions made to the statistical model by including additional energy terms to account for quantum corrections, exchange energy, and correlation energy. This leads to a quantum- and correlation-corrected Thomas-Fermi-Dirac equation involving a density term, kinetic energy density term, and modified potential function. Solving this quartic equation in the electron density provides a way to determine the electron density distribution as a function of distance from the nucleus.
Zero Point Energy And Vacuum Fluctuations EffectsAna_T
The document discusses several topics related to zero point energy and vacuum fluctuations:
1) It explains how the Heisenberg uncertainty principle leads to zero point energy, which is the lowest possible energy of a quantum system in its ground state.
2) It describes vacuum fluctuations as quantum fluctuations of fields even in their lowest energy state. These fluctuations can be thought of as virtual particles being created and destroyed in the vacuum.
3) Several phenomena are discussed that demonstrate the effects of zero point energy and vacuum fluctuations, including spontaneous emission, the Casimir effect, and the Lamb shift.
This document discusses wave equations and their applications. It contains 6 chapters that cover basic results of wave equations, different types of wave equations like scalar and electromagnetic wave equations, and applications of wave equations. The introduction explains that the document contains details about different types of wave equations and their applications in sciences. Chapter 1 discusses basic concepts like relativistic and non-relativistic wave equations. Chapter 2 covers the scalar wave equation. Chapter 3 is about electromagnetic wave equations. Chapter 4 is on applications of wave equations.
Movimiento De Una Partícula Cargada En Un Campo Eléctrico Y En Un Campo Magné...Gregory Zuñiga
The document discusses the mathematical modeling of the motion of a charged particle in electric and magnetic fields. It describes three cases: 1) motion in a uniform electric field, where the particle experiences a constant acceleration; 2) motion in a uniform magnetic field, where the particle travels in a circular path with radius determined by the magnetic field strength; and 3) motion in both uniform electric and magnetic fields perpendicular to each other, where the particle follows a helical path with the forces from the two fields balancing each other out under certain conditions. The modeling of the particle motion incorporates equations for forces, fields, energy, and kinematics.
This document describes a peridynamic model for simulating shape memory alloy composites. It presents the key equations of peridynamic theory, including the balance law accounting for internal forces between particles within a horizon. A simple 2D simulation in MATLAB is outlined using linear springs to model internal forces between particles within a defined horizon based on their displacement. The simulation calculates net internal and external forces on particles over time to model deformation, with the goal of upgrading the model in the future to include failure mechanisms.
This document summarizes key concepts in structural dynamics and aeroelasticity. It discusses three areas of interaction: between elasticity and dynamics, between aerodynamics and elasticity, and among all three. It then provides definitions and equations for rigid body dynamics, including Euler's laws. Subsequent sections cover transverse vibrations of strings, beams, and coupled bending-torsion behaviors in more complex structures. The concepts of stability are introduced, followed by discussions of single-degree-of-freedom systems, including free, forced, and resonant vibrations.
Electromagnetic waves are produced by time-varying electric and magnetic fields. Hertz experimentally proved this by showing that electromagnetic waves could be produced by oscillating electric currents. The electromagnetic wave equation describes electromagnetic waves traveling through space where there are no charges. Electric and magnetic fields of electromagnetic waves oscillate perpendicular to each other and perpendicular to the direction of propagation. Electromagnetic waves carry energy through space in the form of oscillating electric and magnetic fields. The Poynting vector represents the energy flux of an electromagnetic wave, pointing in the direction of wave propagation. Poynting's theorem relates the work done by electromagnetic forces on charges to energy stored in electromagnetic fields and energy flowing out of a given volume.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
Kinetic energy and gravitational potential energyfaisal razzaq
1) The document discusses kinetic energy and gravitational potential energy. Kinetic energy is the energy of an object in motion and depends on the object's mass and speed. Gravitational potential energy is the energy contained in an object above the ground and depends on the object's mass and position.
2) The gravitational field can be compared to an electric field. Both are conservative fields that represent the gradient of potential energy. Calculations of fields and potentials can be adapted from electricity to gravity.
3) The document makes analogies between the Coulomb force law in electricity and the gravitational force law. Both are foundations for their respective fields and phenomena can be described similarly using mathematical formulas.
Relativistic formulation of Maxwell equations.dhrubanka
This document discusses the relativistic formulation of Maxwell's equations. It begins by introducing the key concepts of special relativity that are needed, including Lorentz transformations and four-vectors. It then shows how the electric and magnetic fields transform under Lorentz transformations and how they can be combined into the electromagnetic field tensor. The document also discusses how charge and current densities transform and satisfy the continuity equation as a four-vector. Finally, it presents Maxwell's equations in their compact relativistic form in terms of the field tensor and its derivatives.
EMF ELECTROSTATICS:
Coulomb’s Law, Electric Field of Different Charge Configurations using Coulomb’s Law, Electric Flux, Field Lines, Gauss’s Law in terms of E (Integral Form and Point Form), Applications of Gauss’s Law, Curl of the Electric Field, Electric Potential, Calculation of Electric Field Through Electric Potential for given Charge Configuration, Potential Gradient, The Dipole, Energy density in the Electric field.
1. The document discusses conductors, dielectrics, current density, polarization, and electric susceptibility. It defines key concepts like current, current density, polarization field, dielectric constant, and boundary conditions for electric fields.
2. Conductors allow free electron flow while insulators have a large band gap; semiconductors have a small gap allowing electron excitation. Current density relates to charge velocity and conductivity.
3. Dielectrics have bound electric dipoles that contribute to polarization. The polarization field depends on dipole density and alignment with the electric field. Boundary conditions require continuous tangential E and normal D fields.
The document describes electric potential and how it relates to electric potential energy and electric field. It defines electric potential (V) as the electric potential energy per unit charge at a point. V is a scalar quantity. The potential difference between two points is equal to the work done by the electric field to move a test charge between the points. Equipotential surfaces connect all points of equal potential. The potential due to a point charge or group of point charges can be calculated using equations provided.
This document discusses the origin of inertia and how gravity can account for inertial reaction forces. It summarizes Dennis Sciama's 1953 argument that showed how the gravitational interaction of local matter with distant matter, modeled similarly to electric charges and electromagnetic fields, can produce inertial forces. Later work by D.J. Raine and others showed this is true in general relativity. However, subtleties remain regarding how distant matter could "know" to produce the right reaction forces instantaneously, as inertia is observed. Possible explanations involving instantaneous or retrocausal interactions are discussed.
This document provides an analysis of quantizing energy levels for the Schwarzschild gravitational field using the prescriptions of Old Quantum Theory. It begins with introducing the Schwarzschild metric and deriving the Lagrangian for motion in a central gravitational field. It then applies the Bohr-Sommerfeld quantization rule to obtain expressions for angular momentum and energy as quantized values. Integrating these expressions provides a very simple formula for the quantized energy levels in the Schwarzschild field within the Old Quantum Theory framework.
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
More Related Content
Similar to The Center of Mass Displacement Caused by Field-Charge Interaction Can Solve the Electromagnetic 4/3 Problem
A model is proposed to show that the electron spin may not be purely intrinsic but the result of a loop of current with two different components interacting between them
This document discusses the energy characteristics of interactions between particles and systems. It introduces the concept of a spatial-energy parameter (P-parameter) to describe interactions. The key points are:
1) Interactions along a potential gradient (positive work) calculate the resulting potential energy by adding reciprocals of subsystem energies. Interactions against the gradient (negative work) add subsystem masses and energies algebraically.
2) P-parameter is proposed to quantify the energy of atom valence orbitals based on electron orbital energies and radii. For similar systems, P-parameters are added algebraically.
3) P-parameter is analogous to the quantum mechanical wave function and has wave properties. It provides a way to materialize
This article shows how to use a Green function to calculate the reaction force based in future external forces instead of using the time derivative of the acceleration, which leads to wrong results.
Mass, energy and momentum at cms i2 u2Tom Loughran
The document discusses mass, energy, and momentum at the CMS detector at the LHC. It explains that:
1) At high energies, energy and momentum are practically equivalent according to the equation E2 = p2 + m2, where mass terms become negligible. This allows energy to be calculated from momentum measurements.
2) The mass of a parent particle that decays can be determined by subtracting the momentum term p2 from the total energy term E2 of its decay products, giving m2.
3) At the LHC, initial energies and momenta of collisions are not precisely known, so conservation cannot be used directly, but transverse momentum is assumed to be zero initially and its conservation is used.
Sergey seriy thomas fermi-dirac theorySergey Seriy
This document presents modern ab-initio calculations based on Thomas-Fermi-Dirac theory with quantum, correlation, and multishell corrections. It summarizes extensions made to the statistical model by including additional energy terms to account for quantum corrections, exchange energy, and correlation energy. This leads to a quantum- and correlation-corrected Thomas-Fermi-Dirac equation involving a density term, kinetic energy density term, and modified potential function. Solving this quartic equation in the electron density provides a way to determine the electron density distribution as a function of distance from the nucleus.
Zero Point Energy And Vacuum Fluctuations EffectsAna_T
The document discusses several topics related to zero point energy and vacuum fluctuations:
1) It explains how the Heisenberg uncertainty principle leads to zero point energy, which is the lowest possible energy of a quantum system in its ground state.
2) It describes vacuum fluctuations as quantum fluctuations of fields even in their lowest energy state. These fluctuations can be thought of as virtual particles being created and destroyed in the vacuum.
3) Several phenomena are discussed that demonstrate the effects of zero point energy and vacuum fluctuations, including spontaneous emission, the Casimir effect, and the Lamb shift.
This document discusses wave equations and their applications. It contains 6 chapters that cover basic results of wave equations, different types of wave equations like scalar and electromagnetic wave equations, and applications of wave equations. The introduction explains that the document contains details about different types of wave equations and their applications in sciences. Chapter 1 discusses basic concepts like relativistic and non-relativistic wave equations. Chapter 2 covers the scalar wave equation. Chapter 3 is about electromagnetic wave equations. Chapter 4 is on applications of wave equations.
Movimiento De Una Partícula Cargada En Un Campo Eléctrico Y En Un Campo Magné...Gregory Zuñiga
The document discusses the mathematical modeling of the motion of a charged particle in electric and magnetic fields. It describes three cases: 1) motion in a uniform electric field, where the particle experiences a constant acceleration; 2) motion in a uniform magnetic field, where the particle travels in a circular path with radius determined by the magnetic field strength; and 3) motion in both uniform electric and magnetic fields perpendicular to each other, where the particle follows a helical path with the forces from the two fields balancing each other out under certain conditions. The modeling of the particle motion incorporates equations for forces, fields, energy, and kinematics.
This document describes a peridynamic model for simulating shape memory alloy composites. It presents the key equations of peridynamic theory, including the balance law accounting for internal forces between particles within a horizon. A simple 2D simulation in MATLAB is outlined using linear springs to model internal forces between particles within a defined horizon based on their displacement. The simulation calculates net internal and external forces on particles over time to model deformation, with the goal of upgrading the model in the future to include failure mechanisms.
This document summarizes key concepts in structural dynamics and aeroelasticity. It discusses three areas of interaction: between elasticity and dynamics, between aerodynamics and elasticity, and among all three. It then provides definitions and equations for rigid body dynamics, including Euler's laws. Subsequent sections cover transverse vibrations of strings, beams, and coupled bending-torsion behaviors in more complex structures. The concepts of stability are introduced, followed by discussions of single-degree-of-freedom systems, including free, forced, and resonant vibrations.
Electromagnetic waves are produced by time-varying electric and magnetic fields. Hertz experimentally proved this by showing that electromagnetic waves could be produced by oscillating electric currents. The electromagnetic wave equation describes electromagnetic waves traveling through space where there are no charges. Electric and magnetic fields of electromagnetic waves oscillate perpendicular to each other and perpendicular to the direction of propagation. Electromagnetic waves carry energy through space in the form of oscillating electric and magnetic fields. The Poynting vector represents the energy flux of an electromagnetic wave, pointing in the direction of wave propagation. Poynting's theorem relates the work done by electromagnetic forces on charges to energy stored in electromagnetic fields and energy flowing out of a given volume.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
Kinetic energy and gravitational potential energyfaisal razzaq
1) The document discusses kinetic energy and gravitational potential energy. Kinetic energy is the energy of an object in motion and depends on the object's mass and speed. Gravitational potential energy is the energy contained in an object above the ground and depends on the object's mass and position.
2) The gravitational field can be compared to an electric field. Both are conservative fields that represent the gradient of potential energy. Calculations of fields and potentials can be adapted from electricity to gravity.
3) The document makes analogies between the Coulomb force law in electricity and the gravitational force law. Both are foundations for their respective fields and phenomena can be described similarly using mathematical formulas.
Relativistic formulation of Maxwell equations.dhrubanka
This document discusses the relativistic formulation of Maxwell's equations. It begins by introducing the key concepts of special relativity that are needed, including Lorentz transformations and four-vectors. It then shows how the electric and magnetic fields transform under Lorentz transformations and how they can be combined into the electromagnetic field tensor. The document also discusses how charge and current densities transform and satisfy the continuity equation as a four-vector. Finally, it presents Maxwell's equations in their compact relativistic form in terms of the field tensor and its derivatives.
EMF ELECTROSTATICS:
Coulomb’s Law, Electric Field of Different Charge Configurations using Coulomb’s Law, Electric Flux, Field Lines, Gauss’s Law in terms of E (Integral Form and Point Form), Applications of Gauss’s Law, Curl of the Electric Field, Electric Potential, Calculation of Electric Field Through Electric Potential for given Charge Configuration, Potential Gradient, The Dipole, Energy density in the Electric field.
1. The document discusses conductors, dielectrics, current density, polarization, and electric susceptibility. It defines key concepts like current, current density, polarization field, dielectric constant, and boundary conditions for electric fields.
2. Conductors allow free electron flow while insulators have a large band gap; semiconductors have a small gap allowing electron excitation. Current density relates to charge velocity and conductivity.
3. Dielectrics have bound electric dipoles that contribute to polarization. The polarization field depends on dipole density and alignment with the electric field. Boundary conditions require continuous tangential E and normal D fields.
The document describes electric potential and how it relates to electric potential energy and electric field. It defines electric potential (V) as the electric potential energy per unit charge at a point. V is a scalar quantity. The potential difference between two points is equal to the work done by the electric field to move a test charge between the points. Equipotential surfaces connect all points of equal potential. The potential due to a point charge or group of point charges can be calculated using equations provided.
This document discusses the origin of inertia and how gravity can account for inertial reaction forces. It summarizes Dennis Sciama's 1953 argument that showed how the gravitational interaction of local matter with distant matter, modeled similarly to electric charges and electromagnetic fields, can produce inertial forces. Later work by D.J. Raine and others showed this is true in general relativity. However, subtleties remain regarding how distant matter could "know" to produce the right reaction forces instantaneously, as inertia is observed. Possible explanations involving instantaneous or retrocausal interactions are discussed.
This document provides an analysis of quantizing energy levels for the Schwarzschild gravitational field using the prescriptions of Old Quantum Theory. It begins with introducing the Schwarzschild metric and deriving the Lagrangian for motion in a central gravitational field. It then applies the Bohr-Sommerfeld quantization rule to obtain expressions for angular momentum and energy as quantized values. Integrating these expressions provides a very simple formula for the quantized energy levels in the Schwarzschild field within the Old Quantum Theory framework.
Similar to The Center of Mass Displacement Caused by Field-Charge Interaction Can Solve the Electromagnetic 4/3 Problem (20)
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills MN
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
ESPP presentation to EU Waste Water Network, 4th June 2024 “EU policies driving nutrient removal and recycling
and the revised UWWTD (Urban Waste Water Treatment Directive)”
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
BREEDING METHODS FOR DISEASE RESISTANCE.pptxRASHMI M G
Plant breeding for disease resistance is a strategy to reduce crop losses caused by disease. Plants have an innate immune system that allows them to recognize pathogens and provide resistance. However, breeding for long-lasting resistance often involves combining multiple resistance genes
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...AbdullaAlAsif1
The pygmy halfbeak Dermogenys colletei, is known for its viviparous nature, this presents an intriguing case of relatively low fecundity, raising questions about potential compensatory reproductive strategies employed by this species. Our study delves into the examination of fecundity and the Gonadosomatic Index (GSI) in the Pygmy Halfbeak, D. colletei (Meisner, 2001), an intriguing viviparous fish indigenous to Sarawak, Borneo. We hypothesize that the Pygmy halfbeak, D. colletei, may exhibit unique reproductive adaptations to offset its low fecundity, thus enhancing its survival and fitness. To address this, we conducted a comprehensive study utilizing 28 mature female specimens of D. colletei, carefully measuring fecundity and GSI to shed light on the reproductive adaptations of this species. Our findings reveal that D. colletei indeed exhibits low fecundity, with a mean of 16.76 ± 2.01, and a mean GSI of 12.83 ± 1.27, providing crucial insights into the reproductive mechanisms at play in this species. These results underscore the existence of unique reproductive strategies in D. colletei, enabling its adaptation and persistence in Borneo's diverse aquatic ecosystems, and call for further ecological research to elucidate these mechanisms. This study lends to a better understanding of viviparous fish in Borneo and contributes to the broader field of aquatic ecology, enhancing our knowledge of species adaptations to unique ecological challenges.
Cytokines and their role in immune regulation.pptx
The Center of Mass Displacement Caused by Field-Charge Interaction Can Solve the Electromagnetic 4/3 Problem
1. The Center of Mass Displacement Caused by Field-Charge
Interac on Can Solve the Electromagne c 4/3 Problem
Sergio Prats López, August 2023
Abstract
The 4/3 problem happens when calcula ng the electromagne c (EM) momentum and energy
(ME) for a spherical shell uniformly charged that can be considered a "par cle". It turns out
that for low veloci es the rela onship between the momentum p and the energy U is
𝒗
instead of being just 𝑈 as one would expect.
I assert in this paper that, for a system interac ng with its environment in a way where it is
ge ng energy gains in some regions and energy losses in other regions, there may be a net
contribu on to the system's momentum propor onal to the amount of energy gained at each
point mul plied by the space vector from that point to the system's center of mass. This can
add an extra term to the par cle's momentum even for a system whose overall energy is kept
constant but where the gains and losses of energy happen at different places.
For a charged shell moving with velocity v, the region where 𝑱 · 𝑬 > 0, "the front", is the one
where the EM field is losing energy while the opposite region "the back" is the one where the
field gains energy, I will show how this effect adds a term of momentum whose value is −
1
3
𝒗
𝑐2
.
2. Rela on between iner al momentum and center of mass evolu on
For a classical, non-rela vis c point par cle with mass m and at posi on x, the rela onship
between the iner al momentum and the mass is straigh orward:
𝒑 = 𝑚𝒙̇ [1]
This rela onship is barely modified by the special rela vity, it only adds the "rest mass", which
is constant while the actual mass depends on the speed as 𝑚 = = 𝛾𝑚 , 𝛾 =
𝒑 = 𝛾𝑚 ∗ 𝒙̇ [2]
This defini on can be extended to a non-point par cle whose density at every point is
expressed as 𝐽 = [𝑢, 𝒑], by using the center of mass:
𝑿𝟎 = ∫ 𝑢 ∗ 𝒙𝑑𝒙 [3a]
𝑈 = ∫ 𝑢𝑑𝒙 = 𝑚𝑐 [3b]
The par cle momentum can be defined as the way the center of mass changes per unit of
me, mul plied by the iner al mass:
𝑷 = 𝑿
̇ 𝟎 = 𝑚𝑿
̇ 𝟎 [4]
According to [4], a moving charged sphere whose EM field has energy U, should have a
momentum of 𝒗𝑈, not 𝒗𝑈, which is in fact the issue.
Classically, the only source of movement considered is the flow of mass-energy, which can be
obtained by integra ng the local momentum p, I will call 𝑿
̇ 𝟎 to this quan ty, so that 𝑿
̇ 𝟎 will
include the term introduced in this document.
𝑷′ = ∫ 𝒑𝑑𝒙 [5a]
𝑿
̇ 𝟎 = 𝑷′ [5]
Effect of interac ons in the par cle's center of mass
For any par cle that can be represented as a field 𝐽 , the con nuity equa ons will grant that,
in absence of external sources, energy and momentum will be conserved locally, therefore
expression [1] should not only hold globally, that is, like expression [4], but also locally at every
point of space: the energy at any point flows with velocity 𝒗 =
𝒑
, this is for example the case
for the electromagne c field in open space.
On the other hand, when a system is interac ng with an external source, it is no longer granted
that its momentum-energy (ME) will be conserved, either locally or globally, since the
conserva on rules apply to the sum of the interac ng system, not to each of them individually.
Now I will consider two different scenarios: the first one in which the global ME is not
conserved:
3. [𝑈, 𝑷] = 𝑈̇ , 𝑷
̇ ≠ [0, 𝟎] [6]
The second scenario is the one in which ME is conserved globally but not locally (no ce that if
ME was conserved locally everywhere, there would be no interac on at all).
𝑈̇ , 𝑷
̇ = [0, 𝟎], [𝑢̇, 𝒑] ≠ [0, 𝟎] [7]
In the second scenario the interac on is not affec ng globally the basic physical proper es of
energy and momentum, however, it could be affec ng other proper es such as the angular
momentum or the center of mass, and by affec ng the center of mass, according to [4] the
interac on would be affec ng the global momentum for the par cle. In the second scenario,
the effect of interac on in the center of mass can be defined as:
𝑿
̇ 𝟎 = 𝑿
̇ 𝟎 + ∫(𝒙 − 𝑿𝟎)𝑃 𝑑𝒙 [8]
In the previous expression 𝑿
̇ 𝟎 is the quan ty defined at [5], that is, the classical way to
calculate the iner al momentum.
I will call "Interac on Term" to the second term from [8], it contains the "displacement" caused
by the source or sink of energy (the interac on) in the center of mass. 𝑃 is the amount of
power, transferred from the par cle to the interac ng system. For example, if the EM field
interacts with a charge, the amount of power the EM field would be transferring to the charge
would be 𝑱 · 𝑬, therefore for the charge 𝑃 = 𝑱 · 𝑬, while for the field it would be the opposite,
𝑃 = −𝑱 · 𝑬.
Expression [8] shows us that the existence of sources and sinks (places where our system
interacts with the environment) can affect the way the center of mass of a par cle evolves with
me, if we want [4] s ll to be valid when an interac on is happening then we need to add the
interac on term to the defini on of global momentum:
𝑷 = ∫ 𝒑𝑑𝒙 + ∫(𝒙 − 𝑿𝟎)𝑃 𝑑𝒙 [9]
This is the expression for the iner al momentum of a par cle that I propose. The second term
should be included any me that the par cle is interac ng with its environment, not only in
the interac ons of "second type" defined by [7] but also in the "first type" ones, defined by [6].
It is important to remark that because of the interac on term, the total momentum is no
longer the integra on of local momentums.
One could be tempted to modify the local momentum by doing something like this: 𝒑 = 𝒑 +
(𝒙 − 𝑿𝟎) . However, the idea of adding the interac on term to the local momentum must
be discarded because we want the local momentum to tell us how much is moving the energy
at some point, we expect that, for a point with current [u, p], the energy at this point is moving
with velocity 𝒗 =
𝒑
, with no dependency on where the center of mass is. Besides, the
con nuity equa on 𝜕 𝑢 + 𝑐 ∇ · 𝒑 = 𝑃 is altered in an undesirable way by an unwanted (𝒙 −
𝑿𝟎) · ∇𝑃 + 3𝑃 term.
From the previous considera ons I assert that the interac on term is needed to calculate the
par cle's center of mass me evolu on and therefore, it should be included in the total
momentum, but this term should not be added to the local momentum, which means that the
4. interac on makes the physical proper es for the par cle no to be only the sum/integra on of
its local proper es.
Calcula ng the Effect of the Interac on Term in the 4/3 Problem
Let we have a par cle whose charge is uniformly spread over a spherical surface of radius R,
the overall charge is Q and it is moving with velocity 𝑣 𝑧̂, being v much smaller than the speed
of light (𝑣 ≪ 𝑐) and suffering no accelera on. The EM field is zero inside the sphere and
outside it is the same that would be created by a charge of value q located in the center.
For rela vis c low veloci es we can approximate the EM field energy as the one for a sta c
charge:
𝑈 = ∫ 4𝜋𝑟 𝑑𝑟 = ∗ ≡ [10]
The momentum in the Z direc on can be obtained to first order of v by applying the cross product
to the radial component of E against B.
𝑝 = (𝜀 (𝑬 × 𝑩) · 𝑧̂)𝑧̂ ≅ E (𝑟̂ × (𝑣𝑧̂ × 𝑟̂)) = E sin (𝜃) [11]
When integra ng the momentum over the sphere we get:
𝑃 = ∫ ∫ E sin (𝜃) ∗ 2𝜋𝑟 ∗ sin(𝜃) 𝑑𝜃𝑑𝑟 = = 𝑈 [12]
For the previous result I have used ∫ sin (𝜃)𝑑𝜃 = − cos(𝜃) +
( )
To calculate the "interac on term", since we are studying the EM field created by an isolated
par cle, we only need to evaluate the interac on between the charged surface and the field. If
we center the par cle and use spherical coordinates, the density of charge can be described as:
𝑞 = 𝛿(𝑟 − 𝑅) [13]
Since the charge is moving with velocity v, the current can be defined as:
𝒋 = 𝒗𝑞 = 𝑣𝑞𝑧̂ [14]
Next, we need to calculate the interac on between field and charge, that interac on for the
field is −𝑬 · 𝒋, thus, we need to calculate the electric field on the spherical surface. This is in
fact, troublesome, since the electric field for a spherical surface is defined for values greater or
smaller than the shell radius:
𝑬 = 0 𝑓𝑜𝑟 𝑟 < 𝑅 [15a]
𝑬 = 𝑟̂ 𝑓𝑜𝑟 𝑟 > 𝑅 [15b]
To solve this, we can turn this surface into a very thin sphere, whose thickness is 𝑑𝑙 ≪ 𝑅. We
can now assert that each of the infinitesimal shells creates an electric field that affects only to
the shells outside it, this way, if the charge is between radius R-dl and R, the electric field in the
region where the charge exists will be:
5. 𝑬 = 𝑟̂ = 1 − 𝑟̂, 𝑅 − 𝑑𝑙 ≤ 𝑟 < 𝑅 [16]
𝑄 = 𝑄 1 − is the charge from the shells that are closer to the center than r. This is the
field that a charged shell surface would see at distance r, if we integrate to average it, the result
we get is that the effec ve EM field in the surface is:
𝑬𝒔 = 𝑟̂ [17]
We can define the interac on term on each point of the sphere as:
𝑃 = −𝑬𝒔 · 𝒋 = − ( )
𝑐𝑜𝑠(𝜃) [18]
Now, if we integrate on the surface replacing 𝒙 with 𝑅𝑐𝑜𝑠(𝜃) (since we are only interested in
the Z component), we get the interac on term contribu on to the momentum:
𝑷𝒊𝒕 =
1
𝑐
2𝜋𝑅 ∗ 𝑅𝑐𝑜𝑠(𝜃) ∗ −
1
2
𝑄2
(4𝜋)2𝜀0𝑅4 𝑐𝑜𝑠(𝜃) ∗ sin(𝜃) 𝑑𝜃 𝑧
𝑷𝒊𝒕 = −
𝒗
𝜀0
= −
𝒗
𝜀0
= −
𝒗
𝑈 [19]
For the previous result we use ∫ 𝑐𝑜𝑠 (𝜃) sin(𝜃) 𝑑𝜃 = − cos (𝜃).
Now, when we add the interac on term to the momentum, we get the quan ty in accordance
with the EM's energy:
𝑷 = 𝑷 + 𝑷𝒊𝒕 = 𝑈 − 𝑈 = 𝑈 = 𝑣 ∗ 𝑚 [20]
6. Discussion about the interac on between a par cle's charge and field
In the interac on between the charge and the field from the same par cle several ques ons
may arise. The first one is where the 𝑬𝒔 · 𝒋 energy term is transferred. The integral of this term
around the sphere is zero so there is no net energy transfer between the charge and the field
as one would expect for a charge with no accelera on, however it is also relevant what is
happening locally with the energy and momentum being transferred.
For this ques on I am not going to write an answer in this paper but only to discuss some
possibili es, one might be to consider that the par cle has a "material" mass associated to the
charged surface, that is, where there is charge (and current) there is also mass (and
momentum) in a way that we can define a constant 𝑘 = 𝑚 /𝑞 to define the rela onship
between the quan ty of mass and charge at any point, and this constant will also hold for the
rela onship between the momentum and current.
With this approach, we can assume that the momentum-energy for the field is transformed
into mechanical ME locally, then some forces such as the Poincaré stresses would balance
locally the forces caused by the EM field on the charge, making possible for the charged sphere
to remain in the same shape.
While the previous approach seems consistent on the EM field side, it is not a well-defined
solu on from the "material" or charge side since some ques ons remain: How are the
Pointcaré stresses created? What is causing them? Is there some poten al holding these
stresses?
I would like to suggest another possibility to avoid this problem, it would be to add an internal
EM field that is transparent to everybody except to one charged par cle, which creates it. This
par cle is the only one that can interact with this field which I call "correc ve field".
We can split the EM tensor 𝐹 for the overall EM field into two parts:
𝐹 = 𝐹 ( ) + 𝐹 ( ) [21]
The first part is the field caused by the single par cle's charge distribu on, the second one is the
field created by the rest of the world. The effect of 𝐹 ( ) on the par cle (the self-force), can be
cancelled by crea ng the correc ve field as follows:
The correc ve field is created by an imaginary charge distribu on which is exactly equal to the
par cle's (real) charge distribu on mul plied by the imaginary number i.
𝑞 = 𝑞 ∗ 𝑖 [22]
There will be a correc ve EM field space created by this imaginary charge and nothing more,
since the rest of the charges in the world are not contribu ng to this EM field, they are not going
to interact with it, this field is invisible for them. The field will take this value:
𝐹 ( ) = 𝑖 ∗ 𝐹 ( ) [23]
The field is purely imaginary, but its effects are real since it interacts with 𝑞 , which is also
imaginary ge ng a minus sign, since 𝑖 = −1. The force caused by 𝐹 ( ) on 𝑞 is real and it
cancels the force caused by 𝐹 ( ) on q, since the par cle is experiencing both forces, the result
is that the field created by the charge is not ac ng over it. The correc ve field also has a
7. nega ve density of energy and a momentum that cancels exactly the energy and momentum
that the internal field has.
By using this correc ve field, the Poincaré stresses are no longer needed to keep the charged
shell stable, however it goes further and removes the whole energy from the par cles field,
and causing that, let this approach be valid, the energy in the EM field would be only caused by
the interac ons between different par cles.
The correc ve field approach is not free of issues since it would cancel the Larmor radia on
term when the par cle is accelera ng, this term, connected to the Abraham-Lorentz-Dirac
force, seems to be real, therefore this approach should be enhanced and that goes beyond the
aim of this discussion.
Conclusions
When working with extended par cles, the interac on with external systems can cause a flow
of energy at different points that can cause the center of mass to move, this movement should
be computed as part of the par cle's iner al momentum, although it is not of a local nature
and should not be considered to compute how fast the mass at some point is moving.
By evalua ng the interac on between a par cle's charge and the EM field created by it, we
find that the displacement of the center of mass adds a contribu on to the par cle's field
momentum that makes changes it from 𝑈 to 𝑈 solving the issue.
One last insight can be obtained that can be brought to another areas of physics:
Some mes global magnitudes for a par cle are not equal to the integra on of its local
counterparts but they may also include other terms of a global nature.
References
- The Feynman Lectures on Physics, Volume II – Richard P Feynman:
h ps://www.feynmanlectures.caltech.edu/II_28.html
- Classical theory of radia ng electrons - P. A. M Dirac, 1938:
h ps://royalsocietypublishing.org/doi/10.1098/rspa.1938.0124
- Inclusion of a Field Shi Term for the 4/3 Classical Electrodynamics Problem:
h ps://www.slideshare.net/SergioPL81/adding-a-shi -term-to-solve-the-43-problem-
in-classical-electrodinamics
- An Apology to Dirac's Reac on Force Theory -
h ps://www.slideshare.net/SergioPL81/an-apologytodiracsreac onforcetheory
- Electromagne c mass: h ps://en.wikipedia.org/wiki/Electromagne c_mass