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Timothy H. Boyer

Publications and source records attributed to Timothy H. Boyer.

At least 55 records · Page 3Linked to original sources
arXiv2014

Faraday Induction and the Current Carriers in a Circuit

In this article, it is pointed out that Faraday induction can be treated from an untraditional, particle-based point of view. The electromagnetic fields of Faraday induction can be calculated explicitly from approximate point-charge fields derived from the Liénard-Wiechert expressions or from the Darwin Lagrangian. Thus the electric fields of electrostatics, the magnetic fields of magnetostatics, and the electric fields of Faraday induction can all be regarded as arising from charged particles. Some aspects of electromagnetic induction are explored for a hypothetical circuit consisting of point charges which move frictionlessly in a circular orbit. For a small number of particles in the circuit (or for non-interacting particles), the induced electromagnetic fields depend upon the mass and charge of the current carriers while energy is transferred to the kinetic energy of the particles. However, for an interacting multiparticle circuit, the mutual electromagnetic interactions between the particles dominate the behavior so that the induced electric field cancels the inducing force per unit charge, the mass and charge of the individual current carriers become irrelevant, and energy goes into magnetic energy.

physics.class-ph↗
arXiv2014

Classical Interaction of a Magnet and a Point Charge: The Classical Electromagnetic Forces Responsible for the Aharonov-Bohm Phase Shift

A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of classical electromagnetic theory which are unfamiliar to most physicists, including the Darwin Lagrangian, acceleration-based electric fields, internal electromagnetic momentum in a magnet, and a magnet model involving at least three mutually-interacting particles. Only when the acceleration-based electric forces acting on the passing charge are included do we find consistency with all the relativistic conservation laws: energy, linear momentum, angular momentum, and constant center-of-mass velocity. The electric forces on the passing charge lead to a lag effect which accounts quantitatively for the Aharonov-Bohm phase shift. Thus the classical analysis strongly suggests that the Aharonov-Bohm phase shift (observed when electrons pass a long solenoid which corresponds to a line of magnetic dipoles) is the analogue of the Matteucci-Pozzi phase shift (observed when electrons pass a line of electric dipoles). The classical electromagnetic analysis suggests experiments to distinguish the proposed classical-based lag effect from the presently accepted view that the Aharonov-Bohm phase shift is a quantum topological effect arising from magnetic fluxes in the absence of classical electromagnetic forces.

physics.class-ph↗
arXiv2014

Self-Inductance and the Mass of Current Carriers in a Circuit

In this article, the self-inductance of a circular circuit is treated from an untraditional, particle-based point of view. The electromagnetic fields of Faraday induction are calculated explicitly from the point-charge fields derived from the Darwin Lagrangian for particles confined to move in a circular orbit. For a one-particle circuit (or for N non-interacting particles), the induced electromagnetic fields depend upon the mass and charge of the current carriers while energy is transferred to the kinetic energy of the particle (or particles). However, for an interacting multiparticle circuit, the mutual electromagnetic interactions between particles can dominate the behavior so that the mass and charge of the individual particles becomes irrelevant; the induced fields are then comparable to the inducing fields and energy goes into magnetic energy. In addition to providing a deeper understanding of self-inductance, the example suggests that the claims involving hidden mechanical momentum in connection with momentum balance for interacting multiparticle systems are unlikely to be accurate.

physics.class-ph↗
arXiv2014

Interaction of a Magnet and a Point Charge: Unrecognized Internal Electromagnetic Momentum Eliminates the Myth of Hidden Mechanical Momentum

A model calculation using the Darwin Lagrangian is carried out for a magnet consisting of two current-carrying charges constrained by centripetal forces to move in a circular path in the presence of the electric field from a distant external point charge. In the limit that the magnet's two charges are non-interacting, the calculation recovers the only valid calculation for hidden mechanical momentum. However, if the magnet's charges are mutually interacting, then there is internal electromagnetic linear momentum associated with the perturbed magnet's electrostatic charge distribution and the motion of the magnet's charges. This internal electromagnetic momentum does not seem to be recognized as distinct from the familiar external electromagnetic momentum associated with the electric field of the external charge and the magnetic field of the unperturbed magnet. In the multiparticle limit, the hidden mechanical momentum becomes negligible while the internal electromagnetic momentum provides the compensating linear momentum required by the relativistic conservation law connecting the total linear momentum to motion of the center of energy. Whereas the changes in the external electromagnetic momentum are often associated with magnetic forces of order $1/c^{2},$ changes in the internal electromagnetic momentum are associated with the electrical forces of order $1/c^{2}$. These electrical forces are relevant to the Shockley-James paradox and to the experimentally observed Aharonov-Bohm and Aharonov-Casher phase shifts.

physics.class-ph↗
arXiv2014

Classical Interaction of a Magnet and a Point Charge: The Shockley-James Paradox

It is pointed out that Coleman and Van Vleck make a major blunder in their discussion of the Shockly-James paradox by designating relativistic hidden mechanical momentum as the basis for resolution of the paradox. This blunder has had a wide influence in the current physics literature, including erroneous work on the Shockley-James paradox, on Mansuripur's paradox, on the motion of a magnetic moment, on the Aharonov-Bohm phase shift, and on the Aharonov-Casher phase shift. Although hidden mechanical momentum is indeed dominant for non-interacting particles moving in a closed orbit under the influence of an external electric field, the attention directed toward hidden mechanical momentum represents a fundamental misunderstanding of the classical electromagnetic interaction between a multiparticle magnet and an external point charge. In the interacting multiparticle situation, the external charge induces an electrostatic polarization of the magnet which leads to an internal electromagnetic momentum in the magnet where both the electric and magnetic fields for the momentum are contributed by the magnet particles. This internal electromagnetic momentum for the interacting multiparticle situation is equal in magnitude and opposite in direction compared to the familiar external electromagnetic momentum where the electric field is contributed by the external charged particle and the magnetic field is that due to the magnet. In the present article, the momentum balance of the Shockley-James situation for a system of a magnet and a point charge is calculated in detail for a magnet model consisting of two interacting point charges which are constrained to move in a circular orbit on a frictionless ring with a compensating negative charge at the center.

physics.class-ph↗
arXiv2013

Is Planck's Constant h a "Quantum" Constant? An Alternative Classical Interpretation

Although Planck's constant h is currently regarded as the elementary quantum of action appearing in quantum theory, it can also be interpreted as the multiplicative scale factor setting the scale of classical zero-point radiation appearing in classical electromagnetic theory. Relativistic classical electron theory with classical electromagnetic zero-point radiation gives many results in agreement with quantum theory. The areas of agreement between this classical theory and Nature seem worth further investigation.

physics.class-ph↗
arXiv2012

Two Models Relevant to the Interaction of a Point Charge and a Magnetic Moment

An understanding of the interaction of a point charge and a magnetic moment is crucial for understanding the experiments involving electromagnetic momentum carried by permeable materials as well as the experimentally-observed Aharonov-Bohm and Aharonov-Casher phase shifts. Here we present two simple models for a magnetic moment which have vastly different interactions with a distant point charge. It is suggested that a satisfactory theoretical understanding of the interaction is still lacking and that the "hidden momentum" interpretation has been introduced into the textbook literature prematurely.

physics.class-ph↗
arXiv2012

Examples and Comments Related to Relativity Controversies

Recently Mansuripur has called into question the validity of the Lorentz force in connection with relativistic electromagnetic theory. Here we present some very simple point-charge systems treated through order v^{2}/c^{2} in order to clarify some aspects of relativistic controversies both old and new. In connection with the examples, we confirm the validity of the relativistic conservation laws. The relativistic examples make clear that external forces may produce a vanishing torque in one inertial frame and yet produce a non-zero torque in another inertial frame, and that the conservation of angular momentum will hold in both frames. We also discuss a relativistic point-charge model for a magnetic moment and comment on the interaction of a point charge and a magnetic moment. Mansuripur's claims of incompatibiltiy between the Lorentz force and relativity are seen to be invalid.

physics.class-ph↗
arXiv2012

Contrasting Classical and Quantum Vacuum States in Non-Inertial Frames

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. Based upon the classical analysis, it is suggested that the claimed heating effects of acceleration through the vacuum may not exist in nature.

gr-qc↗
arXiv2011

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.

physics.class-ph↗
arXiv2011

Any Classical Description of Nature Requires Classical Electromagnetic Zero-Point Radiation

Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. However, this zero-point radiation also leads to classical explanations for a number of phenomena which are usually regarded as requiring quantum physics. Here we provide a cursory overview of the classical electromagnetic theory which includes classical zero-point radiation, and we note the areas of agreement and disagreement between the classical and quantum theories, both of which contain Planck's constant h.

physics.class-ph↗
arXiv2010

Classical and Quantum Interpretations Regarding Thermal Behavior in a Coordinate Frame Accelerating Through Zero-Point Radiation

A relativistic classical field theory with zero-point radiation involves a vacuum corresponding to a scale-invariant spectrum of random classical radiation in spacetime with the overall constant chosen to give an energy (1/2)\hbarωper normal mode in inertial frames. Classical field theory with classical zero-point radiation gives the same field correlation functions as quantum field theory for the symmetrized products of the corresponding free massless fields in inertial frames; however, the interpretations in classical and quantum theories are quite different. Quantum field theory has photons in thermal radiation but not in the vacuum state; classical theory has radiation in both situations. The contrast in interpretations is most striking for the Rindler coordinate frame accelerating through zero-point radiation; classical theory continues tensor behavior over to the Rindler frame, whereas quantum theory introduces a new Rindler vacuum state. The classical interpretation of thermal behavior rests on two fundamental principles. i) A scale-invariant distribution of random radiation cannot correspond to thermal radiation at non-zero temperature. ii) A scale-invariant distribution of random radiation can acquire a correlation time which reflects the parameters of a spacetime trajectory through the scale-invariant radiation. Based on these principles, classical theory finds no basis for an accelerating observer to reinterpret zero-point radiation in terms of thermal radiation. In contrast, quantum field theory claims that an observer uniformly accelerated through zero-point flucturations of the Minkowski vacuum encounters a thermal bath at the temperature T=\hbar a/(2πck).

physics.class-ph↗
arXiv2010

Classical Physics of Thermal Scalar Radiation in Two Spacetime Dimensions

Thermal scalar radiation in two spacetime dimensions is treated within relativistic classical physics. Part I involves an inertial frame where are given the analogues both of Boltzmann's derivation of the Stefan-Boltzmann law and also Wien's derivation of the displacement theorem using the scaling of relativitic radiation theory. Next the spectrum of classical scalar zero-point radiation in an inertial frame is derived both from scale invariance and from Lorentz invariance. Part II involves the behavior of thermal radiation in a coordinate frame undergoing (relativistic) constant acceleration, a Rindler frame. The radiation normal modes in a Rindler frame are obtained. The classical zero-point radiation of inertial frames is transformed over to the coordinates of a Rindler frame. Although for zero-point radiation the two-field correlation function at different spatial points at a single time is the same between inertial and Rindler frames, the correlation function at two different times at a single Rindler spatial coordinate is different, and has a natural extension to non-zero temperature. The thermal spectrum in the Rindler frame is then transferred back to an inertial frame, giving the familar Planck spectrum.

physics.class-ph↗
arXiv2010

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.

physics.class-ph↗
arXiv2009

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter -radiation interaction are illustrated in a simple relativistic classical electromagnetic example.

physics.class-ph↗
arXiv2008

Illustrating Some Implications of the Conservation Laws in Relativistic Mechanics

The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the nonrelativistic conservation law for the center of restmass. Extension of the nonrelativistic interaction of particles through a potential to a system which is Lorentz-invariant through order v^2/c^2 is found to require new velocity- and acceleration-dependent forces which are suggestive of field theory where the no-interaction theorem of Currie, Jordan, and Sudershan does not hold.

physics.class-ph↗
arXiv2008

Relativistic Mechanics and a Special Role for the Coulomb Potential

It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz transformation through order v^2/c^2. However, this invariance requires the introduction of velocity-dependent and acceleration-dependent forces between particles. The textbook treatments of "relativistic mechanics" can be misleading; the discussions usually deal with only one particle experiencing prescribed forces and so make no mention of these additional velocity- and acceleration-dependent forces. A simple example for a situation analogous to a parallel-plate capacitor is analyzed for all the conservation laws of Galilean invariance or Lorentz invariance. For this system, Galilean invariance requires that the mechanical momentum is given by pmech=mv but places no restriction on the position-dependent potential function. On the other hand, Lorentz invariance requires that the mechanical momentum is given by pmech=mv/(1-v^2/c^2)^1/2, and in addition requires that the potential function is exactly the Coulomb potential V(|r1-r2|)=k/|r1-r2|. It is also noted that the transmission of the interparticle-force signal at the speed of light again suggests a special role for the Coulomb potential. A nonrelativistic particle system interacting through the Coulomb potential becomes the Darwin Lagrangian when extended to a system relativistic through order v^2/c^2, and then allows extension to classical electrodynamics as a fully Lorentz-invariant theory of interacting particles.

physics.class-ph↗