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.Comment: 10 page

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.Comment: 10 page

Interaction of a Point Charge and a Magnet: Comments on "Hidden Mechanical Momentum Due to Hidden Nonelectromagnetic Forces"

The interaction of a point charge and a magnetic moment (and by extension a point charge and a solenoid) is explored within well-defined point-charge magnetic-moment models where full calculations are possible. It is shown explicitly how the "hidden mechanical momentum" is introduced by the "hidden" external forces of constraint, requiring a prescribed response (through order 1/c^2) of the system to electromagnetic forces. These external forces often go unmentioned in the textbook and research literature. The dependence of "hidden mechanical momentum" upon detailed external (nonelectromagnetic) forces may undermine the idea's usefulness in describing nature. Some statements of dubious validity in the textbook literature are noted.Comment: 36 page

Connecting blackbody radiation and zero-point radiation within classical physics: A new minimum principle and a status review

A new thermodynamic analysis is presented for the intimate connections between blackbody radiation and zero-point radiation within classical physics. First, using the thermodynamic behavior of an oscillator under an adiabatic change of frequency, we show that the thermodynamic functions can all be derived from a single function of w/T, analogous to Wien's displacement theorem. The high- and low-frequency limits allow asymptotic energy forms involving T alone or w alone, corresponding to energy equipartition and zero-point energy. It is then suggested that the actual thermodynamic behavior for a harmonic oscillator is given by the function satisfying the Wien displacement result which provides the smoothest possible interpolation between scale-decoupled energy equipartition at low frequency and scale-invariant zero-point energy at high frequency. This leads to the Planck spectrum. Second, we turn to radiation in a box with conducting walls and a conducting partition so that the discrete normal mode structure of the box becomes important. The contrasting Casimir energies are explored for the Rayleigh-Jeans and zero-point spectra. The Rayleigh-Jeans spectrum involves no change of energy with partition position, and the zero-point spectrum involves no change of entropy. It is suggested that the Planck spectrum with zero-point radiation satisfies a natural minimum principle which corresponds to greatest independence of the system energy from the position of the partition for a fixed temperature. Numerical calculation is used for confirmation. Third, we review the previous derivations of the Planck radiation spectrum in classical physics, all of which involve zero-point radiation.Comment: 22 page

Concerning Hidden Momentum

The fact that the author of an excellent textbook on electromagnetism could be duped by "hidden momentum" vividly illustrates the problematic nature of its use.Comment: 4 page

Blackbody Radiation in Classical Physics: A Historical Perspective

We point out that current textbooks of modern physics are a century out-of-date in their treatment of blackbody radiation within classical physics. Relativistic classical electrodynamics including classical electromagnetic zero-point radiation gives the Planck spectrum with zero-point radiation as the blackbody radiation spectrum. In contrast, nonrelativistic mechanics cannot support the idea of zero-point energy; therefore if nonrelativistic classical statistical mechanics or nonrelativistic mechanical scatterers are invoked for radiation equilibrium, one arrives at only the low-frequency Rayleigh-Jeans part of the spectrum which involves no zero-point energy, and does not include the high-frequency part of the spectrum involving relativistically-invariant classical zero-point radiation. Here we first discuss the correct understanding of blackbody radiation within relativistic classical physics, and then we review the historical treatment. Finally, we point out how the presence of Lorentz-invariant classical zero-point radiation and the use of relativistic particle interactions transform the previous historical arguments so as now to give the Planck spectrum including classical zero-point radiation. Within relativistic classical electromagnetic theory, Planck's constant h appears as the scale of source-free zero-point radiation.Comment: 40 page

Connecting Blackbody Radiation, Relativity, and Discrete Charge in Classical Electrodynamics

It is suggested that an understanding of blackbody radiation within classical physics requires the presence of classical electromagnetic zero-point radiation, the restriction to relativistic (Coulomb) scattering systems, and the use of discrete charge. The contrasting scaling properties of nonrelativistic classical mechanics and classical electrodynamics are noted, and it is emphasized that the solutions of classical electrodynamics found in nature involve constants which connect together the scales of length, time, and energy. Indeed, there are analogies between the electrostatic forces for groups of particles of discrete charge and the van der Waals forces in equilibrium thermal radiation. The differing Lorentz- or Galilean-transformation properties of the zero-point radiation spectrum and the Rayleigh-Jeans spectrum are noted in connection with their scaling properties. Also, the thermal effects of acceleration within classical electromagnetism are related to the existence of thermal equilibrium within a gravitational field. The unique scaling and phase-space properties of a discrete charge in the Coulomb potential suggest the possibility of an equilibrium between the zero-point radiation spectrum and matter which is universal (independent of the particle mass), and an equilibrium between a universal thermal radiation spectrum and matter where the matter phase space depends only upon the ratio mc^2/kT. The observations and qualitative suggestions made here run counter to the ideas of currently accepted quantum physics.Comment: 31 page

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.Comment: 19 page

Semiclassical Explanation of the Matteucci-Pozzi and Aharonov-Bohm Phase Shifts

Classical electromagnetic forces can account for the experimentally observed phase shifts seen in an electron interference pattern when a line of electric dipoles or a line of magnetic dipoles (a solenoid) is placed between the electron beams forming the interference pattern.Comment: 8 page

The Contrasting Roles of Planck's Constant in Classical and Quantum Theories

We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.Comment: 9 page