V. Hnizdo

Hidden momentum and the electromagnetic mass of a charge and current carrying body

The contribution of the electromagnetic self-field to the energy and momentum of a charge and/or current carrying body is considered within classical physics and discussed in simple terms using nontrivial exactly solvable examples. The Lorentz-transformation properties of the energy and momentum of the body can be maintained by taking into account the relativistic effects of the mechanical stresses due the sources of the self-field, or by separating the energy and momentum of a moving self-field from those of a nonelectromagnetic origin in a relativistically covariant way. In either procedure, a proper account must be taken of the hidden mechanical momentum that, in general, is contained in a stationary body that carries both charge and current, and which is equal and opposite to the momentum of the static electromagnetic self-field. Hidden momentum and the momentum of a static electromagnetic field are indispensable concepts of direct physical significance in classical electrodynamics.

Conservation of linear and angular momentum and the interaction of a moving charge with a magnetic dipole

The operation of the laws of momentum and angular momentum conservation in the interactions between current‐carrying bodies and charged particles is analyzed using the correct expression for the force on a magnetic dipole, which takes into account the possible presence of hidden momentum in a current‐carrying body. At nonrelativistic velocities, Newton’s third law holds for the interactions, and thus the mechanical momentum associated with the motion of current‐carrying bodies and charged particles in a closed system is conserved itself in the nonrelativistic limit. There is no conflict with overall linear momentum conservation because the electromagnetic field momentum is equal and opposite to the hidden momentum of the current‐carrying bodies. However, the field angular momentum in a system is not compensated by hidden angular momentum, and thus only the sum of mechanical angular momentum, which must include any hidden angular momentum, and field angular momentum is conserved.

Hidden mechanical momentum and the field momentum in stationary electromagnetic and gravitational systems

The existence of hidden momentum, i.e., the mechanical momentum of a body the constituents of which move in a stationary manner but the center of mass of which is at rest in an external static field of force, is shown to follow from the general requirements of relativistic mechanics of continuous media, independently of whether the external forces are electromagnetic or gravitational. The hidden mechanical momentum is compensated by the momentum of the static fields in the system, necessitating, in the gravitational case, the existence of a gravinetic quasistatic gravitational field, which, in analogy to the magnetostatic field, is generated by a quasistationary current of mass and acts on a moving mass.

MICROSCOPIC T-VIOLATING OPTICAL POTENTIAL : IMPLICATIONS FOR NEUTRON-TRANSMISSION EXPERIMENTS

We derive a [ital T]-violating [ital P]-conserving optical potential for neutron-nucleus scattering, starting from a uniquely determined two-body [rho]-exchange interaction with the same symmetry. We then obtain limits on the [ital T]-violating [rho]-nucleon coupling [ital [bar g]][sub [rho]] from neutron-transmission experiments in [sup 165]Ho. The limits may soon compete with those from measurements of atomic electric-dipole moments.

Covariance of the total energy–momentum four-vector of a charge and current carrying macroscopic body

The relativistic covariance of the four-vector of the total energy–momentum of a macroscopic body that, in its rest frame, carries general stationary macroscopic charge and current distributions is demonstrated in explicit detail using the balancing of the forces in the body, the existence of hidden mechanical momentum, and the Lorentz-transformation properties of the energy-momentum four-tensors of the “mechanical” and “electromagnetic” parts of the system.

Hidden Momentum and the Force on a Magnetic Dipole

The problem of the correct expression for the force on a magnetic dipole in vacuum is discussed. Different models of magnetic dipole are considered and particular attention is given to the presence of hidden momentum, which modifies the usual expression for the force on a current-loop dipole when the external electromagnetic field is not static.

Geometric factors in the Bohr-Rosenfeld analysis of the measurability of the electromagnetic field

The geometric factors in the field commutators and spring constants of the measurement devices in the famous analysis of the measurability of the electromagnetic field by Bohr and Rosenfeld are calculated using a Fourier-Bessel method for the evaluation of folding integrals, which enables one to obtain the general geometric factors as a Fourier-Bessel series. When the space regions over which the factors are defined are spherical, the Fourier-Bessel series terms are given by elementary functions, and using the standard Fourier-integral method of calculating folding integrals, the geometric factors can be evaluated in terms of manageable closed-form expressions.

Analytical evaluation of the finite-radius Fourier transform of the Uehling potential

The finite-radius Fourier transform of the first-order vacuum-polarization correction to the Coulomb potential of a point charge, required for a Fourier-Bessel evaluation of vacuum-polarization potentials of extended charges, is calculated by an efficient analytical method.

Evaluation of folding integrals using Fourier-Bessel expansions

The conditions are examined under which Fourier-Bessel expansions can be used correctly in the evaluation of multiple folding integrals. A proper formulation of the method is given.

Vacuum-polarization potentials of extended nuclear charges

Abstract FORTRAN program VACPOL is presented that calculates accurately and efficiently the first-order vacuum-polarization potential of two electric charges as a function of their separation. The charges can be extended, with distributions specified by density functions that are most often used to model the distribution of charge in atomic nuclei. The code employs analytical methods of calculation, utilizing a Fourier-Bessel expansion of the potential and an analytical evaluation of the finite-radius Fourier transform of the point-charge Uehling potential.