cases, the frequency is not generally a conserved quantity.) Feld-Tai reciprocity In 1992, a closely related reciprocity theorem was articulated independently by Y.A. Feld and C.T. Tai, and is known as Feld-Tai reciprocity or the Feld-Tai lemma. t relates two time-harmonic localized current sources and the resulting magnetic fields: However, the Feld-Tai lemma is only valid under much more restrictive conditions than Lorentz reciprocity. It generally requires time-invariant linear media with an isotropic homogeneous impedance, i.e. a constant scalar / ratio, with the possible exception of regions of perfectly conducting material. More precisely, Feld-Tai reciprocity requires the Hermitian (or rather, complex-symmetric) symmetry of the electromagnetic operators as above, but also relies on the assumption that the operator relating and is a constant scalar multiple of the operator relating and which is true when is a constant scalar multiple of (the two operators generally differ by an interchange of and ). As above, one can also construct a more general formulation for integrals over a finite volume. Optical reciprocity in radiometric terms Apart from quantal effects, classical theory covers near-, middle-, and far-field electric and magnetic phenomena with arbitrary time courses. Optics refers to far-field nearly-sinusoidal oscillatory electromagnetic effects. Instead of paired electric and magnetic variables, optics, including optical reciprocity, can be expressed in polarization-paired radiometric variables, such as spectral radiance, traditionally called specific intensity. In 1856, Hermann von Helmholtz wrote: "A ray of light proceeding from point arrives at point after suffering any number of refractions, reflections, &c. At point let any two perpendicular planes , be taken in the direction of the ray; and let the vibrations of the ray be divided into two parts, one in each of these planes. Take like planes , in the ray at point ; then the following proposition may be demonstrated. If when the quantity of light polarized in the plane proceeds from in the direction of the given ray, that part thereof of light polarized in arrives at , then, conversely, if the quantity of light polarized in proceeds from , the same quantity of light polarized in will arrive at ." This is sometimes called the Helmholtz reciprocity (or reversion) principle. When the wave propagates through a material acted upon by an applied magnetic field, reciprocity can be broken so this principle will not apply. Similarly, when there are moving objects in the path of the ray, the principle may