The Borgnis technique is used to solve the Maxwell equations under the following conditions: (a) Complex field strengths are used such that H=±iE, that is, circularly polarized waves of positive or negative helicity; (b) there is only harmonic time dependence through a factor exp(iWt), that is, a pure energy state of the photons; (c) there is no z dependence, that is, no kz component of the photons' momentum; (c) there is no restriction on the x, y dependence of the solutions. It is then shown that the Sz component of the Poynting vector obeys the formula ±2WSz=∂ₓSy-∂ySₓ and is in general nonzero. This fact, together with the postulated nullity of kz, is the expression of the "translational inertial spin effect." An experiment using the limiting case of total reflection is proposed to test the effect. A discussion of gauge-dependent expressions of the effect, using potentials, is also given, in connection with de Broglie's formulas for the current- and spin-density 4-vectors of the photon waves.
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O. Costa de Beauregard (1965) studied this question.