The motional effects of the maxwell æther-stress
There is an outstanding gap in electromagnetic theory in respect to the attempt to reconcile the analysis of æthereal stress on the lines initiated by Maxwell with Newton’s third law and the law of the conservation of energy. In the present condition of theory there is assigned to the æther a certain distribution of electromagnetic energy and momentum. The hypothetical distribution of energy is necessarily associated with the Poynting vector which measures its rate of transference. The distribution of momentum is so defined that the rate of increase of the total amount, within any given volume supposed at rest in the æther, is equivalent to the resultant of the Maxwell stresses on the bounding surface. There is, however, no connection established between the transference of energy across an area and the stress across that area. Such a connection would require that it should be possible to assign to the medium in which stress and energy reside a state of motion whereby the stresses might do the necessary amount of work, and this again would require the revision of the specification of stress, inasmuch as the ordinary expressions are computed for an element of surface which is at rest. Numerous other questions arise as soon as such a process is attempted, but the present paper seeks only to analyse what types of motion must be looked for, and to specify the field of stress upon the elements of area moving with the velocities obtained. Strictly, it is incorrect to speak of the stresses on elements of area in the æther at the same point having different velocities. The true stress in a continuous medium can only be estimated on an area moving with the medium. All that can be done in the absence of a knowledge of the velocity of the medium is to analyse the transference of momentum across an element of area having a specified velocity. Only when this velocity is that of the medium is it legitimate to interpret this transference as due to a state of stress in the medium. Thus, unless the æther is supposed at rest, the Maxwell expressions have no significance, except as giving the rate at which momentum is crossing an element of area at rest. If, however, the æther is assumed at rest, then no state of stress can give rise to any transfer of energy. 1. The flux of momentum across an element of area moving with velocity v differs from that across a similar element at rest by the vector v v g per unit area, g being the intensity of the electromagnetic momentum (=[EH]/4 πc ) and v v being the component of v normal to the area.