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Conservation laws that are based on the divergence of a second-rankfour-tensor are fundamentally different from conservation laws based on thedivergence of a four-vector. This article investigates the consequences of thisdifference for understanding the relation between electromagnetic fieldmomentum and the flow of electromagnetic field energy. Momentum and energyconservation require electromagnetic field momentum and energy to be treated asphysically real, even in static fields. This motivates the conjecture thatfield momentum might be due to the flow of a relativistic mass density (energydensity divided by the square of the speed of light). This article investigatesthe velocity of such flow and finds a conflict between two differentdefinitions of it. This investigation is careful to respect the transformationrules of special relativity. The paper demonstrates that the consensusdefinition of the flow velocity of electromagnetic energy is inconsistent withthe transformation rules of special relativity, and hence is incorrect. Acorrect flow velocity is then derived which is completely consistent with thosetransformation rules. The conclusion is that these conflicting definitions offlow velocity cannot be resolved in a way that is consistent with specialrelativity and that also allows electromagnetic field momentum to be the resultof energy flow. Though real, field momentum cannot be explained as the flow offield energy. As a byproduct of the study, it is also shown that there is acomoving system in which the electromagnetic energy-momentum tensor is reducedto a simple diagonal form, with two of its diagonal elements equal to theenergy density and the other two diagonal elements equal to plus and minus asingle parameter derived from the electromagnetic field values, a result thatplaces constraints on possible fluid models of electromagnetism.

Is Electromagnetic Field Momentum Due to the Flow of Field Energy?