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In the energy-momentum density expressions for a relativistic perfect fluidwith a bulk motion, one comes across a couple of pressure-dependent terms,which though well known, are to an extent, lacking in their conceptual basisand the ensuing physical interpretation. In the expression for the energydensity, the rest mass density along with the kinetic energy density of thefluid constituents due to their random motion, which contributes to thepressure as well, are already included. However, in a fluid with a bulk motion,there are, in addition, a couple of explicit, pressure-dependent terms in theenergy-momentum densities, whose presence to an extent, is shrouded in mystery,especially from a physical perspective. We show here that one suchpressure-dependent term appearing in the energy density, represents the workdone by the fluid pressure against the Lorentz contraction during transitionfrom the rest frame of the fluid to another frame in which the fluid has a bulkmotion. This applies equally to the electromagnetic energy density ofelectrically charged systems in motion and explains in a natural manner anapparently paradoxical result that the field energy of a charged capacitorsystem decreases with an increase in the system velocity. The momentum densityincludes another pressure-dependent term, that represents an energy flow acrossthe system, due to the opposite signs of work being done by pressure on twoopposite sides of the moving fluid. From Maxwell's stress tensor we demonstratethat in the expression for electromagnetic momentum of an electric chargedparticle, it is the presence of a similar pressure term, arising fromelectrical self-repulsion forces in the charged sphere, that yields a naturalsolution for the notorious, more than a century old but thought by many asstill unresolved, 4/3 problem in the electromagnetic momentum.

Contribution of pressure to the energy-momentum density in a moving perfect fluid: A physical perspective