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

TL;DR

This paper clarifies the physical meaning of pressure-dependent terms in the energy-momentum density of a moving perfect fluid, linking them to work done during Lorentz contraction and energy flow, and extends this understanding to electromagnetic systems.

Contribution

It provides a physical interpretation for pressure terms in energy-momentum densities, explaining their roles in relativistic fluids and electromagnetic systems, resolving longstanding conceptual puzzles.

Findings

Pressure term in energy density represents work against Lorentz contraction.

Pressure-related energy flow occurs across the moving fluid system.

Electromagnetic momentum includes pressure effects from electrical self-repulsion, addressing the 4/3 problem.

Abstract

In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure 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 the energy-momentum densities, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell's stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural solution for the notorious, more than a century old but thought by many as still unresolved, 4/3 problem in the electromagnetic momentum.