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The Physics of Energy Flow – No Sources or Sinks

2026-03-11

# 4. No Sources or Sinks Across the extent of $u$, continuity holds. Energy transported across a region does not create or destroy energy there. Rather, it changes how much energy is stored there by moving it across regions. In the present book we derive the transport core without introducing primitive source or sink terms. Energy transported across a region does not create or destroy energy there. A primitive source or sink would require either that the total amount of $u$ change or that disconnected regions compensate one another without transport between them. This is the source-free continuity statement used from here on: no added creation term, no added destruction term, only transport. Nothing here says that one cannot later write effective source terms. It says only that they are not needed to recover the observed effects later attributed to charge, mass, and gravity. Charge, mass, and other related source-like quantities appear here as organized closures or effective summaries of one continuous energy flow, not as primitive terms inserted from outside. Point-like behavior, including radial $1/r^2$ effects, will be recovered later within this same source-free energy flow. Even if one later writes ad hoc source terms in Maxwell's equations, those terms must still be understood in this framework as belonging to the same flow and its organized closures. So the point is not that source notation is forbidden. The point is that it is not necessary, and hence not primitive. The core of the transport of energy and the behaviors later recovered as charge or mass are already present once structured configurations of the same flow are allowed. If a reader prefers sourced Maxwell notation, those terms can be introduced later as ideal or effective summaries. Continuity gives local accounting. We now explore what it implies for the shape of the continuous flow as a complete process. Although $\mathbf{S}$ handles a directional accounting of how energy is transported from one registration to another, it does not yet reveal the structure of the continuous flow $\mathbf F$ itself. The next chapters develop that structure. We next consider the transport of energy across empty space.
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