# 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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