  An overlap between the general relativist and particle physicist views of
Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and
Klein's reflections on the conservation laws. Energy-momentum is just a term
proportional to the field equations and a 'curl' term with identically zero
divergence. Noether proved a \emph{converse} "Hilbertian assertion": such
"improper" conservation laws imply a generally covariant action.
  Later and independently, particle physicists derived the nonlinear Einstein
equations assuming the absence of negative-energy degrees of freedom ("ghosts")
for stability, along with universal coupling: all energy-momentum including
gravity's serves as a source for gravity. Those assumptions (all but) imply
(for 0 graviton mass) that the energy-momentum is only a term proportional to
the field equations and a symmetric "curl," which implies the coalescence of
the flat background geometry and the gravitational potential into an effective
curved geometry. The flat metric, though useful in Rosenfeld's stress-energy
definition, disappears from the field equations. Thus the particle physics
derivation uses a reinvented Noetherian converse Hilbertian assertion in
Rosenfeld-tinged form.
  The Rosenfeld stress-energy is identically the canonical stress-energy plus a
Belinfante curl and terms proportional to the field equations, so the flat
metric is only a convenient mathematical trick without ontological commitment.
Neither generalized relativity of motion, nor the identity of gravity and
inertia, nor substantive general covariance is assumed. The more compelling
criterion of lacking ghosts yields substantive general covariance as an output.
Hence the particle physics derivation, though logically impressive, is neither
as novel nor as ontologically laden as it has seemed.
