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She discusses different ways to picture the cosmological redshift in view of the fact that total energy is not conserved in a dynamic non-static geometrodynamic field (spacelike 3D geometry), therefore, Noether's theorem that continuous symmetries have conserved global invariants no longer applies naively as it does on a non-dynamical globally flat Minkowski spacetime.
Tamara gives two ways of looking at the problem. Another equivalent way is John Archibald Wheeler's "Geometrodynamics." The square root of Einstein's spin 2 tensor gravity field is the spin 1 tetrad field of zero g-force local freely falling detectors in curved spacetime in accord with the Equivalence Principle.  Formally, this geometrodynamic field lives on a fictictious non-dynamical Minkowski spacetime of 1905 Einstein Special Relativity. Therefore, the cosmological redshift of both light and de Broglie matter waves can be understood in terms of Ehrenfest's theorem of the statistical expectation value of the inelastic scatterings of the matter fields with the time-changing geometrodynamic field. The statistical expectation value agrees with the classical Einstein general relativity predictions.

Rocky Kolb - SLAC Summer School 2005 - obviously the total real photon energy is not conserved ~ a^-1, neither is the total dark energy conserved. Therefore, Scientific American editors have garbled the point - it is stretching the point (pun intended) to say the photon energy is really conserved.

"Total energy must be conserved. Every student of physics learns this fundamental law. The trouble is, it does not apply to the universe as a whole."
By Tamara M. Davis

Category: Science