What crucial difference exists between the Doppler and Cosmological redshift mechanisms regarding energy loss?

Answer

The cosmological photon truly loses energy steadily over its trajectory.

For a standard Doppler shift, the wavelength is effectively different between frames, but the photon's energy is measured the same at creation and interception; conversely, the cosmological photon steadily loses energy as space expands during its long travel.

What crucial difference exists between the Doppler and Cosmological redshift mechanisms regarding energy loss?
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