I find it helpful to conceptualize radial redshift as nothing more than a longitudinal stretching out or elongation of an incoming light beam segment, as measured in the observer's rest frame. For example, a light beam segment which has been redshifted by a factor of 2 has been stretched to twice its length (as measured in the observer's frame) as when it was originally emitted (as measured in the emitter's frame.)(adsbygoogle = window.adsbygoogle || []).push({});

This makes it clear that no energy is "lost" by the light beam segment as a consequence of its redshifting. Instead, the same total energy is spread over twice the length. The energy density striking the observer at each instant is half of the original energy density, but that density decrease is exactly offset by the doubling of the duration over which the total light beam segment is received.

The CMB radiation has been redshift by about 1089 times since it was emitted from the surface of last scattering, and its temperature (kelvin) as measured at earth has decreased by that factor. The distance between our earth and that surface of last scattering is constantly increasing approximately at the rate of the cosmic Hubble flow. Each segment (of arbitrarily assigned length) of the CMB radiation beam we observe at earth has been cumulatively stretched during its transit to what has finally become 1089 times the length of that segment when it was originally emitted. The CMB energy has not been lost as a result of this stretching. Rather, the same total radiation energy merely has been spread out into a configuration of lower energy density.

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# Conceptualize radial redshift

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