"Lionel" lionel wrote in message
...
Can anybody explain why the frequency of an observed source of EM
radiation cannot be proportional to the distance the radiation has
travelled to the observer?

L

The frequency is inversely proportional to distance. Red-shifting means an
increase in wavelength toward the red end of the spectrum. Since frequency
is inversely proportional to wavelength, that yields an inverse relationship
between frequency and distance. Hubble realised the cosmological red-shift
of light due to the metric expansion of space-time. The greatest red-shift
we observe comes from the most distant source, namely the cosmic background
radiation. One way of visualising the effect is to consider photons
travelling through a space-time continuum which is slowly expanding, thereby
stretching them and increasing their wavelength. (Fold a piece of paper,
concertina fashion to simulate waves, then slowly stretch it). Recent
observation suggests that the universe is not only expanding, but doing so
at an increasing rate, i.e literally accelerating apart. If that proves to
be correct, we will have a non-linear (but still inverse) relationship.

The red-shift due to metric expansion is not to be confused with Doppler
red/blue shift due to sources receeding/approaching, nor with gravitational
red-shift due to light passing through the gravity fields of massive
objects. For objects relatively close to us, those effects dominate. The
cosmological shift due to space-time expansion only becomes noticeable for
very distant objects.

This is my understanding, but there are hopefully some here present who can
refine it.