Davies & Gribbin (1992: 107-8):
How, indeed, do we know that the Universe is expanding? The most direct evidence comes from examining the quality of light received from distant galaxies. It was found by Hubble and others that this light is systematically shifted from the blue towards the red end of the optical spectrum. This means that the light waves are stretched somewhat compared with light from similar sources (the same kinds of atoms) in laboratories on Earth. Such a 'red shift' is a familiar sign to physicists on Earth that the source of light is moving rapidly away from the observer, and this is how Hubble interpreted it. He concluded that the galaxies are rushing apart at great speed.
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From the perspective of Systemic Functional Linguistic Theory, the General Theory of Relativity models the cosmological expansion as the relative expansion of space intervals and the relative contraction of time intervals.
Also from this perspective, the wave-particle duality of Quantum Theory is the duality of potential and instance, such that wave probabilities are instantiated as the statistical properties of particles.
On this basis, the "stretching of light waves" (red shift) in the cosmological expansion is actually the relative expansion of the space intervals between the photons of a given frequency.
On the other hand, the "stretching of light waves" (red shift) due to the motion of a light source away from an observer is the resultant increased distance between photons created by the direction of motion, independent of any expansion of the space intervals by which the distance is measured.
That is, the expansion of space is independent of motion through space. The cosmological expansion is not the motion of galaxies through space. Some galaxies are moving away from each other, some are moving toward each other. Whatever the motion of galaxies, the cosmological expansion means that the space in which all galaxies are located is expanding.
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