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Question by David Morgan
I am only a layman and not an academic but I would be grateful to receive a response to my question, below.
I understand that the most distant galaxies from earth are accelerating away from us faster than the nearer galaxies. (On the basis of their red shift readings). Assuming the light from a distant galaxy has taken say 12 Billion years to reach us and the light from a nearer galaxy say 2 billion years to reach us If the distant galaxy is travelling faster than the nearer galaxy couldn't you say that 12 Billion years ago galaxies were travelling apart faster than they were 2 Billion years ago. This suggests to me that the rate of expansion is slowing down and not accelerating.

Where have I gone wrong in my thinking ?

The observation that Hubble made almost 100 years ago is that more distant galaxies have a larger redshift than galaxies closer to us, and that this relationship is linear. So, to take your figures, a galaxy 12 billion light years away has 6 times the redshift of a galaxy 2 billion light years away. Now, first of all, it is a mere theoretical assumption that the observed redshift is linked to recessional velocities (Hubble himself never fully subscribed to this interpretation, which in fact is logically and physically flawed). But even assuming we are dealing with recessional velocities here, there is no implication that any of the galaxies are accelerating. On the contrary, you can only have the observed linear relationship if their velocities are constant. As an illustration, consider an explosion where the fragments are flying away with different velocities. If each fragment has a constant velocity, the distance covered within a given time will be exactly proportional to its velocity, that is a fragment with velocity v1 will travel a distance x1=v1.t within time t, whereas the fragment with velocity v2 will be at distance x2=v2.t, so the ratio x2/x1=v2/v1= const., which is nothing but Hubble's law. As long as the velocities of the fragments are constant, it doesn't even matter that you see the fragments at different times due to the finite speed of light. You see a galaxy that is 2 billion light years at the distance and with the redshift it had 2 billion years ago, but a galaxy that is 12 billion light years at the distance and with the redshift it had 12 billion years ago. Now this 'time layering' doesn't matter if the velocities are constant, because the redshift of each galaxy would never change with time. The distance changes of course, but by the same proportion for both galaxies (if the distance for the slow galaxy doubles, the distance for the fast galaxy doubles as well), so the distance/velocity ratio would change by the same factor in the same time, which means the different travel times of the light signal to us do not affect the Hubble law as such. However, if the velocity of the galaxies would be increasing with acceleration 'a' (rather than being constant), there will be the same velocity Δv=a*t added within time t; but as you observe the further galaxy 2 at an earlier time than the closer galaxy 1 t2<t1, we have Δv2<Δv1, that is the further galaxy has less redshift added due to the acceleration than the closer galaxy. This means that with increasing distance of the galaxies, the redshift is increasingly smaller than expected on the basis of the linear Hubble law. Or you can see it the other way around: the apparent distance (as judged from the brightness) gets increasingly larger than expected from the observed redshift. This is at least what the data are claimed to show (see this reference), but if you look at the given data points in Fig.2 in this reference, then this does not appear at all obvious, contrary to the claim made towards the end of the figure caption (if the data would somehow relate to either of the dashed curves in Fig.2, it should be obvious to the naked eye, which it clearly isn't). A very recent re-analysis of the supernova data also concludes that an acceleration does not conclusively follow from the data (see this reference).

Anyway, as indicated above already, an expansion of the universe (whether uniform or accelerated) is a flawed physical concept as it violates mass conservation. The redshift must be due to causes other than a recession, and I have suggested a mechanism for this on my page Plasma Theory of the Hubble Redshift of Galaxies and, based on this, on my page Galactic Redshifts and Supernova Light Curves I have also given an explanation for the fainter than expected objects at larger distances that has led to the conclusion of the accelerating expansion (if that could be substantiated by the data at all).

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