I’ll be away surfing in Biarritz next week, so I’ll leave readers with a puzzle to mull over. Nigel Cook’s comments on the post below reminded me of a slight problem I have with Hubble’s Law. The problem is laid out below: the challenge is for anyone to supply a straightforward answer in simple language (damned if I can).
As every schoolgirl knows, Hubble discovered that distant galaxies are moving away from us (or any other point) with a velocity that is proportional to their distance. This is the crux of the evidence for the expanding universe, not to mention a major piece of the evidence for the Big Bang.
The law arises from experimental observation and is usually written as
v = Hd
where v is the recessional velocity of a galaxy, d is the displacement of the galaxy from us and H is the Hubble ‘constant’, or the slope of the graph.
(Note that relativity predicts that it’s really space that’s expanding and the galaxies ride the wave, but this doesn’t affect the question coming. We can also ignore the fact that there is a correction factor for the time it takes light to reach us).
Every physicist reads this law as v1/d1 = v2/d2 =v3/d3 = H and it works fine. However, consider what Hubble’s Law says about any one particular galaxy. The equation clearly implies that the velocity v of a galaxy A (relative to some point) is proportional to its displacement d (relative to that point). But for non-zero velocity, the displacement d must be changing in time – therefore Hubble implies that the galaxy’s velocity is also changing in time – which is another way of saying that galaxy A is accelerating!
So there’s the puzzle: Does Hubble’s Law predict that distant galaxies are not just moving away from us, but accelerating? On the face of it, it does. If so, then a force must be acting. Hmm. Suspect the equation is misleading. After all, why all the fuss/surprise about the recently observed acceleration of the universe expansion? According to the logic above, it must be accelerating..
P.S. The question can be framed in terms of basic mechanics – surely any object that has a velocity that is proportional to its displacement it must be accelerating?