There are some very interesting answers to the Hubble puzzle I posed below (see the comments section of the original post). Let’s review the question and then I’ll try a solution in simple language:
Hubble discovered that distant galaxies are moving away from us (or any other point) with a velocity that is proportional to their distance. 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.
Every physicist reads this law as v1/d1 = v2/d2 =v3/d3 = H and it works fine. However, if we 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: Doesn’t Hubble’s Law predict that distant galaxies are accelerating away from us? If so why all the fuss/surprise about the recently observed acceleration of the universe?
My solution (simple version): Yes, Hubble’s Law implies that distant galaxies are accelerating away from one another. However, this has nothing to do with the so-called acceleration of the universe. The latter term refers to the recent observation that the universe expansion seems to have speeded up (an acceleration of the acceleration if you like.)
My solution (more sophisticated version): if the solution above sounds a bit cumbersome, it’s because it should really be framed in terms of general relativity. Of course relativity affects the puzzle, contrary to what I said in the original post (teachers!). Relativity tells us that that the expansion of the universe is an expansion of space-time (or space expanding as time unfolds). Hence, the common ‘explosion-picture’ of galaxies rushing away from one fixed point is simply wrong. Instead, space itself is expanding and this expansion has a scale factor. The recent evidence of ‘acceleration’ simply suggests that the scale factor has increased in the last few million years. (This is a surprise because most cosmologists expected the expansion to slow down, if anything, due to gravitational effects). In this context, the idea of a non-constant scale factor is not so way out – for example, the theory of cosmic inflation posits that an exponential expansion of space occurred in the very early universe, before the expansion settled down to the scale factor we see today.
That’s my best explanation in simple language. For a slightly more technical explanation, see the comments by Chris Oakley and SomeRandomGuy in the original Hubble post. Chris, you have won the princely prize of a guest post – let me know when you read this!