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Why we call "constant" to the Hubble constant?,

if the universe were really expanding then the Hubble "constant" should change, being variable, smaller and smaller..with "time".

Other example/view of this question: if Hubble constant were constant then the universe "age" would be constant too, so let's say 13.7 billion years, and stop growing. That's not an expanding universe.

On the other hand:

If the Hubble constant and universe age were not so constant then:

There is some property that is changing like a "time" that -everyone in universe- could get same number, so there would be an absolute time..

I see the Hubble Constant, and even the age of the universe, a really too speculative theory (perhaps it is as speculative as the posibility of measuring), having more accuracy will lead to better theories...

Is it because some theoric impossibility in measuring that kind of variation?

I see a lot of inconsistency. Any light at this respect is welcome, thanks

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A perhaps better name is the Hubble parameter $H(t)$. It is constant in space but not in time. If you like, you could call the value of the Hubble parameter $H_0=H(t_0)$ today for the Hubble constant. –  Qmechanic May 26 '11 at 12:19
    
@Qmechanic hello, please read David Zaslavsky answer and then my comment on it ( and the question's title itself ), space is not separable of time, so whatever we call "time" here is a kind of absolute time, and that's the question about –  HDE May 26 '11 at 13:19

1 Answer 1

up vote 6 down vote accepted

Actually, you're right: the Hubble constant is not really constant. At least, it's not constant in time.

The reason it's called a constant is that, when Edwin Hubble originally compared the recession velocities of galaxies with their distances in 1929, there was no reason to expect any particular pattern. After all, just a few years prior, people had thought there were no other galaxies. But what Hubble found was that, except for a small amount of random variation, the velocities of galaxies were proportional to their distances; in other words, the ratio $v/d$ was roughly the same for all galaxies he observed. The value of this ratio came to be known as Hubble's constant, $H_0 \equiv \frac{v}{d}$, because it was constant from one galaxy to the next, rather than varying randomly as one might have guessed at the time.

Of course, it wasn't long before people realized that if the recessional velocity of each galaxy was proportional to its distance, you could extrapolate back to some point in the past at which $d = 0$: all the galaxies would have started out in the same place. This gives you an effective age for the universe. If you use a simple linear extrapolation, from basic kinematics you get

$$t = \frac{d}{v} = \frac{1}{H_0}$$

So the Hubble "constant" is not constant in time, but rather is inversely related to the age of the universe. As the universe gets older, the Hubble constant gets smaller, as you would expect. This happens because the distance $d$ to any given galaxy increases with time.

However, the fact that the universe has an age doesn't create an absolute time. Sure, different observers at different points in spacetime will measure different values for the age of the universe. And sure, you could define a time coordinate system by specifying that the time coordinate for any observer is the age of the universe as measured by that observer. This is called the comoving time, and it is a useful and sensible way to set up a coordinate system in time. But it is not the only possibility, and there is certainly nothing so special about it that it deserves to be called "absolute." Any observer who is moving with respect to the universe as a whole (i.e. relative to the Hubble flow) would not measure time at the same rate as this comoving time.

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Why do you say that "different observers at different points in spacetime will measure different values for the age of the universe" ? If that were so, how could we talk about an "age of the universe"?, not measuring the same value would put earth in a "preferred frame" of reference!, defining an absolute coordinate system, a whole issue. –  HDE May 26 '11 at 12:10
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The key phrase in that sentence is at different points in spacetime. For instance, consider the two points in spacetime corresponding to the Earth today and the Earth 3 billion years ago. Observers at those two points will measure different values for the age of the Universe. –  Ted Bunn May 26 '11 at 23:21
    
@Ted Bunn You are right +1, although it let me thinking...thanks –  HDE May 27 '11 at 0:51

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