29.1 The age of the universe  (Page 2/10)

The hubble time

If we had a movie of the expanding universe and ran the film backward , what would we see? The galaxies, instead of moving apart, would move together in our movie—getting closer and closer all the time. Eventually, we would find that all the matter we can see today was once concentrated in an infinitesimally small volume. Astronomers identify this time with the beginning of the universe . The explosion of that concentrated universe at the beginning of time is called the Big Bang    (not a bad term, since you can’t have a bigger bang than one that creates the entire universe). But when did this bang occur?

We can make a reasonable estimate of the time since the universal expansion began. To see how astronomers do this, let’s begin with an analogy. Suppose your astronomy class decides to have a party (a kind of “Big Bang”) at someone’s home to celebrate the end of the semester. Unfortunately, everyone is celebrating with so much enthusiasm that the neighbors call the police, who arrive and send everyone away at the same moment. You get home at 2 a.m., still somewhat upset about the way the party ended, and realize you forgot to look at your watch to see what time the police got there. But you use a map to measure that the distance between the party and your house is 40 kilometers. And you also remember that you drove the whole trip at a steady speed of 80 kilometers/hour (since you were worried about the police cars following you). Therefore, the trip must have taken:

So the party must have broken up at 1:30 a.m.

No humans were around to look at their watches when the universe began, but we can use the same technique to estimate when the galaxies began moving away from each other. (Remember that, in reality, it is space that is expanding, not the galaxies that are moving through static space.) If we can measure how far apart the galaxies are now, and how fast they are moving, we can figure out how long a trip it’s been.

Let’s call the age of the universe measured in this way T ₀ . Let’s first do a simple case by assuming that the expansion has been at a constant rate ever since the expansion of the universe began. In this case, the time it has taken a galaxy to move a distance, d , away from the Milky Way (remember that at the beginning the galaxies were all together in a very tiny volume) is (as in our example)

where v is the velocity of the galaxy. If we can measure the speed with which galaxies are moving away, and also the distances between them, we can establish how long ago the expansion began.

Making such measurements should sound very familiar. This is just what Hubble and many astronomers after him needed to do in order to establish the Hubble law and the Hubble constant    . We learned in Galaxies that a galaxy’s distance and its velocity in the expanding universe are related by