THE INDIAN DREAMER

This is the first post of the aforesaid The Astro Logic Series. The Logic question for today is:

If we say that light from a distant galaxy took 10 billion years to reach earth (10 billion light years from Earth), why isn't it true that the galaxy is actually much further away since during that 10 billion year time since the light started its journey toward us, the galaxy has continued to move still farther away?

Before presenting the answer to this question, I would like you to know few small but important facts. One light year is the distance that the light travels in a year. Light travels nearly 3 Lakh kilometers per second. So, you can imagine how much it would travel in a year. The true age of the universe is still not firmly known but it is expected to be around 14 billion years. Now, for the above question, it is completely legitimate to say that the galaxy is farther than 10 billion light years away from Earth - if you're using a particular definition of the distance to the galaxy. Unfortunately, distance is one of those things that has an intuitive meaning in everyday life but is not so intuitive in our expanding universe! Astronomers (and other people) are not always very clear about what they mean when they talk about an object's distance, leading to a lot of confusion about this topic.

First of all, the expansion of the universe doesn't consist of galaxies moving through some static space, but rather the stretching of the space itself. The light is moving through this expanding space and has to travel the initial distance plus whatever distance is added due to the universe's expansion during the course of the journey. It's like running on a racetrack that is being stretched - if the racetrack started off 100 meters long but got stretched to a final length of 400 meters as you were running from start to finish, then the total distance you've run is more than 100 meters.

In fact, when you talk about the distance between the start and finish lines in this racetrack, you might mean several different things:
(1) You could mean 100 meters, since that's the distance when you start running; it's also what the markings on the track say the distance is.
(2) You could mean 400 meters, since that's the distance between start and finish at the moment you reach the finish line.
(3) You could mean the actual distance you've run, which is more than 100 meters (since the track stretches while you're running on it), but less than 400 meters (since some of the stretching happens on parts of the track you've already passed through).

You can see from the above example that when astronomers talk about the distance to a faraway galaxy, there are several things they might mean! If we somehow know that “light from a distant galaxy took 10 billion years to reach Earth”, as our question says, then clearly, if we are using definition 3 we would say that the distance to the galaxy is 10 billion light years. However, if we are using definition 1, we would say that the distance to the galaxy is less than 10 billion light years (i.e. it was closer than 10 billion light years when the light was emitted), and if we are using definition 2 we would say that the distance to the galaxy is greater than 10 billion light years (i.e. it is greater than 10 billion light years right now, when the light is received by us).

If you are interested more in the above discussion and want a more detailed description, just leave your message as a comment to this post. Also don’t forget to leave your email address.