At the end of last week, I wrote a post explaining how the Universe is so big (93 billion light years across) when it’s only 13.7 billion years old. The key visualization is to think of space as being the surface of an expanding balloon, while all the things in the Universe (stars, galaxies, etc.) are like ants on that surface.
Now, I explained to you that two ants will appear to move apart from one another due to the expansion of the Universe, even though neither ant is moving relative to the surface of the balloon. If I use light to measure whether this other ant is moving away from me, I find that she is; the light coming off from her is redshifted, in the same way that a fast-moving automobile speeding away from you has a lower pitched sound.
And yet, last week, I said that:
It’s only that space (i.e., the balloon) is expanding; there’s no matter that’s moving. So, in principle, space can expand as quickly as it wants, even faster than the speed of light, because there’s nothing moving.
This statement is confusing, and I realize this. After all, you measure how quickly that other ant is moving relative to you, you find that she’s moving away from you, and yet here I am telling you that neither one of you is moving. This is a very deep problem. Here’s how to help make sense of it.
When you think of the word “motion” or of something “moving”, you probably think of something being at one place at one point in time and then being at a different place at a different point in time. After all, that’s how we conventionally use the word. The act of going from one time and place to another is what we think of as moving.
But when we think about this, we make an implicit assumption. We assume that we can do something like put a grid down — or in general terms, put a system of coordinates down — and measure our changes in position relative to those coordinates.
Seems like a reasonable assumption, doesn’t it? After all, that’s what we do on Earth. In fact, that’s what we do within our entire galaxy, and we never have a problem with it.
But beyond our galaxy, there is a problem with that. The reason? The “grid” that we would put down to measure our Universe is not constant in time.
Want an analogy? Imagine the following hypothetical situation: imagine that the Earth is expanding. Let’s even pretend it’s expanding rapidly; by this time next year, the Earth will have double the radius that it has now.
From New York, Los Angeles appears to be 2,400 miles (3,900 km) away, and vice versa. But a year later, they measure the distance again, and find the distance between them is 4,800 miles (7,800 km). In New York, they accuse Los Angeles of moving away from them. In Los Angeles, they accuse New York of moving away from them. Yet both cities insist they’ve been stationary the entire time.
Things get worse when they start measuring velocities. In New York, they use light to measure how quickly Los Angeles is moving away from New York, and find that Los Angeles is moving away at 0.27 miles per hour (0.44 km per hour). In Los Angeles, they make the same measurement of New York, and find that New York, too, appears to be moving away from them at 0.27 miles per hour (0.44 km per hour).
But, in truth, neither one is moving. What’s going on is that the world that these cities live on is growing, and it makes them perceive that they’re all moving away from each other. It gets worse for things that are farther away; Shanghai, China, is presently 7,400 miles (11,900 km) away from New York. But a year from now, if the Earth is expanding, it will be 14,800 miles (23,800 km) away, and so appears to be moving away (in our expanding Earth example) at 0.84 miles per hour (1.36 km per hour). Yet Shanghai, Los Angeles, and New York are not moving at all. They simply appear to be moving relative to one another.
So it is with the Universe, with an expanding Universe instead of the expanding Earth, and with unchanging galaxies instead of unchanging cities. And that’s — probably — the last tricky part: the expansion is restricted to the Universe on the largest scales. Galaxies, stars, planets, cells, and atoms do not expand as the Universe does; the expansion of the Universe is far too weak to affect any of the dynamics of these relatively small objects. (Yes, compared to the expanding Universe, even a galaxy is too small to be of consequence.)
So does that clear things up? Or does that make them worse? Something as fundamental and seemingly simple as distances, positions, and velocities are — even among professional cosmologists — one of the most confusing (and poorly understood) things that we can talk about. It isn’t intuitive at all, because it runs so contrary to our everyday experience. And that’s part of what makes it so interesting.