How the universe expands

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: lawrence@krubner.com, or follow me on Twitter.

Interesting:

The whole “expanding universe” thing is, unfortunately, a bit misleading at first glance. Normally when we throw the word “expanding” around, we’re talking about things getting bigger in some sense. The deficit is expanding, my waistline is expanding, something like that.
Not so, when the subject turns to modern cosmology.
See, the idea that lies at the core of what’s generally called the “standard model of cosmology” — that is, the cosmological model of the universe that best explains all our observations — is one of metric expansion.
Metric expansion basically works like this: Given any two fixed points in space, the distance between them is not a constant. It increases with time. That does not mean the two points are moving away from each other. Those two points are fixed, pinned down as it were. They ain’t moving. But the distance between them is increasing.
This is a surprisingly simple idea to express mathematically. You just write down the equation for calculating the distance between any two points — the one we use in this universe is similar to, but not the same as, the good ol’ Pythagorean theorem that imaginary people living in an imaginary Euclidean universe would use — and toss in a coefficient that depends on time. We call that coefficient a(t), and give it the name “the scale factor.” The distance between any two points in the universe is the coordinate distance — that is, the distance you get when you use that almost-Pythagorean equation I alluded to — times the scale factor, which in turn depends on the age of the universe.
If you know anything about basic geometry, this should give you a splitting headache. How can the distance between two unmoving points vary? The answer is that in Euclidean space — the space we talk about when we’re studying basic geometry — it can’t. The distance between points in Euclidean space is constant with respect to time … and indeed, with respect to everything else except the points’ positions. But the geometry of our universe is not Euclidean geometry. On certain scales — the scale of your living room, for instance — it sure looks Euclidean. But on larger scales, or at high relative velocities, or in the presence of strong gravitation, it’s very much not Euclidean. And one of the non-Euclidean properties of the geometry of our universe is that distances between fixed points can vary with time. It’s permitted by the rules of geometry that govern our universe, and furthermore it appears to be fact.
Now, this might all sound like mathematical wankery and abstract folderol. But it really isn’t. Take a minute to google up a recent experiment called Gravity Probe B. Gravity Probe B did something remarkable: it directly measured the geometry of spacetime around the Earth. And the way it did it was very, very clever.
Imagine a sheet of paper with an arrow drawn on it. The arrow starts somewhere, and points off in some arbitrary direction; doesn’t matter which one. Now imagine moving the arrow around on the paper while keeping its direction constant. Think of it like a game of pin-the-tail-on-the-donkey. The arrow is the donkey’s tail, and you can move the pin holding it down wherever you want, as long as you keep it pointed in the same direction.
Move the arrow around any path you like, ending back at the same place where it started. You can move it in a circle, or in a complicated curlicue, or whatever. When you get the arrow back to the same point where it started, you’ll see that it points in exactly the same direction it did when we began. We moved the arrow around a closed path, and its direction did not change.
That’s Euclidean geometry at work, right there. But as we talked about before, the geometry of our universe is not Euclidean. In our universe, if you do that same experiment — move an arrow around without changing its direction — it may not necessarily end up pointing where it pointed when you started.
That’s what the Gravity Probe B experiment did. Except instead of an arrow, it used incredibly precise gyroscopes. A gyroscope, due to its angular momentum, resists any motion that would change the direction of its axis of rotation. If you get a gyroscope spinning in a sufficiently low-friction environment, it becomes a sort of compass, always oriented in the same direction. The Gravity Probe B experiment carried a gyroscope on a closed path around the Earth — aboard an orbiting satellite — and compared the direction it pointed when it was done to the direction it was pointing when they started … and found a difference.
Now, the reason for this has to do with gravitation. The Earth’s mass induces a curvature in the structure of spacetime around our planet; that’s how gravity works. But another result of this curvature is that the parallel transport of a vector — moving an arrow around without changing its direction — results in a deviation. This was long predicted by general relativity, but the Gravity Probe B experiment actually tested it directly. We went out there and directly measured the geometry of the universe. And I think that’s pretty damn awesome.
The same truth about the universe that causes parallel vectors transported around closed paths to deviate also permits metric expansion. And metric expansion explains all that weird, bizarre stuff we see when we look up at the night sky. The universe isn’t expanding into anything. It isn’t really expanding at all, in the sense that people normally use the word. Rather, stuff that’s at rest relative to other stuff is staying pretty much where it is … but all distances in the universe are gradually increasing with time.

Post external references

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    http://www.reddit.com/r/askscience/comments/eru42/so_if_the_universe_is_constantly_expanding_what/
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