Several years ago I wrote a blog stating that the world revolved around me. I used Galileo's Principle of Relativity (later expanded in Einstein's Theory of Relativity) to state how we measure motion relative to one another. I said that, from a General Relativity viewpoint, it's correct to say that the universe revolves around me - because from my vantage point it does! (I don't notice myself hurling through space, spinning as the Earth spins, etc.)
Well, now I have more fuel to add to my conjectural fire, and that fuel is called geodesics.
Basically, a geodesic is the generalization of a "straight line" when dealing with "curved spaces." It's part of General Relativity.
Let's review an example to see how geodesics work. Have you ever heard the saying that the shortest path between any two places on Earth is NOT a straight line, but is in fact a curve? It's true!
Let's say that you want to drive from Santa Monica, California, to Jacksonville, Florida. So of course you're on I-10. While driving along this route, you stop by the greater Baton Rouge area and pick me up so that I can discuss geodesics with you in between Meatloaf's Bat Out of Hell I and II CDs, which I've conveniently brought along, and which I annoyingly (says you) play on repeat.
Why Meatloaf, you ask? Because the world revolves around me and that's what I want to listen to right now. Now stop turning down the best piano parts, I'm trying to listen, dammit!
OK, so we're driving along I-10. Let's pretend that you didn't have to swerve to miss any potholes in Louisiana, or swerve to avoid (or hit) the jackass drivers in Texas. ("Drive friendly, the Texas way!") Let's also pretend that I-10 was perfectly straight.
So, once we complete our trip down a single highway connecting the West Coast to the East Coast, I ask you: "Did we drive in a straight line the whole way here?"
To which you answer, rather condescendingly I might add, "Of course we did! And you could have helped drive instead of bogarting all our Mickey D's!"
"But it's not a straight line at all, is it?" I ask, eating the rest of the fries which you've bought me because I forgot my wallet in Baton Rouge. "Because we drove along the Earth, and the Earth is a sphere, which means we drove along the outer edge of it. So we actually drove on a circular route, but we didn't complete the circle obviously. So we drove on a segment of a circle. It wasn't a straight line at all! You've failed geometry!"
"But! But!" No buts! You said we drove on a straight line, and I've proven that we haven't. And the idea that we could get to two places on a curve but think that we're on a straight line is the general concept of a geodesic.
And once we know that we can think in those terms, then it doesn't take much to add that the Earth is not only round, but is also spinning and wobbling. But to our eyes, we drove on a straight line.
Which is why geodesics explains why the Earth revolves around me. Or around you, for that matter!
It's all on how you view it.
Hacker, Hack Thyself
3 weeks ago