Thursday, October 20, 2011

How Gravity Works

Some time ago, I promised an explanation of how gravity works — in particular, how general relativity, Einstein's theory of gravity, works. Today I'm going to deliver. This one's a little mind bending, so definitely ask questions if you're confused. I like questions. Questions are cool.
In the beginning, there was Newton
To understand general relativity, we need to go back to one of Newton's laws — not Newton's law of gravity but rather Newton's first law: objects tend to travel at constant speed and in a constant direction (or remain at rest) unless some force acts on them. In simple terms, stuff that goes straight keeps going straight unless you push on it.

Believe it or not, I just explained gravity.

Newton may well have called me crazy. To him, gravity was a force, and it's easy to see why. Suppose we, your friends, hold you a hundred feet off the ground and then let go. You will fall, and then you will cry. In fact, we'll launch you sideways so you make a pretty arc as the earth careens toward you.

Now, if you buy Newton's First Law, there must be some force that acted on you. You went from stopped to falling — some force must have been behind that. So says Newton.

Silly Einstein's silly thought experiment
Let's probe deeper. Newton says that an object (namely, you) will stay on a straight line going at constant speed unless some force acts on it.

Well, when do you actually feel a force?

If we forget about wind resistance, you don't feel one while you're falling. You do feel a force before you're dropped — the force of us, your soon to be ex-friends, holding you up.

Catch that? In this way of thinking, you feel a force when your friends are holding you eight stories up about to drop you. If that's right, then Newton's laws say they're keeping you from going straight and at constant speed. Then when are you going straight and at constant speed? When you can't feel a force. In other words, when you're falling and making that pretty arc across the sky.

I'm glossing over some details, but this is Einstein's puzzling insight: falling is going straight. It's right there in Newton's laws. In other words, if can't feel a force but it doesn't look like you're going straight, you need to redefine what you mean by straight.

Long walks, curved spacetime, and gravity
It may seem like a contradiction to say you're going on a straight line at constant speed while making a pretty arc and accelerating toward the earth, but in fact it's not such an odd idea.

Consider starting at your house and walking due West. If you can manage to walk on water, you'll come back to where you started. You walked in a straight line, and yet you made a big circle.

We wouldn't infer from this that a force somehow bent your path. We'd infer that the surface of the earth is curved — which of course it is.

The same thing holds for astronauts orbiting the planet. They're floating up there, so they don't feel any forces acting on them. Yet orbiting the planet they make a great big circle in space. We don't infer that there's a force acting on the astronauts — after all, they can't feel one — so instead we infer that space and time are curved.

And that's what gravity is: curved spacetime. Explaining all the details — like exactly what it means to be going straight at constant speed while appearing to be doing the opposite — would take longer, but you've got the basic idea. No force? Go straight. No force, not going straight? It's not you that's not going straight. It's spacetime.


  1. So when applying these explanations to black holes, why is it that a black holes curvatures appear to more of a vortex than a sphere? :) This explanation covers why the vortex can be orbited, but not why the focus appears to have a weaker pull on its sides or back than the "hole" itself.

  2. The picture you probably have in mind is one where stars, dust, and other cosmic stuff seem to be swirling down in to a black hole. There are a couple ways this can happen, but the simplest and most important is that not everything starts at rest and falls straight down into the hole. It's like satellites that fall toward earth. If they're moving fast enough, they'll make a few orbits as they descend, so they're trajectories are spirals. Same thing with stars and dust and other stuff that fall into a black hole.

    Does that answer the question? I suspect you might have something a little different in mind...

  3. Mostly how an idea like this one extrapolates itself over a sphere. I can understand the curve around the entry point fairly easily, but the overall sphere having the same amount of pull? Is there just an infinite # of these around each black hole?

  4. Ah, I see. The picture you're thinking of — and with good reason, since it's the one people often use when talking about black holes — is misleading in a subtle way. (For those reading, here's another version of the picture:

    What it actually depicts is the relationship between the distances two observers, one near the black hole and one very far away, measure. So, for example, an observer at the black hole's event horizon could hold up a yard stick and measure some the length of, say, a Volkswagen. We can also ask how long the VW appears to someone very far away — the answer is, it looks longer to the far-away observer than it does to the observer near the event horizon.

    That idea is actually encoded in the picture: the "horizontal" distance is the distance a local observer would measure, while the distance along the curve is the distance a far-away observer would measure.

    The conceptual problem with the picture is that it makes it look a physical hole, like a hole you'd dig in the ground, even though what it really represents is the relationship between two different observers' measurements.

    Hmm. I may have to turn this into a proper blog post....let me know if what I've written is clear.