There once was a doctor with cool white hair. He was well known because he came up with some important ideas. He didn’t grow the cool hair until after he was done figuring that stuff out, but by the time everyone realized how good his ideas were, he had grown the hair, so that’s how everyone pictures him. He was so good at coming up with ideas that we use his name to mean “someone who’s good at thinking.”
Two of his biggest ideas were about how space and time work. This thing you’re reading right now explains those ideas using only the ten hundred words people use the most often.1 The doctor figured out the first idea while he was working in an office, and he figured out the second one ten years later, while he was working at a school. That second idea was a hundred years ago this year. (He also had a few other ideas that were just as important. People have spent a lot of time trying to figure out how he was so good at thinking.)
The first idea is called the special idea, because it covers only a few special parts of space and time. The other one—the big idea—covers all the stuff that is left out by the special idea. The big idea is a lot harder to understand than the special one. People who are good at numbers can use the special idea to answer questions pretty easily, but you have to know a lot about numbers to do anything with the big idea. To understand the big idea—the hard one—it helps to understand the special idea first.
People have known for a long time that you can’t say how fast something is moving until you’ve said what it’s moving past. Right now, you might not be moving over the ground at all, but you (and the ground) are moving very fast around the sun. If you say that the ground is the thing sitting still, you’re not moving, but if you say that the sun is, you are. Both of these are right: it’s just a question of what you say is sitting still.
Some people think that this idea about moving was the space doctor’s big idea, but it wasn’t. This idea had been around for hundreds of years before him. The space doctor’s idea came up because there was a problem with the old idea of moving.
The problem was light. A few dozen years before the space doctor’s time, someone explained with numbers how waves of light and radio move through space. Everyone checked those numbers every way they could, and they seemed to be right. But there was trouble. The numbers said that the wave moved through space a certain distance every second. (The distance is about seven times around Earth.) They didn’t say what was sitting still. They just said a certain distance every second.
It took people a while to realize what a huge problem this was. The numbers said that everyone will see light going that same distance every second, but what happens if you go really fast in the same direction as the light? If someone drove next to a light wave in a really fast car, wouldn’t they see the light going past them slowly? The numbers said no—they would see the light going past them just as fast as if they were standing still.
The more people thought about that, the more it seemed like something must be wrong with their numbers. But every time they looked at light waves in the real world, the waves followed what the numbers said. And the numbers said that no matter how fast you move, light moves past you at a certain distance every second.
It was the space doctor who figured out the answer. He said that if our ideas about light were right, then our ideas about distance and seconds must be wrong. He said that time doesn’t pass the same for everyone. When you go fast, he said, the world around you changes shape, and time outside starts moving slower.
The doctor came up with some numbers for how time and space must change to make the numbers for light work. With his idea, everyone would see light moving the right distance every second. This idea is what we call his special idea.
The special idea is really, really strange, and understanding it can take a lot of work. Lots of people thought it must be wrong because it’s so strange, but it turned out to be right. We know because we’ve tried it out. If you go really fast, time goes slower. If you’re in a car, you see watches outside the car go slower. They only go a little slower, so you wouldn’t notice it in your normal life; it takes the best watches in the world to even tell that it’s happening. But it really does happen.
After the doctor figured out the special idea, he started thinking about weight. Things with weight pull on each other. Earth pulls things down toward it, which is why you can’t jump to space. Earth also pulls on the moon, keeping it near us, and the sun pulls on Earth in the same way. It turns out that light gets pulled by weight, too. (People weren’t sure about this for a while, because it moves so fast that it only gets pulled a little.)
Someone very careful might notice that this gives us a new problem: How can light turn? The numbers that explain how light moves also say that it can only go forward. It can’t change direction in empty space. That’s just what the numbers for light say—the same numbers that say it always moves a certain distance every second.
If a light wave is pulled down, it has to turn to point down, since it can’t travel to the side. To turn, the bottom part of the wave has to go slower than the top part, since it’s going a shorter distance in the same time. But that can’t be right, because the numbers say that light can’t go faster or slower. We’re in trouble again. And, once again, the space doctor has an answer.
The space doctor figured out that to explain how weight pulls things like light, we have to play around with time again. He showed that if time itself goes slower near heavy things, then the side of the light near the heavy thing won’t go as far every second. This lets the light turn toward the heavy thing.
The doctor’s idea was that weight slows down time, and it explained how light could bend. But to figure out how much light bends, we need to look at the other part of the doctor’s big idea. To talk about that part, let’s forget about light and instead visit another world.
There’s a small world very near the sun. Nobody has visited it. We’ve sent some space boats to look at it, but none of them have landed there. The world goes around the sun in a stretched circle, like this:
(In this picture, I drew it sticking out more than it really does, to make it easier to see.)
When things fall around the sun, they should come back to where they started, like this:
(They get pulled on a little by other worlds, but we’re going to ignore that here to make things simpler.)
The problem is that the world closest to our sun doesn’t do that. When it goes around the sun, it comes back to a spot a little ahead of where it started, like this:
The space doctor was the one who figured out why: Weight changes distance, just like it changes time.
The distance around the edge of a circle is a little more than three times the distance across it. That number—a little more than three—is the same for all circles.
At least, it’s usually the same. But the space doctor figured out that heavy things change the shape of space as well as time. This changes how circles work. If you draw a circle around something heavy, he said, the distance around the edge will be a little shorter than the usual three times the distance across it. Since the distance around the sun is shorter than it should be, the world goes around a little farther than we expect.
When people checked the space doctor’s numbers about how weight changes the shape of space, they found that they explained the small world’s strange path in a way that no other idea did. The numbers also explained how much the sun’s weight bends the light going past it, showing that the bending was twice as much as other people thought it would be. When everyone learned how good the space doctor’s big idea was at explaining things like this, they got very excited. They started putting his face on the cover of the papers, and everyone learned his name.
Over the past hundred years, people have checked the doctor’s ideas in lots of ways, and they’ve always come out right. In fact, our phones use the doctor’s ideas every day—both the special idea and the big idea—to figure out where we are.
When your phone needs to know where in the world it is, it talks to a group of space boats flying around Earth. It checks how long it takes for radio waves to get here from each space boat and uses that to figure out how far away from each one it is.
For this to work, the space boats need very good watches. Since the boats are going fast, the space doctor’s special idea says that their watches will run a little slower than the ones on Earth. And since the boats are far away from Earth’s weight, the big idea says that their watches will run a little faster than the ones on Earth. To know exactly what time it is on a space boat, they have to change the watches a little to make up for both of these problems. If the space doctor’s ideas were wrong, your phone wouldn’t be able to tell where it was.
Even if you’re very good at numbers, the big idea is hard to work with. It talks about time and space changing in ways that we can’t see in our normal lives, so our brains never learned to think about them. The space doctor himself couldn’t finish all the work. He got help from some friends who were even better at numbers than he was, like a man who asked a lot of questions2 and a woman who walked while she talked3.
To make the ideas easier to explain, people will often tell you to imagine something more familiar, like a big flat sheet with weights on it. These pictures are good, but sometimes they make you think of new questions, and when you try to use the picture to answer the new questions, you get answers that don’t fit with each other.
When you get answers that don’t fit together, it can make you feel like you’re not very good at thinking. Or, if you’re the kind of person who feels like you’re good at thinking, it can make you think that the space doctor’s numbers must be wrong. But a lot of the time it’s not you or the numbers—instead, it’s the picture that’s wrong in some small way.
We need people to keep asking questions, because there are problems with the space doctor’s big idea. The numbers in the idea give us the right answers for almost every problem we use them on, but when we use it to talk about things that are very small and very heavy, like the middles of dying stars that fall in on themselves, it gives answers that don’t fit together with other things that we know. We’re still looking for a better idea that can fit everything together, and someday, the right question might help us find it.
1 “Thousand” isn’t one of them.
2 David Hilbert.
3 Emmy Noether.
