In the early 1960s, the well-known physicist Richard Feynman said something cool in a lecture.

I mean, he said a lot of cool things in his lectures. But what he said this time, according to a transcript published later, was that the center of the Earth should be a day or two younger than the surface.

As strange as that sounds, the basic idea behind it makes sense, if you know something about the theory of relativity. And it was Feynman saying this, so people kept quoting him in lectures and textbooks, and nobody really questioned it. That is, until April 2016, when three Danish physicists actually did the math, and realized that Feynman was wrong.

The center of the Earth isn’t a day or two younger than the surface. It’s two and a half years younger. And the center of the Sun?

It’s 39,000 years younger than its surface. All because of general relativity. General relativity is basically the science of the very fast, and the very massive.

It takes the big-picture universe — like planets, stars, and galaxies — and describes it using math. That math is built around a few fundamental ideas. One of those ideas is that the speed of light in a vacuum is always the same — it’s about 300,000 kilometers per second, no matter what perspective you’re looking at it from.

And that rule — that the speed of light is set — can seriously mess with both time and space, if you start to consider situations that are way more extreme than your everyday life on Earth. For example, when you’re traveling close to the speed of light — say in some hypothetical, ridiculously fast train — time will pass more slowly for you than for someone standing on the ground watching you zoom past. Relativity shows that space and time are so closely interconnected that you can really think of them as parts of the same thing.

That’s spacetime. And another thing relativity shows is that something with a lot of mass, like Earth or the Sun, will warp spacetime. One of the effects of this warping is that the closer you get to the center of one of these massive objects, the slower time will pass.

It’s a brain-bendy idea, but we know it’s true. We have to correct GPS systems because of it. GPS satellites orbit Earth from about 20,000 kilometers up, so they’re much farther from Earth’s center than we are on the ground.

That means that time passes a little more quickly for a GPS satellite than for us. It’s a tiny difference, which adds up to only about 38 millionths of a second per day. But for the satellites to keep track of your position, their clocks need to be synced up pretty much exactly.

So GPS satellites are designed to take relativity into account and correct their clocks. And this is the same basic idea Feynman pointed out in his lecture: If something with lots of mass warps spacetime, and if time passes more slowly the closer you are to Earth’s center, that means the center of the Earth must be younger than the surface. And that part was right.

The thing is, he said that in the 4.5 billion years or so that Earth’s been around, the center would be younger than the surface by a day or two. And no one checked his math for more than 50 years, until that group of Danish physicists decided to look into it, in a paper published in the European Journal of Physics. First, they did a simpler version of the calculation, using equations that treated Earth like a uniformly dense sphere.

Which it’s not, by the way, because of all those different layers of rock. But it’s still a pretty good way to get a sense of the physics, and that’s probably how Feynman would’ve done the calculations.. They found that the center of the Earth would be about a year and a half younger than the surface, which was their first sign that Feynman’s famous fact was wrong.

Next, the team did a more detailed calculation, using a model that takes into account the variations in Earth’s density. That gave them a more exact answer: Earth’s center is about 2.5 years younger than its surface. It’s hard to know whether Feynman himself was wrong, or whether the people transcribing his lectures just wrote down “day” instead of “year”.

But, either way, the fact that people kept repeating in all those lectures and textbooks was wrong. While they were at it, the Danish researchers did the same detailed calculation for the Sun, since there’s a similar model of the Sun’s density that they could use. And they found that the Sun’s center is about 39,000 years younger than its surface, which is a much bigger age difference than for Earth.

A lot of that is because much more of the Sun’s mass is concentrated close to its center, and warps spacetime so much more. Practically speaking, the fact that time passes more slowly at the center of the Earth and the Sun doesn’t really matter that much. But relativity is one of our most useful tools for learning about the universe, so it’s important to understand the way it affects everything around us.

And for scientists, the fact that Feynman’s numbers were wrong is a reminder of one of the most fundamental aspects of scientific thinking: question everything. Thanks for watching this episode of SciShow Space, and thanks especially to our patrons on Patreon who help make this show possible. If you want to help us keep making episodes like this, you can go to patreon.com/scishow to learn more.

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