## Time runs slower wherever gravity is strongest.

Here’s a little something you probably didn’t know about the Earth: its center is two-and-a-half years younger than its surface, and it has nothing to do with how the Earth formed. It is thanks to the effects of gravity as described by general relativity.

According to Einstein, your position in a gravitational field changes the rate at which you experience time passing, an effect known as gravitational time dilation. In other words, time runs slower wherever gravity is strongest, and this is because gravity curves space-time. This idea has been rigorously tested, and in fact, has an impact on Global Positioning System (GPS) satellites.

GPS satellites are positioned about 12,550 miles above Earth’s surface and therefore are not as close to Earth’s gravitational field. The clocks on these satellites actually tick faster than the clocks on Earth’s surface, so scientists put a correction into satellite programs to ensure that the GPS data sent back to Earth has matching times.

*SEE ALSO: Wrinkles in Space-time: The Quest to Detect Gravitational Waves*

However, these time differences are normally fractions of a second, not a couple of years.

Back in the 1960s, physicist Richard Feynman estimated that the difference in age between the Earth’s center and surface was about a day or two — a figure that has been repeated and cited in numerous papers by other physicists since. However, Ulrik Uggerhøj of Aarhus University in Denmark and his colleagues realized that the effect of gravitational time dilation would be much more pronounced for Earth, and decided to re-examine Feynman’s claim.

To calculate this age difference, the team worked out the difference in gravitational potential — a measure of the work done by gravity in moving a mass from one location to another — between Earth’s center and surface. Plugging this difference into the equations of general relativity, resulted in a time dilation factor of around 0.0000000003, meaning every second at the Earth’s center ticks this much slower than it does on the surface.

Now, this may not seem like very much, but you have to remember that Earth is over four-and-a-half billion years old, so this cumulative effect of time dilation adds up to a difference of around a year and a half.

But wait, didn’t I say the center of the Earth is two and a half years younger? That first calculation conducted by Uggerhøj assumed that the Earth had a uniform density. However, we know that is not true — the core is much denser than the mantle. Using a more realistic model of Earth’s density, the team found the difference in age is actually around two-and-a-half years.

Of course, this number can’t be confirmed experimentally, explained Uggerhøj to *New Scientist*. However, general relativity has passed every test thrown its way so far, so it is likely correct.

Uggerhøj said it is unclear if Feynman made the error originally, or whether there was an error in the transcription of his lectures — using days instead of years. “One should always be cautious and test even famous people’s suggestions,” he said. “I fell into the trap of not doing it, I must admit.”

To have a little fun, but also show that this method works for any massive cosmological body, the team calculated that the center of the sun is around 40,000 years younger than its surface — a substantial difference.

These results give a whole new meaning to the phrase “young at heart.”

The paper is available online at arxiv.org.

You might also like: *The Math Adds Up: How to Create and Manipulate Gravity*

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