Journey to the Center of the Earth

One of the next challenges for me as an artist is to take on the topic of time. I recently read a scientific paper suggesting that, because of the effects of gravity on spacetime, the center of the Earth was 2.49 years younger than the surface of the planet.

Journey to the center of the earth
It turns out that the center of the Earth is now 2.49 years younger than the surface of the Earth due to the effects of gravity. Image: Argonne National Laboratory.

Richard Feynman, a renowned physicist, once proclaimed that the center of the Earth was a couple of days younger than the surface. Yet, no one had bothered to check (!) until Ulrik Ingerslev Uggerhoj, head of the Department of Physics and Astronomy at Aarhus University in Denmark came along. He and his colleagues did the math and corrected Feynman, which is not an easy thing to do. The result was the paper mentioned above.

The idea makes sense. Time slows down when there is more gravity, or, more correctly put, gravitational potential. This is called time dilation. So, time moves more slowly at the center of the Earth where there is more gravity than on the surface. The effect is such that for every second that passes on the surface of the Earth, a tiny fraction of a second less has passed in the center of the Earth. If you multiply all those fractions of a second by 5.4 billion years, which is the age of the Earth, they add up to 2.49 years.

It dawned on me that this was a great example of spacetime right in front of our noses. For anyone, like me, who has difficulty with the concept of spacetime, there it was. The center of the Earth is in a different spacetime “place” than the surface of the planet, just due to the effects of gravity.

I wondered why no one had ever prepared an information visualization showing spacetime this way. I couldn’t believe it could be so simple. So, I put together a quick diagram and ran it by Professor Uggerhoj. He confirmed that it was correct. Here is that graphic.

There are some fascinating implications from the graphic. The first is that spacetime is not something weird and unimaginable. it is something we live with—and in—every day. Our spacetime just happens to be the surface of the Earth. 

Another way of thinking about spacetime, in very simple terms, is as a sort of gravity-determined time zone. Here’s how it works. The gravity on the surface of the Earth, measured as gravitational acceleration, is 9.8 meters per second squared. Anywhere you go on the surface of Earth, the gravity is more or less the same. So, anyone living on the surface is in this “gravity time zone.” 

If someone were living about halfway to the center of the Earth, however, gravity would be increased. The result is that time would be moving more slowly for them. They would be in a different spacetime or gravity time zone that has come to be about 1.25 years younger than the surface over the last 5.4 billion years. 

What about the moon? According to Professor Uggerhoj, anyone living on the surface of the Moon would be living 687 billionths of a second per second faster than someone on the surface of Earth. And the moon, which has been around for 4.4 billion years, has accumulated a time lead over Earth of about 51 minutes. This means when we look at the Moon, we are seeing it in a spacetime “future.”

Interstellar space has even less gravity, so time moves even faster there.

There is very little gravity in interstellar space so time passes relatively quickly there. Black holes, like this one imaged in 2019 by the Event Horizon Telescope, are the opposite. There is so much gravitational pull from a black hole that time stops.

The difference between how fast time flows at the center of the Earth and on the surface is measured in billionths of a second. The same is true of the difference between the surface of Earth and the Moon. These differences are not perceived by humans and, from what I understand, they are essentially ignored in calculations made to get to the Moon.

When we look at the Moon, we are looking at something that exists in a spacetime about an hour in the “future,” relative to the surface of the Earth. For every second the Earth and Moon have existed, the Moon has “aged” a few billionths of a second more than the surface of Earth.

Because we cannot perceive something, however, doesn’t mean we should ignore it. The Explorations of the Invisible Domain series of paintings I did at the Johns Hopkins Extreme Materials Institute dealt with visualizing matter and energy at scales beyond human vision. Gravity and time are two more things that are beyond human vision. 

Before jumping into a big effort to create more artwork about the invisible domain, I wanted to make sure my understanding of spacetime was correct. I needed a second opinion. So, I sent the information visualization to Professor Carlo Rovelli, who studies loop theory and gravitational energy. He has written many books about physics, relativity, and time. 

Rovelli’s response to my graphic was a green light for launching into an artistic exploration of gravity and time. 

He said, “Beautiful way of putting it!” 

That’s all I needed.


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