Relativity is one of those fascinating branches of physics whose consequences might seem a bit illogical when compared to everyday life, like the twin paradox. Now, another quirk of relativity has been revealed: due to gravity, Earth’s core is younger than the crust.
Ulrik Uggerhøj from Aarhus University in Denmark and his colleagues used both a very simple approach and then a more sophisticated one to work out the effect the accumulated action of gravity has on the different layers of our planet. They found, in the more accurate model, that the crust is about 2.49 years older than the core, reported New Scientist.
According to the principles of general relativity, the stronger the gravity field is, the slower time will move. If we had two clocks, one near the center of the Earth and one on the surface, the first one will appear to tick more slowly than the second one. This research shows that the core clock loses 0.3 nanoseconds for each second it passes.
Uggerhøj decided to investigate the difference while writing an undergraduate book on physics. He wanted to include a quote by Richard Feynman about the effects of gravity, on how the “the center of the earth should be a day or two younger than the surface.” This number has often been quoted, even by Uggerhøj, but in writing the book he wanted to also include a calculation, and that’s when he noticed the discrepancy.
The researchers started with a model in which Earth is a perfect sphere with the same density everywhere. The formulas used, although borrowed from general relativity, are simple enough to be followed by most high school students. They can be seen in the team's paper on arXiv. The simplest scenario indicates that the center is 1.58 years younger the surface.
To produce a more precise estimate for the crust-core age difference, the team used a more realistic density distribution. The Earth becomes denser towards the center but not linearly, so geologists have different models to describe the interior of our planet.
In their paper the team used the Preliminary Reference Earth Model, a one-dimensional model used to work out where the different layers separate. The realistic model needs a more complex mathematical calculation, but the answer was still easily obtained. The team stated that this is a purely physical calculation and only take into account the elapsed time from Earth's formation.
The researchers applied these calculations to the Sun as well. They worked out, based on a realistic model called Model S, that the core of the Sun is 39,000 years younger than its surface.
This work also highlights the need to always double check calculations. Uggerhøj states how many physicists, including himself, have just assumed the calculations were correct but somebody, either Feynman or the transcriber, must have switched years for days.
The authors believe this is very important from an educational point of view. In the paper, they write: “Realising that even geniuses make mistakes may make the scientist more inclined towards critically examining any postulate on his/her own.”
[H/T: New Scientist]