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Earth's core is younger than its crust surface

Time is 'bigger on the inside'

Back in the early 1960s, physicist Richard Feynman remarked that the centre of the Earth had to be a little younger than the surface, since it would experience gravitational time dilation.

Now, boffins from two Danish universities have put a value to that difference, and while they agree with his hypothesis, they've corrected his estimate of the difference: while Feynman thought it would be “a couple of days”, a full calculation suggests it's two-and-a-half years.

The paper is here at Arxiv and has been accepted by the European Journal of Physics.

The authors – Ulrik Uggerhøj and Rune Mikkelsen at Aarhus University and Jan Faye of the University of Copenhagen – don't expect their “back of the envelope” calculation to change the world, but say it should be useful for teaching physics students.

The paper actually runs two calculations for Earth, with a “realistic” model of earth yielding the 2.5-year difference in age. Even if Earth's mass was homogeneously distributed, which it's not, the difference in gravitational potential from centre to surface would cause a 1.5-year difference.

The same mathematics works just fine for the sun as well, except that because of its size, mass, and age, the core-to-surface time dilation is much bigger.

In a non-homogeneous model of the Sun, the core is around 39,000 years younger than the surface.

As the paper says: “The pedagogical value of this discussion is to show students that any number or observation, no matter who brought it forward, must be critically examined” – especially since nobody had thought to question Feynman's remark until now. ®

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