The young centre of the Earth

TL;DR

This paper analyzes the gravitational time dilation effect at Earth's center, correcting previous estimates and providing an accessible calculation for educational purposes, emphasizing critical evaluation of scientific claims.

Contribution

It offers a detailed, undergraduate-level analysis of Earth's core aging difference due to gravity, correcting prior oversimplified estimates and highlighting the importance of critical assessment.

Findings

The time difference at Earth's center is approximately two and a half years.

Previous estimates of one or two days are significantly underestimated.

The analysis demonstrates the importance of careful calculation in scientific claims.

Abstract

We treat, as an illustrative example of gravitational time dilation in relativity, the observation that the center of the Earth is younger than the surface by an appreciable amount. Richard Feynman first made this insightful point and presented an estimate of the size of the effect in a talk; a transcription was later published in which the time difference is quoted as 'one or two days'. However, a back-of-the-envelope calculation shows that the result is in fact a few years. In this paper we present this estimate alongside a more elaborate analysis yielding a difference of two and a half years. The aim is to provide a fairly complete solution to the relativity of the 'aging' of an object due to differences in the gravitational potential. This solution - accessible at the undergraduate level - can be used for educational purposes, as an example in the classroom. Finally, we also briefly discuss why exchanging 'years' for 'days' - which in retrospect is a quite simple, but significant, mistake - has been repeated seemingly uncritically, albeit in a few cases only. 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.