The young centre of the Earth
Abstract
We treat, as an illustrative example of gravitational time dilation in relativity, the observation that the centre 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 backoftheenvelope 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.
 Publication:

European Journal of Physics
 Pub Date:
 May 2016
 DOI:
 10.1088/01430807/37/3/035602
 arXiv:
 arXiv:1604.05507
 Bibcode:
 2016EJPh...37c5602U
 Keywords:

 Physics  Physics Education;
 Physics  Popular Physics
 EPrint:
 Published version, apart from minor editing (e.g. corrections of 'center' to 'centre')