TY - JOUR

T1 - The young centre of the Earth

AU - Uggerhøj, Ulrik Ingerslev

AU - Mikkelsen, Rune E.

AU - Faye, Jan

PY - 2016

Y1 - 2016

N2 - 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 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.

AB - 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 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.

U2 - 10.1088/0143-0807/37/3/035602

DO - 10.1088/0143-0807/37/3/035602

M3 - Journal article

VL - 37

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 3

M1 - 035602

ER -