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TI-189Time2010

Your head is older than your feet

A clock higher in a gravitational field runs faster. Over a human life the difference between head and feet is less than a microsecond.

Established2 min read

The fractional rate difference between two clocks separated by a height h is gh/c². For h of about two metres that fraction is roughly 2 × 10^−16. Over eighty years the accumulated difference is on the order of half a microsecond. Your head, having lived slightly higher, has experienced slightly more proper time. It is the older end of you.

This is not a metaphor. Chou, Hume, Rosenband, and Wineland compared optical clocks raised by 33 centimetres and measured the shift. GPS has to apply the same correction or it fails, which is a different entry. The body version is the same equation with a ridiculous, and real, scale.

Caveats

  • Half a microsecond over a lifetime is far below anything a birthday, a wrinkle, or a doctor can detect.
  • The feet of a person who spends their life on a ladder are the older ones, by the same rule. Height in the field is what counts, not anatomy.

Sources

  1. 1Chou C. W., Hume D. B., Rosenband T., Wineland D. J.. Optical clocks and relativity. Science 329, 2010.

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