Your head ages faster than your feet, and this has been measured
Two optical clocks separated vertically by 33 centimetres tick at measurably different rates. The effect is not a thought experiment or an extrapolation from satellites — it was observed on a laboratory bench in 2010, at the height of a table.
Aluminium-ion clocks with fractional stability near 10⁻¹⁷ resolved the gravitational redshift over a third of a metre. Since then a single cloud of strontium atoms has shown the shift across a millimetre of its own height. Over a human lifetime, the head-versus-feet difference amounts to tens of nanoseconds: real, cumulative, and completely ordinary.
General relativity is presented as a story about black holes and starlight. It is also a fact about furniture. Clocks are now precise enough that measuring altitude by timekeeping is a working surveying technique rather than a demonstration.
Invert the relationship and a clock measures gravitational potential, which means height. Chronometric levelling now resolves elevation differences of roughly a centimetre over long baselines, without a line of sight, which is difficult by any other method across continents. Transportable optical clocks have been carried into road tunnels to compare against geodetic surveys.
The caesium microwave standard that defines the second is a hundred times less stable than the best optical clocks. A redefinition around an optical transition is being prepared. When it lands, the base unit of time will be pinned to a physical system whose rate depends measurably on where you put it — which will have to be written into the definition.
“Your head ages faster” is a good line and a bad description.
Nothing about biological ageing has been tested. Clocks were compared; bodies were not. The claim is exactly true about proper time along two worldlines and says nothing about senescence — a distinction the popular phrasing exists to blur.
Nothing on the physics; the objection is to the framing, and it is correct.