Gravity slows time

Your head ages faster than your feet. Measured in 1959 up a lift shaft at Harvard, using an effect discovered the year before, at a precision that required controlling a speed of one micron per second.

1907 – 202217 min

By the end you should be able to

Derive gravitational time dilation from the equivalence principle alone
Say why the effect is so hard to measure and what made it possible in 1959
Distinguish gravitational redshift from ordinary Doppler shift

This prediction you can derive yourself, using nothing but the sealed box from two lessons ago. Put a light source in the floor of an accelerating rocket and a detector in the ceiling. The light is emitted and takes a little time to cross the cabin. During that time the rocket has sped up. So by the moment the light arrives, the ceiling is moving away from the velocity the floor had when it emitted. A receding detector sees light shifted towards the red. That much is just ordinary Doppler shift and a rocket.

Try the Pound–Rebka tower, then Everest. Nothing is moving, so this is gravity alone.

Loading the clocks…

Two clocks at different heights, with the drift enormously amplified — over the Harvard tower the real difference is 2.5 parts in 10¹⁵, about 0.2 nanoseconds per day. The rate is computed from the exact Schwarzschild potential rather than gh/c², which is why it stays honest all the way up to orbit.

What made the measurement possible was an accident of nuclear physics found in 1958 by Rudolf Mössbauer, then a graduate student. He had the Nobel Prize three years later, at 32. When a nucleus emits a gamma ray it recoils, like a rifle. The recoil carries away energy, and because the recoil varies, the emission line is smeared out — far too broad to see a shift of one part in 10¹⁵ against. Mössbauer found that a nucleus bound in a crystal lattice can sometimes emit with the entire crystal absorbing the recoil. The crystal is perhaps 10²⁰ times heavier than the nucleus, so the recoil energy becomes utterly negligible. What comes out is a gamma ray line of extraordinary sharpness — for iron-57, a fractional width of about 3 × 10⁻¹³. That is still a hundred times wider than the effect being hunted. But a line you can locate to a small fraction of its own width is a usable ruler, and this one was sharp enough.

The experiment

Weighing a photon in a lift shaft

Robert Pound and Glen Rebka Jr. · 1959, published 1960; refined by Pound and Snider, 1964 · Jefferson Physical Laboratory, Harvard University

The question: Does light climbing out of a gravitational field lose energy — and by exactly gh/c², the amount the equivalence principle demands?
The apparatus: An iron-57 source emitting 14.4 keV gamma rays at the bottom of the building’s lift shaft, with an iron-57 absorber 22.5 m above, exploiting the Mössbauer effect for a line sharp enough to work with. The shaft was bagged in mylar and filled with helium to stop the gammas being absorbed by air. The source was mounted on a loudspeaker cone and driven slowly up and down, adding a controlled ordinary Doppler shift to cancel the gravitational one — the compensating speed being under a micrometre per second. Source and absorber were then swapped so the measurement ran in both directions.

Theory predicted

A fractional frequency shift of 2.46 × 10⁻¹⁵ each way, so 4.92 × 10⁻¹⁵ for the difference between the two orientations.

They measured

(5.13 ± 0.51) × 10⁻¹⁵ — a ratio to prediction of 1.05 ± 0.10. The 1964 Pound–Snider refinement gave 0.9990 ± 0.0076.

How sure could they be? About 10% in 1959, under 1% by 1964. Running the experiment in both directions was essential: it doubles the signal and cancels temperature-dependent systematics, which at this sensitivity included the fact that a warmer source has faster-vibrating nuclei and therefore a slightly shifted line.

Why it mattered

The first laboratory measurement of gravitational time dilation, and the first test of general relativity that did not require an astronomical event. It is also the most direct: no orbits, no eclipses, no inference — a beam of light climbing 22.5 m and arriving measurably redder.

Measuring an effect by cancelling it

The experimental idea is worth admiring on its own. Rather than trying to measure a frequency shift of 2.5 parts in 10¹⁵ directly, Pound and Rebka cancelled it with a Doppler shift they controlled, and measured the cancelling motion instead. Move the source slowly towards the receiver and you blueshift the gamma rays by just enough to undo the gravitational reddening; the absorber comes back onto resonance and starts absorbing again. So the measurement becomes: how fast must the loudspeaker move to restore resonance? The answer is 0.74 micrometres per second — about a millimetre every 25 minutes — and that is a thing you can arrange and know. Converting an impossible measurement into a difficult one is most of what experimental physics consists of.

You might think

Gravitational redshift is really just a Doppler shift — the light is somehow moving relative to the detector.

Actually

Nothing is moving. In Pound–Rebka the source and absorber were both bolted to the same building, stationary with respect to each other for the whole experiment. The frequency changes because the two ends of the building sit at different depths in a gravitational field and their clocks genuinely run at different rates. Pound and Rebka used a Doppler shift as an instrument — to cancel the effect and thereby measure it — which is a nice irony but says nothing about the effect’s origin. Nor is it light "losing energy fighting gravity" in any straightforward Newtonian sense; the honest statement is that the emitter and receiver disagree about what one second is.

The measurement has since become almost domestic. 2010, NIST. Two optical atomic clocks separated vertically by 33 centimetres — one step of a staircase — showed the predicted difference in rate. 2022, JILA. The shift was resolved across one millimetre, within a single cloud of ultracold strontium atoms. Inside a sample about the width of a pencil lead, the top is measurably ageing faster than the bottom. This has stopped being a test and become a nuisance. The best optical clocks now keep time well enough that you must specify their altitude to within a centimetre for the reading to mean anything at all. Proposals to redefine the second are entangled with the fact that "the same time" is not well defined across a laboratory bench. Geodesists have started using clocks to measure the shape of the Earth's gravitational field, because a clock is now a better altimeter than an altimeter.

1907Einstein derives gravitational redshift from the equivalence principle, eight years before the field equations.
1925Adams claims to see the effect in the white dwarf Sirius B. The measurement was later shown to be badly wrong — and to have agreed with theory by accident.
1958Mössbauer discovers recoilless nuclear resonance, making a sharp enough gamma line possible.
1959Pound and Rebka measure the shift up 22.5 m of lift shaft.
1964Pound and Snider refine it to better than 1%.
1976Gravity Probe A flies a hydrogen maser to 10,000 km and confirms the effect to 70 parts per million.
2022JILA resolves the shift across a single millimetre of atomic cloud.