Can Two Clocks a Millimetre Apart Keep Different Time?

Raise a clock by the thickness of a credit card. Would it run any differently? Near Earth’s surface, general relativity predicts that it would gain a tiny amount of time relative to a lower clock. In 2022 a JILA team measured this effect across about a millimetre inside one sample of atoms. The result makes an abstract word in relativity surprisingly concrete: to say how fast a clock runs, specify what you compare it with.

What counted as a clock?

An atomic clock uses a reproducible transition between atomic energy levels as a frequency reference. The JILA researchers trapped roughly 100,000 ultracold strontium atoms in a pattern of laser light. Instead of putting two clock housings on a bench, they compared the transition frequencies in the upper and lower parts of the same cloud. The atoms shared much of their environment. That helped the team distinguish a small vertical trend from noise common to the sample.

The size of the effect

For a small height change near Earth, the expected fractional frequency difference is approximately g times the height change divided by the speed of light squared. With a height of one millimetre, that gives about one part in ten billion billion. The upper atoms should tick a little faster relative to the lower ones. Measuring the variation across the cloud, and averaging repeated observations, let the team resolve a shift consistent with that prediction.

Nothing unusual happens to an observer beside either group of atoms. A second measured with a local clock feels ordinary. The difference appears when the two clock rates are compared. That is why a clock comparison is a stronger example of relativity than a story about time feeling slow or fast.

What does observer mean here?

A physicist can specify the locations, motions and comparison procedure precisely enough for a second laboratory to predict the result. No conclusion about a person’s awareness follows from changing the clock’s height. The interesting philosophical question comes afterward: what other disagreements in description become intelligible when we specify the conditions of observation as carefully?

See the JILA researchers’ paper and NIST’s explanation of the apparatus. For the wider argument, read The Observer Problem.