Müller and his lab use an atomic interferometer to split a Cesium atom wave in two. One half of the wave will remain stationary, and the other half will be sent through a long tube before reflecting down to where it started. Here, the clocks represent the frequency of oscillation of each half of the particle wave. They initially tick at the Compton Frequency.
This frequency is far too fast to measure directly (if we made the clocks actually spin this fast, you would not be able to perceive their movement!), so they must calculate this frequency in a different way.
Clock #1 on the left represents the reference half of the wave, which remains fixed in space.
Clock #2 on the right will be sent up the atomic interferometer using a series of calibrated lasers.
Both waves continue to oscillate as clock #2 on the right moves up the long tube of the atomic interferometer. As clock #2 moves through space, its clock starts to move more slowly than reference clock #1, in a relativistic phenomenon known as "time dilation."
The difference in clock hand position is measured at a detector, and is used to calculate the measured interference between the two waves.
This and the known speed of the moving particle allows Müller's lab to determine the original frequency of the atoms (the Compton Frequency).
Using equations for the relationship between mass and frequency (via Planck's constant, h, and Einstein's equations), they can then calculate the mass of the Cesium particle.