A CNN article written by Jackie Wattles and titled “Why scientists say we need to send clocks to the moon — soon” grabbed my attention and quickly sent me down several rabbit holes that involved some ideas in physics that I knew but had not internalized. First, the moon needs its own timekeeping system because it sits in a different spacetime gravity well. The moon’s gravity is roughly one sixth that of the Earth’s so time flows faster on the moon – about 56.02 microseconds per 24-hour day at the moon’s equator.

This gravitational time dilation concept first fell out as a result of Einstein’s general theory of relativity. It was later confirmed during the Hafele-Keating experiment, conducted in 1971. For that experiment, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, flew two round-the-world trips on commercial airliners with two pairs of Hewlett-Packard (HP) 5061A cesium-beam atomic clocks, first flying eastward and then flying westward.

The flying clocks lost 59±10 nanoseconds during the eastward trip and gained 273±7 nanoseconds during the westward trip. These losses and gains had two relativistic components: one caused by gravity and one due to the aircraft’s speed. The predicted gravitic contribution was a gain of 144 ± 14nsec in the eastbound direction and 179 ± 18nsec in the westbound direction. The difference in the eastbound and westbound legs was caused by a difference in the average altitude of each flight.

Many refined versions of the Hafele-Keating experiment have been conducted over the decades. Most recently, physicists at JILA, formerly known as the Joint Institute for Laboratory Astrophysics, in Boulder, Colorado, conducted an experiment that verified gravitic time dilation over the distance of one millimeter. This experiment measured the redshift in the light emitted by a cloud of about 100,000 ultracold strontium atoms.

It’s unlikely that we’re going to send a science experiment like this recent one at JILA to the moon for timekeeping purposes, but there are several interesting and far more practical alternatives. First, there’s the current version of the HP 5061A cesium-beam atomic clock. The current version is the Microchip 5071A and 5071B Cesium Primary Time and Frequency Standard. Here, we have the second rabbit hole. How did Microchip end up with the evolved HP cesium-beam clock? HP developed the 5071A in the 1990s. When HP split into HP Enterprise, HP Inc, and Agilent, the HP 5071A went into the Agilent product portfolio. Agilent sold the 5071A to Symmetricom in 2005 and Microchip bought Symmetricom in 2013. If you look at a photo of the Microchip 5071A, you’ll see it’s housed in an HP System 2 cabinet, first introduced in the 1970s.

Microchip 5071A Cesium Primary Time and Frequency Standard. Image credit: Microchip

The Microchip 5071A weighs 30kg, consumes 100W, and is not space-qualified, so it’s not an excellent candidate for use as a precision timepiece on the moon, which leads to the next rabbit hole. Microchip appears to be in the business of supplying component-level, precision time references with atomic-clock performance levels. How did I miss that?

One of the most demanding applications for timekeeping on the Earth is for the Global Navigation Satellite System (GNSS), the term for the metaconstellation of satellites used for the Global Positioning System (GPS), the BeiDou Navigation Satellite System (BDS) operated by the People’s Republic of China, the European Union’s Galileo system, Russia’s GLONASS, and Japan’s regional Quasi-Zenith Satellite System (QZSS). All of these systems measure distance through precise time measurements. In fact, that’s one of the main reasons that the moon needs its own precision time reference – for navigation on and near the moon.

GNSS needs nanosecond accuracy from clocks to measure distances with 1m resolution. Quartz crystals have no chance in this rarified metrology domain. GNSS clocks come in three flavors: cesium-beam (like the Microchip 5071A), rubidium-cell, and hydrogen masers. The GPS satellites use cesium-beam or rubidium-cell clocks, but they require semi-daily updates from clocks on the ground based on hydrogen masers, which are really precise but are too large and fragile to send into space.

Microchip currently offers two types of precision clocks based on commercial designs originally developed by Symmetricom in conjunction with the Charles Stark Draper Laboratory and Sandia National Laboratory. The first such clock is the Chip Scale Atomic Clock (CSAC), which uses a miniaturized cesium light source to discipline a quartz crystal. NIST demonstrated the first CSAC in 2003, and Microchip’s CSAC-SA65 offers 1.5 E-11 @1000s short-term stability and an average aging rate of 9E-10 per month while consuming less than 140mW. NIST developed an even more stable Miniature Atomic Clock (MAC) based on rubidium in 2019, and Microchip’s MAC-SA55 offers 5E-13 @1000s short-term stability and an average aging rate of 5E-11 per month while consuming 4 to 14W. The Microchip chart below positions these various oscillators using axes of package size and frequency drift. Note that the cesium-beam and hydrogen maser clocks have much better drift specifications, but they’re much larger and require far more operating power.

Current precision timekeeping sources range from inexpensive and less stable MEMS oscillators to low-drift cesium-beam tubes and hydrogen masers. Image credit: Microchip

CSACs and MACs are not likely to be the last word in compact timekeeping, however, which leads us to the next rabbit hole. A team of researchers at the German Metrology National Institute (PTB) and the Technical University of Vienna, Germany recently managed to coax the nuclei of the isotope thorium-229 (²²⁹Th) into an excited state using vacuum ultraviolet (VUV, 100 to 200nm) light and were able to measure the energy differential of this state with much better precision than previously achieved (8.338 ± 0.024 eV).

The fact that atomic nuclei can be excited into higher states like electrons surprised me, but it makes sense upon reflection. While most of us are accustomed to seeing physical models of atoms with the proteons (protons and neutrons) in the nucleus glued together in something that looks like a rigid popcorn ball, that’s not really what’s going on in the nucleus. Each proteon has a multidimensional state consisting of angular momentum, parity, and isospin. These states occupy different energy levels, and nuclei therefore can occupy many different composite energy levels.

Most atomic nuclei have widely separated energy states that cannot be excited by a photon, but ²²⁹Th is different. It can be excited by VUV photons, and when it returns from its excited state to its ground state, the ²²⁹Th nucleus emits a photon with a precise wavelength of 148.3821nm. When the thorium is diffused into a calcium-fluorite crystal, as it was in this experiment, the crystal will fluoresce in the presence of these emitted photons. This nuclear state transition can be used to create a rugged, precise, solid-state clock in ways like those used to harness electron-state transitions in rubidium, cesium, and hydrogen atoms.

Perhaps, in the future, we’ll develop instantaneous communications using entangled particles. Then we can maintain tight synchronization with Greenwich Mean Time wherever we and our artifacts go in space. However, entangled-particle communications look very unlikely for the moment, and thorium-based clocks are not on the near-term horizon, so the moon’s near-term timekeeping needs will need to be based on current, more practical methods, including the two physics experiments in a package discussed in this article: Microchip’s CSAC and MAC.

References

“Hafele–Keating experiment,” Wikipedia

Peter Thirolf, “Shedding Light on the Thorium-229 Nuclear Clock Isomer,” Physics, April 29, 2024

“Chapter 6 – Nuclear Energy Levels,” Nuclear Science—A Guide to the Nuclear Science Wall Chart, Contemporary Physics Education Project (CPEP), Lawrence Berkeley National Laboratory

R. Lutwak et al, “The Chip-Scale Atomic Clock – Recent Development Progress”

R. Lutwak et al, “The MAC – A Miniature Atomic Clock”