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Small But Significant Variances in Gravity and Time (Part Two of Two)

One-of-a-Kind TOKYO SKYTREE

TOKYO SKYTREE is taller than fireworks are high, and clouds often hug its upper decks, creating a veil of mist. During times of clear weather, it offers a sweeping view of the Kanto Plain—home to one of the world's largest population center. It is Japan's highest self-supporting built structure and the world's second highest. TOKYO SKYTREE was completed in 2012 as a successor to the 333-meter (1,093-foot) Tokyo Tower completed in 1958, equipped with broadcasting antennas, radio repeater equipment and more.

The newer tower, coming in at 634 meters (2,080 feet) in height, far surpasses its predecessor, now serves as Tokyo's symbol, and plays new roles in addition to that of a radio tower. For example, it is used for meteorological observations of rainfall, temperatures and thunder, and it even functions as a scientific observation platform for cloud droplet and fine particle sampling. It's crowded observation deck could also be called a wide area observation platform for visible-range electromagnetic radiation.
It is a vital facility in research such as urban stationary observation via infrared cameras to monitor heat island effects, and R&D in concentrated heavy-rain disaster prediction technology via digital terrestrial broadcasting equipment (as described in a previous article, "Reliable Clocks Help Us Find a Silver of the Clouds").

The following is an overview of an incredibly unique and cutting-edge experiment carried out in 2020 which made full use of TOKYO SKYTREE's unparalleled height.

What is an Eighteen-digit-precision Clock?

On April 7, 2020, a research group comprising members from The University of Tokyo and the Institute of Physical and Chemical Research (RIKEN) made a press release titled as follows:

The release was likely read by many since its title contained the two eye-catching phrases "TOKYO SKYTREE" and "Einstein's theory of general relativity." Although the description therein is somewhat hard to grasp from a quick skim, in short, it states that a wholly unprecedented clock was successfully created for the experiment. Allow me to provide a quick and logical overview of my own:

1. What is an optical lattice clock?
An optical lattice clock is a type of atomic clock invented right after the turn of the century—in 2001—by (at the time) Assistant Professor Hidetoshi Katori of The University of Tokyo. It uses a lattice made of light to create numerous, regularly spaced, tiny "compartments" containing atoms (which provide the reference frequency), achieved via precise laser control. Rapid measurements are taken of average frequency values for numerous atoms contained therein—an approach that enables the acquisition of frequencies with extremely few inconsistencies which serve as the basis for measuring a length of time. The reason it is called an "optical" lattice clock is that electromagnetic waves in the visible-light spectrum are used. These have higher frequencies than the microwaves (in the gigahertz band) in traditional cesium atom clocks and similar.

2. Just how precise is 18-digit accuracy?
The optical lattice clock has a reported accuracy down to 18 digits, which means 10–18 frequency variations (representing timekeeping precision). For comparison, accuracy down to two digits would mean a precision to one-hundredth of a second, and accuracy to nine digits would be precision to one-billionth of a second. Eighteen-digit accuracy represents precision of a further one-billionth of this previous (10–9) one-billionth-of-a-second accuracy! News outlets have frequently described this level of accuracy as "losing one second over 30 billion years," and although this number is actually based on a calculation of 1018 ,the inverse of 10–18, the point of this quantitatively understandable, sensationalized phrasing is to emphasize that the length of time required for 1 second's error to occur easily surpasses the entire age of the universe as measured from the Big Bang (approximately 13.8 billion years). Just as Chinese Tang-dynasty poet Li Bai used the exaggerated expression "as long as 3000 zhàng [a unit of mesure] of my white hair" to indicate extremely advanced age, the press's use of the "one second over 30 billion years" phrasing has a nice ring to it, and thus has become commonplace when explaining optical lattice clock technology.

But I digress. Cesium atomic clocks have reached a precision of 15 to 16 digits relative to the standard measurement unit of 1 second; the optical lattice clock has added 2 more digits on top of this, making it a leading candidate for the cesium clock's successor. Research is underway around the world using atoms of strontium (Sr), mercury (Hg), Ytterbium (Yb) and other elements in optical lattice clocks. However, actual verification of their 18-digit precision is difficult to achieve using existing cesium atomic clocks. In simple terms, one could liken this to attempting to measure something at 0.1-millimeter accuracy using a tape measure that only shows precision down to the centimeter.

It was necessary to come up with a new method of verification that did not rely on existing atomic clocks in order to confirm the optical lattice clock's 18-digit accuracy.

3. Applying the theory of general relativity to measure precision
This is where Albert Einstein's theory of general relativity comes in. Although I won't go into extensive detail here, suffice it to say that this theory relates to gravitational time dilation, which is a trope seen often in science fiction. As stated in the theory, time runs at different speeds in deep and shallow gravitational fields—in short, the higher the elevation above Earth's surface, the faster time's progression. A verification experiment was planned to put this theory to the test and, at the same time, verify the optical lattice clock's 18-digit precision.

In 2016, a research team performed a verification test using three optical lattice clocks installed at a RIKEN facility in Wako City, Saitama Prefecture and on The University of Tokyo's Hongo Campus (main campus) in Bunkyo Ward, Tokyo, wherein they measured frequency differences to check for variances in time's rate of progression. And because it was necessary to obtain precise elevation measurements in order to check the effects on time's progression of elevation differences—more precisely, the effects of gravitational potential disparities—the Geospatial Information Authority of Japan (GSI) joined the project to provide high-precision measurements. The frequencies of the three clocks at the two locations were compared in real time using a fiber-optic cable link between the sites.

The two clocks installed at RIKEN realized an identical frequency measured at 18-digit precision, whereas the one clock at The University of Tokyo exhibited a slightly lower frequency. The elevation difference calculated by the GSI (approximately 15 meters) and the elevation as calculated based on frequency disparity according to the theory of general relativity were identical within the permissible range of error for the experiment, so the team announced their success in measuring the elevation difference via optical lattice clocks.

4. Where does the TOKYO SKYTREE experiment come into play?
The 2016 experiment measured an elevation difference to demonstrate the potential of measurements using Einstein's theory of general relativity. However, the clocks used in the experiment were large, unwieldy units which could not be moved easily. Future measurement experiments would require new clocks of a more practical size with the durability necessary to survive transport unaffected.

The research group recruited Shimadzu Corporation to create two optical lattice clocks, each of which fit inside a 19-inch (48-centimeter) rack, and installed them at two locations in TOKYO SKYTREE: the ground-level floor and the TEMBO GALLERIA (highest-level observation deck).

An Indispensable Invention for Tracking Time Precisely

When the results of the two clocks were compared, the one installed on the observation deck showed a frequency 21.18 hertz higher than that of the clock at ground level. In other words, the upper clock oscillates 21.18 times in addition, in 1 second of the lower clock. As long as the properties of the atoms used therein were identical, this meant that time had progressed faster for the upper relative to the lower.

Using laser equipment, total station (TS), and GNSS receiver, the elevation difference between two clocks achieved centimeter-level accuracy. High-accuracy measurement was also carried out using a relative gravimeter—a technology introduced in part one of this article. Dedicated and passionate measurement professionals had confirmed the elevation difference (gravitational potential difference), and the 21.18-hertz frequency disparity described above fit with the theory of general relativity. Moreover, the two clocks were taken back to the lab afterward and measured at identical elevations for verification purposes, which confirmed the correctness of the 18-digit precision observed in the experiment—

in short, it proved that both clocks exhibited the same 18-digit timekeeping precision when at differing heights and when at identical heights. During the 2016 experiment, researchers were unable to definitively disprove device-related error between the three clocks used—error stemming from differences between the individual clock hardware—but they were able to do so with the 2020 experiment units. As a result, they could announce the successful completion of optical lattice clock technology.

In mid-18th century France, a chronometer capable of being transported and used with precision aboard ships was invented. If this were to be announced in the news today, the headline might read, "Completion of a Wholly Unprecedented Clock!," as this technology enabled humankind to precisely measure longitudes on our planet. The portable optical lattice clock, with elevation measurement precision down to the centimeter, will likely prove of even greater use than we can imagine in the future. Regardless of future developments, I believe the completion of this clock has already exhibited the same significance for humankind as the completion of the chronometer did to seafarers back in the Age of Discovery.

The abovementioned article also states, in its original Japanese text, that this technology achieves similar precision to that of experiments related to the theory of general relativity conducted using rockets and satellites with roughly 10,000-kilometer elevation differences. However, this latest experiment using optical lattice clocks—a type of clock with 10,000 times the precision of previous atomic clocks—proves that the same precision can be achieved with an elevation disparity of less than one ten-thousandth that of the space experiments. Proving the accuracy of time and frequency measurements provided by satellites orbiting Earth at high altitudes and speeds is of vital importance in the GNSS field (which includes GPS). This also shows just how integral the theory of relativity is to understanding it all, which is a theme I plan to explore further in a future article.

Small But Significant Variances in Gravity and Time (Part One of Two)