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Atoms as the Basis for Measuring Both Fleeting Moments and Near-Eternities

Carbon is Present in All Living Things

The opening line of the children's song Sei-Kurabe ("Comparing Heights"), familiar to many in Japan, goes as follows: "The mark on the pillar is my height from the year last before." The song serves as the common human experience, the importance of eating and sleeping well to foster a healthy body. The markings on a wooden pillar serves as a tangible record of a child's development, becoming a cherished part of family history.

All living organisms on Earth rely on organic molecules composed primarily of carbon atoms. These carbon-based molecules are constantly consumed and processed throughout an organism's life. Carbon exists in nature as three primary isotopes: carbon-12 (12C), accounting for approximately 99% of all carbon; carbon-13 (13C), which is slightly heavier than 12C due to an additional neutron; and carbon-14 (14C), a radioactive isotope that decays into nitrogen-14 over time. While 12C and 13C are stable isotopes, 14C is unstable and undergoes radioactive decay.

Radioactive decay, the process by which an unstable atomic nucleus spontaneously transforms into a different nucleus, is a probabilistic event. While it is impossible to predict when a specific atom will decay, scientists can determine the "half-life" of a radioactive isotope. The half-life represents the time required for half of the atoms in a given sample to undergo radioactive decay. This period varies significantly among different isotopes. For 14C, the half-life is approximately 5,730 years.

In the Earth's upper atmosphere, cosmic rays interact with nitrogen atoms, transforming them into 14C isotopes. These 14C atoms readily combine with oxygen to form carbon dioxide (CO2), which is then distributed throughout the atmosphere. Living organisms incorporate this atmospheric carbon dioxide into their tissues through photosynthesis and the food chain. Although the abundance of 14C in the atmosphere is minuscule, representing only about one part per trillion of the total carbon, all living organisms contain a measurable amount of 14C at any given time.
For instance, a 70-kilogram (154-pound) human contain only a minuscule amount of 14C, roughly one part per trillion of the total carbon in their body. However, this translates to an astonishing number of 14C atoms – approximately 632 trillion. (This calculation is based on the following: human weight × 18% carbon content in the human body × Avogadro's constant (6.02E23) × 14C abundance rate (1E-12).)

At the time metabolism stops, the 14C content ratio have fixed. This allows scientists to utilize the known half-life of 14C (approximately 5,730 years) to estimate the time elapsed from stop. If a 70-kilogram human body were preserved for 5,730 years, the amount of 14C within the body would be reduced by half. After 11,460 years, only one-quarter of the original 14C would remain, and after 57,300 years, less than 0.1% of the original 14C would be detectable. By measuring the current 14C abundance in a sample and comparing it to the expected level in a living organism, scientists can effectively "reverse-engineer" the time of metabolism stops, a technique known as radiocarbon dating.

Corrections and Calibration: Keys to Improved Measurement Accuracy

Radiocarbon dating is a chronological dating technique that leverages the well-defined half-life of radioactive carbon isotopes. However, accurately determining the age of an organism using this method requires more than simply measuring the decay rate. Various natural factors and environmental influences must be carefully considered and incorporated into the calculations to ensure accurate results.

This scenario is analogous to GNSS positioning and time synchronization calculations. Determining the distance between a satellite and a receiver involves multiplying the signal travel time by the speed of light. However, achieving accurate results necessitates accounting for various factors that delay signal propagation, such as ionospheric plasma and atmospheric precipitation. To further enhance accuracy, it is crucial to incorporate information on the satellite's orbital parameters, discrepancies of satellite's atomic clock time and other relevant variables. In essence, true accuracy hinges on compensating for these hidden factors that are not explicitly considered in the initial distance calculation.

The IntCal20 calibration curve serves as a fundamental reference for radiocarbon dating, providing a more accurate and precise timeline for events occurring within the last 50,000 years. Constructed through meticulous analysis of various natural archives, including lake sediments, stalagmites, and tree rings, the curve accounts for fluctuations in atmospheric 14C concentrations over time. By aligning measured 14C values from a sample with the IntCal20 curve, researchers can obtain calibrated radiocarbon ages with a typical uncertainty of ±170 years.

A Global-Scale Measurement Standard Going Back Fifty Thousand Years

In summary, high-precision radiocarbon dating relies on two key elements: the universally accepted constant of radionuclide half-life and meticulously developed calibration models, the result of extensive scientific research and innovation. I see striking parallels between this technique and GNSS positioning and time synchronization operations:

1. Shared Reliance on Fundamental Principles and Corrections: Both disciplines rely on fundamental physical constants, such as atomic frequencies in GNSS clocks and the half-life of radionuclides in radiocarbon dating. Furthermore, both require the application of correction factors to account for real-world influences, such as radio wave propagation delays in GNSS and variations in atmospheric 14C production in radiocarbon dating.

2.Impact of Solar Activity: Solar activity significantly influences both systems. In radiocarbon dating, solar activity directly affects the production of 14C. Similarly, high solar activity can disrupt GNSS signals, leading to increased positioning and timing errors.

3.Global Timekeeping and Synchronization: Radiocarbon dating provides a global temporal framework by utilizing the ubiquitous presence of 14C in living organisms throughout Earth's history. With a different scales and resolution, GNSS also plays a crucial role in global time synchronization, providing precise time information across the planet.

Very-long-baseline interferometry (VLBI), ancestors of GNSS, leverages celestial phenomena – in this case, radio waves from distant celestial objects – to make precise measurements. Just as radiocarbon dating utilizes the naturally occurring presence of 14C, VLBI capitalizes on the ubiquitous presence of celestial radio sources to provide valuable insights into Earth's rotation, plate tectonics and other scientific facts.

Going Back Further in Time Using Chemical Elements

Radiocarbon dating is a highly accurate method for determining the age of organic materials up to approximately 50,000 years old. For events that occurred much further back in time, such as the dinosaur extinction estimated to have happened 66.05 million years ago, other dating techniques are necessary. This preciseness a significant improvement over the estimates found in many older children's books, was established through a combination of methods, including the analysis of past geomagnetic reversals and radiometric dating using isotopes with much longer half-lives than 14C.

Commonly used nuclides for radiometric dating include potassium-40 (decaying to argon-40 with a half-life of 1.25 billion years) and uranium-238 (decaying to lead through a series of steps with a half-life of 4.50 billion years). These isotopes allow for dating events that occurred hundreds of millions of years ago with a relatively high degree of accuracy, typically within 0.1 to 1 percent.

One particularly long-lived nuclide is rubidium-87, which decays to strontium-87 with a remarkably long half-life of approximately 48.8 billion years – significantly longer than the estimated age of the Universe. The rubidium-strontium (Rb-Sr) dating method, which exploits this extremely slow decay process, is capable of dating geological events that occurred over 10 million years ago. By analyzing the ratio of 87Rb to 87Sr in rocks, while also considering the stable isotope strontium-86, scientists can determine the time at which the rock formed.

Researchers and professionals who rely on precise time synchronization are likely familiar with commercial atomic clocks that utilize rubidium. Next-generation optical lattice clocks are poised to employ strontium instead. It is remarkable to consider that the measurement of time, spanning from fractions of a second as small as one quintillionth (1/100,000,000,000,000,000) to the vast expanse of billions of years, can involve the same chemical element.
This suggests a possible, perhaps even imaginative, connection between the microcosmic and macrocosmic realms, linking the world of fleeting moments with the vastness of cosmic time.