Section 5–4 Long Times

(Natural time / Radioactive time / Astronomical time)

A measurement of long times is relatively easier by means of counting. In this section, the three main ideas discussed are a natural time, radioactive time, and astronomical time.

1. Natural time:

“…we can use these natural time markers to determine the time which has passed since some early event (Feynman et al., 1963, section 5.4 Long times).”

According to Dr. Sands, measurements of longer times are easy because we can just count the number of days as long as there is someone around to do the counting. Similarly, we can count the number of years for a physical phenomenon based on the natural periodicity of earth’s revolutions. Sands elaborates that nature has also provided a counter for years, in the form of tree rings or river-bottom sediments. In other words, we can use these “natural time” clocks to determine the age of a tree or compare the age of a river.

Dendrochronology (dendro = tree, chronology = time) is a scientific method to determine the age of a tree by counting the characteristic patterns of tree rings in tree trunks. Tree rings, also known as growth rings or annual rings, can be seen in a horizontal cross section of the trunk of the tree. They are due to the growth in diameter or layers of cells near the bark over the four seasons of a year. The rings are more visible where there are greater variations of temperature. They can be used as a calibration or verification check for radiocarbon dating. Similar seasonal patterns or “cycle of erosion” can be observed in layers of sediment deposition in a lake, river, or seabed.

If Feynman were to deliver this lecture, he might elaborate that “[t]he Maya Indians were interested in the rising and setting of Venus as a morning ‘star’ and as an evening ‘star’—they were very interested in when it would appear. After some years of observation, they noted that five cycles of Venus were very nearly equal to eight of their ‘nominal years’ of 365 days (they were aware that the true year of seasons was different and they made calculations of that also). To make calculations, the Maya had invented a system of bars and dots to represent numbers (including zero) and had rules by which to calculate and predict not only the risings and settings of Venus but other celestial phenomena, such as lunar eclipses… (Feynman, 1985, p. 11).”

2. Radioactive time:

“…One of the most successful is the use of radioactive material as a ‘clock’ (Feynman et al., 1963, section 5.4 Long times).”

Dr. Sands says that one of the most successful clocks for longer times is based on the use of radioactive materials. He explains that these so-called “clocks” do not have a periodic occurrence during the decay of radioactivity material. For example, the carbon dioxide molecules in the air contain a certain small fraction of the radioactive carbon isotope C¹⁴ that has a half-life of 5000 years and they are replenished continuously by the action of cosmic rays. If we measure the total carbon content of an object, there is a certain fraction of which that was originally the radioactive carbon. By careful measurements, we can measure the amount left after 20 half-lives and can, therefore “date” organic objects which grew as long as 100,000 years ago.

Radioactive clocks, such as the use of carbon-14 or uranium, help to determine intervals of natural time or geological time. They are sometimes described as non-cyclic clocks because the disintegration of a nucleus does not repeat periodically. More important, the disintegrations of nuclei are based on Rutherford and Soddy’s theory of radioactive decay in which the number of disintegrations in unit time is proportional to the total number of undecayed nuclei. However, radioactive clocks are subject to errors due to contaminations from other radioactive sources. These errors cannot be completely eliminated by calibration with the use of tree rings.

3. Astronomical time:

“… It is now believed that at least our part of the universe had its beginning about ten or twelve billion years ago. We do not know what happened before then. In fact, we may well ask again: Does the question make any sense? (Feynman et al., 1963, section 5.4 Long times).”

Dr. Sands explains that the age of the earth is found to be approximately 4.5 billion years and it is the same as the age of the meteorites which land on the earth, as determined by the uranium method. He hypothesizes that the earth was formed out of rocks floating in space and that the meteorites are likely come from some of these materials. Currently, it is questionable to say that the universe had its beginning about ten or twelve billion years ago (as mentioned by Sands). Based on Planck, a space observatory operated by the European Space Agency, the universe is estimated to be 13.82 billion years old. This is deduced using the concept of Hubble time or the time it would take for all the galaxies to converge at one point if they continue traveling at the same speed but in the opposite direction.

In the last few sentences of this section, Sands asks whether an earlier time has any meaning. In short, one possible answer is “no clock exists”. Interested students should read how Wilczek discusses this question as follows: “a question that vexed Saint Augustine: ‘What was God doing before He created the world?’ Saint Augustine gave two answers.

First answer: Before God created the world, He was preparing Hell for people who ask foolish questions.

Second answer: Until God creates the world, no ‘past’ exists. So the question doesn’t make sense… (Wilczek, 2008, pp. 103-104).”

Questions for discussion:

1. How is a natural time such as the age of a tree or river related to the revolution of the earth (astronomical time)?

2. How is the age of the earth determined by using radioactivity materials?

3. How is the age of the universe determined?

The moral of the lesson: the age of a tree is determined by counting the number of tree rings, the age of the earth is determined by the proportion of radioactive materials, and the age of the universe is determined by measuring the intensity of photons.

References:

1. Feynman, R. P. (1985). QED: The strange theory of light and matter. Princeton: Princeton University Press.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

3. Wilczek, F. (2008). The lightness of being: Mass, ether, and the unification of forces. New York: Basic Books.