Accuracy of timekeeping based on the age of Earth
In many countries, we number the years based off of proximity to an event in the Christian religion - we are over 2016 years past that date. However, in this scenario, religion has become less mainstream, as, you could argue, it has been doing steadily over time in real life.
In this scenario, the world no longer wants to count based on proximity to that date - it wants to count years relative to the age of the Earth.
Clarifying how the system will work
- The length of one revolution around the sun (a "year") changes significantly after millions of revolutions, so the "years" counted in this system are all equal; conversion has taken place. The actual number of revolutions around the sun since the "birth" of Earth will be divided into a number of revolutions roughly equivalent to the time it took to orbit the sun from January 1st, 2015 to January 1st, 2016.
- Leap days and associated added dates are averaged into the length of the "year".
- This system assumes that the Earth was "born" once it became relatively spherical, and did not have sufficient debris in orbit. The moon doesn't need to be present at this time.
Answer Criteria
Technology based on scientific reasoning but out of the grasp of modern science that allows absolute dating of the age of the Earth will be accepted.
Answers should justify how close we can get to perfect accuracy when estimating the age of the Earth within the bounds of what we can physically observe (or otherwise calculate) assuming, as above, that we can "invent" whatever we need for it.
Time travel, asking aliens when they saw the Earth form, and other extremely bizarre methods are unlikely to be accepted.
How accurately can we calculate the starting date for this system, so that December 3rd, 2016 becomes December 3rd, 4,543,(?)(?)(?),(?)(?)(?)?
This post was sourced from https://worldbuilding.stackexchange.com/q/63295. It is licensed under CC BY-SA 3.0.
1 answer
Try radiometric dating. Accuracy: $\pm0.11\%$.
Radiometric dating - see also the excellent USGS page - uses the decay of radioactive isotopes of elements to determine the age of a sample. It works as follows:
- Assume that you have a sample of $N_0$ atoms of element $A$ at time $t=0$, and that no atoms enter or leave the sample during the period of study.
- Assume also that the atoms have a constant rate of exponential decay, i.e. $N$ behaves as $$N(t)=N_0e^{-\lambda t}$$ for some positive constant $\lambda$. Young-Earth creationists have disputed radiometric data measurements by saying that $\lambda$ can change over time. This is patently false - or, as I like to put it, a load of fetid dingo's kidneys.
- At some time $t'$, measure $N(t')$. Then, solve for $t'$ using the equation $$t'=-\frac{1}{\lambda}\ln\left(\frac{N(t')}{N_0}\right)$$
The precision (and accuracy, which is something different!) of the measurement depends on:
- The purity of the sample, for obvious reasons.
- The number of samples you have. Any imperfections become less important. if you have many samples and can essentially get rid of outliers.
- $N_0$, because smaller values make it much harder to determine how much is left after $t'$. Pick elements with long enough half-lives that they are still around in large enough quantities from the beginning of Earth, but short enough such that we can still observe decay happening.
According to Shoene et al. (2013), the uncertainty in the decay constant of uranium-238 is $\pm0.11\%$ - or about 5 million years, over the age of Earth. This has the most precisely determined $\lambda$.
Now, you don't have to use slow-decaying isotopes in all of your system. All you have to do is a trick: Have a reference time $t^*$ at which $N_A(t^*)$ is known, where $A$ is an isotope with a long half-life. Then, pick an isotope $B$ with a shorter half-life that can be observed over shorter timescales - that is, you can observe a significant amount of decay over the course of a year in a relatively small sample.
There have been some objections to this, namely, that it is difficult to determine the age of Earth through this method alone (there is a difference of 100 million years). I have some responses:
- That's an error of only 2%.
- It can be accounted for by studying meteorites that formed elsewhere in the Solar System, and by modeling the Sun.
- It does not affect our ability to measure the passage of time, only when it started on Earth. This is equivalent to not knowing when Jesus supposedly lived, to within 20 or so years (not bad).
- There is no other method capable of determining the age of Earth to this accuracy.
I do have one final note. Giacomo Catenazzi pointed out that the length of a year - the time it takes Earth to move around the Sun, from an astronomical point of view - has changed over time. Over the long term, we can calculate tidal recession effects from the Sun, and over the short term, we can calculate precession changes (see Simon et al. (1993)), but as Giacomo pointed out, this is not necessarily enough early in Earth's history. Even as late as the Late Heavy Bombardment, there could have been other changes from impacts and various other events.
I'll still hold that our models can account for most of these discrepancies, but he's right; they can't account for all of them.
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