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:

1. 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.
2. 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.
3. 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.

posted almost 8 years ago

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