# 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.

• 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,(?)(?)(?),(?)(?)(?)?

• Note that this isn't asking if such a system is feasible, if countries would actually adopt it, if you can convert years accurately, etc. If you find any of these to be impossible, handwaving covers them. I am just interested in how accurately we can predict the age of Earth if technology is not a constraint. – Zxyrra Dec 4 '16 at 3:23
• What do you consider the "birth" of the Earth to be? Geologically, our planet formed very slowly as different smaller bodies consolidated together. So do you consider the beginning of earth to be the first collision in this cycle? The point at which the surface became solid? The impact that formed the Moon? Or some other point? – Timpanus Dec 4 '16 at 3:31
• @Timpanus The question answers that under "Clarifying how the system will work" – Zxyrra Dec 4 '16 at 4:01
• You can't do it with the age of the Earth, because there's no single instant at which the Earth was 'born'. It developed through a slow process of gradual accretion. Now you could THEORETICALLY do it from the 'birth' of the universe, since that was (at least according to current evidence) an instantaneous process. Of course the problem becomes figuring out exactly how long ago that was. Current estimates is 13.772 billion years, with an uncertainty of 59 million years, which is rather less than exact. – jamesqf Dec 4 '16 at 5:32
• Just to note that the Common Era is not based on "an event in the Christian religion". In the early 6th century they tried to compute a chronology based on that event, but their computation was incorrect (or maybe the event is not datable). The Common Era is simply the common era, with 1 CE / AD1 being by definition the year 754 AUC (Ab Urbe Condita, sice the foundation of Rome), or, equivalently, the 2nd year of the 194th Olympiad. And we do not actually have a chronology precise to the year for events in the 2nd millenium BCE or earlier. – AlexP Dec 4 '16 at 14:04

I would say this is impossible, as there is no actual point in time where you could say that the Earth was formed. The Earth, like all planets, was formed from dust and gases gathering into asteroids and then asteroids crashing together and "piling up" on each other. This process would lead to a spherical body very quickly (Ceres is speherical with just 0.015% the mass of Earth). And the process of asteroids crashing into Earth and adding mass to it is continuing to this day, with the planet growing by about 50,000 tons every year.

Asking when a planet was formed is like asking at what exact number of grains of sand you have a "heap" of sand.

You can narrow it down to a range of a few million years but it's physically impossible to define a single moment by which you could calibrate an atomic clock. Any method of time keeping has to set the starting point at a completely arbitrary point.

I believe the lasws of physics do not rule out that one might calculate the exact moment of the Big Bang, but I have great doubts that there will ever be the technology to do so.

Any system of measuring time for daily use that would have the starting point that early (even just as early as the age of the Earth) would also be widely impractcal. You probably would end up with a system that has something like 30 digits of which the first 20 digits are always identical for every event in human history. There's no practical use to count the seconds since the beginning of the world when human civilization covers only the last 12,000 years out of 4,500,000,000 years for the age of Earth or 13,800,000,000 years for the age of the universe.

I think the most practical thing to do is to take the current international calendar and add a one to the number of the year. That would make right now 12016.12.04.10:32:30 UST. It's still arbitrary, but you get a way of counting that is roughly beginning around the time civilization starts developing on Earth.

• What do you mean with your excerpt about the Big Bang (our error there, interestingly enough, isn't much greater than the error in uranium-238 dating - only about 20 million years)? – HDE 226868 Dec 4 '16 at 13:40

# 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.

• I have considered this but I'm wondering if there is another characteristic of the material within Earth (besides, for instance, ratio of parent to daughter isotope in a given sample) that would allow more accurate measurements if we developed the technology or calculations to observe it. – Zxyrra Dec 4 '16 at 4:00
• @Zxyrra There is not. – kingledion Dec 4 '16 at 4:03
• @Zxyrra Lord Kelvin tried to do it by studying heat transfer in the Earth-Sun system, and ended up with a value of 20-100 million years - off by two orders of magnitude. There are no reasonable alternatives. – HDE 226868 Dec 4 '16 at 4:04
• define original, we have 4.4 billion year old crystals, post moon forming impact but probably among the first solid rock on the planet. But you can't escape the margin of error becasue it is exponential decay on the tail end of such decay small changed make for big differences. – John Dec 4 '16 at 7:27
• That could work (with such a little precision) for a single rock sample, but we can't tell that a rock is as old as the Earth. We just have rocks that are older than any other extant rock, but they can be milions of years younger than the Earth itself. – Pere Dec 4 '16 at 11:02

## All prehistoric starting years will be arbitrary

All date estimates of past events based on physical measurements (as opposed to recorded history) will by necessity involve uncertainty. Depending on the particular event and dating method, that uncertainty will be measured in millions of years or thousands of years, possibly even just a century for some very recent prehistoric events - but choosing any single year will be arbitrary, as none of these methods can be accurate enough to convincingly state that a single year, or a particular exact number of revolutions around the sun is more valid than one year before or after that.

You are free to choose any historic event and use that as a reference, but all earlier events (e.g. the impact that formed the moon is a nice singular, exact event - unlike "earth becoming relatively spherical" which is slow and gradual) aren't suitable unless you find some aliens or time travelers for whom that event is included in observed and recorded history.

• The impact that formed the moon might serve, but you'll be hard put to find an alien who noticed. I was thinking about the supernova of the star that preceded our sun. Far more visible, and not that much longer ago. ;-) – Karl Dec 22 '18 at 14:58

There is no one agreed upon "date," but there are some interesting times we can base our estimate off of. I don't usually consider Quora to be a good scientific source, but in this case, Tim Kaye seems to be pretty knowledgable in the topic. He was asked the time frame in which the earth was formed:

The starting point is 4.568 billion years ago. That's the latest estimate for when our solar system got hit by a cloud of radioactive fallout (probably from a supernova) containing a great deal of the isotope aluminum 26. Evidence is found in CAIs (Calcium–aluminium-rich inclusion) in some meteorites. This event happened when the solar system was very young, maybe 250,000 years or so. This date is used as a substitute for the age of the solar system, and for the beginning of the formation of the earth.

he most widely accepted end date is the giant impact with a Mars-sized object called Theia (planet). The old estimate was 4.53 gya, but a newer estimate, 4.47, is now supported by two independent lines of evidence: 1) re-analysis of moon rocks from Apollo 12, and 2) meteorites containing debris from the collision.

So as you can see, there are a few interesting dates, but note the change in estimates for the end date: 4.53 to 4.47. Those are about 1% apart, but that 1% accounts for 60,000,000 years! This shows the real issue with this sort of measurement. All of our measurements have errors, and they are typically in the form of a fraction of the measured duration. If we wanted the disagreement over the start of our new calendar to only be, say, the difference in time between when George Washington was elected president of the united states and when Barack Obama was sworn in, you would need a measurement scheme which is accurate to 0.00000487%! Science can barely get answers that accurate in carefully constructed particle accelerator experiments!

Of course, the start of an epoch (the official term for the start of a time system like this) is rarely actually important. As long as you know your period and your epoch, you can convert from one epoch to another at will. If I were your society, seeking to free itself from the tyranny of religion, I'd pick a convenient epoch rather than a unreliable one. I'd pick midnight of Jan 1, 1958 as my epoch. Why? Because that's the assigned start epoch (as a Julian date) of the UTC time system. That's the assigned point where the atomic clocks governing UT2 were turned on and started keeping time. Instead of trying to manage time around some measurement billions of years ago, why not make the epoch right at the start of our atomic clock based era. You could measure everything in seconds since the epoch of UT2. Dates could be listed as "before the atomic clock era" and "after the atomic clock era."

Of course, if you're really interested in taking a good solid grasp on what measuring time really means, I recommend one of my other answers, which includes our (rather recent) history of trying to standardize time since the invention of atomic clocks.