A discussion of carbon dating is indeed rather interesting especially given the large amounts of correlating chronologies that can be generated using this technique. I will address these later, but first it is required to know a bit about how carbon dating works and where the carbon comes from in order to fully understand it and avoid any misconceptions
(1) Introduction to the Elements and Radioactivity.
All atoms are made of protons, neutrons (collectively called nucleons) and electrons, with the exception of Hydrogen which consists only of a single proton and an electron. We determine the element of an atom by counting the number of protons that it has. Elements may have different numbers of neutrons, and these are called isotopes. For example, Hydrogen has two additional isotopes called deuterium and tritium which have one and two neutrons respectively. Deuterium and Tritium are unusual in that these isotopes have names, most are identified by a number alone. for example c14 or U235 for Carbon with 14 neutrons or Uranium with 235 neutrons respectively.
An unstable atom is one which can decay to form a lighter atom, and the stability of atoms can be determined from the semi-empirical-mass-formula[1]
from this we can determine the binding energy of the nucleons in the nucleus. If the binding energy of the particular atom is higher than the binding energies of the lighter atoms, then that atom can decay to lighter atoms and emit energy. From this we can deduce the decay rate of an atom, or the time it is expected to live. Radioactive decays however are random, so we cannot give a lifetime to a specific atom, however we can derive the half life, or time that it would take on average for half the atoms in a sample to decay. The larger the sample of atoms, the more accurately we approach the half life in our measurements.
Going back to the SEMF once again, it is also possible to form atoms by adding energy and groups of nucleons, for example if we bombard a source of atoms with neutrons or high energy particles, sometimes those nucleons will stick together and make new atoms.
(2) The Origins of C14[2].
The carbon with which we are most familiar is C12, that is, 6 neutrons and 6 protons. C14 is an unstable isotope consisting of 8 neutrons and 6 protons, with a half life of 5730 years. there is another stable form of carbon called C13, that we will not address here, but is very useful for NMR scans. C14 is produced constantly in the upper atmosphere as a result of the interaction of nitrogen and cosmic rays in the following nuclear reaction:
N14 (proton -> neutron) C14
and decays back to nitrogen
Since it is being produced at a constant rate and decaying at a rate proportional to the amount of C14 eventually we will reach an equilibrium where the amount being produced is the same as the amount that is decaying and the concentration of c14 in the atmosphere remains constant. There will however be fluctiations since the solar wind is not constant, however we will look at this later.
(3) Misconceptions of C14 Dating.
There are a number of common misconceptions made when discussing C14 dating, and these will be covered in this section. The quantity of C14 is detected via dosimetry (for example using a geiger counter that detects atomic decays). One of the problems that this presents is that there are decay events occuring all the time, from materials naturally released by the earth through to fallout from nuclear weapons testing. The amount of background radiation around us varies depending on where one goes and is high in areas where there is alot of granite because of the Uranium content for example. Now when measuring a sample, this background radiation creates noise, which, if our sample only contains a tiny amount of C14, will wash out the radiation released from the sample; in short we simply cannot tell the difference between the radiation from the sample and the natural background. This limits the age of objects which we can date. A rough guide is 10 half lives, or in the case of C14, about 50,000 years. So C14 can only be used to date things up to around 50,000 years - it is useless for dating dinosaurs and so on, because there is not enough C14 in the fossils to detect, regardless of how old they actually are. so all we can say about such fossils is that they are over 50,000 years old.
From earlier we noted that C14 is produced in the atmosphere. well what about other carbon sources? well we know that there is lots of dissolved carbon in the sea, which originates from limestone and other ancient deposits. Now this carbon is all extremely ancient - often referred to as "dead" carbon as it contains little or no C14. So if anything gets their carbon from these sorts of sources, or is contaminated by these sources, then it will appear much older than it actually is. So for example we cannot date fish, seals, mussels, limpets and so on using C14, as their primary carbon source is the ocean, and hence dating them will make the organism look much older than it really is. You may have heard of freshly killed seals and mussels dated to several thousand years old - this is why. If you fed a seal on a primarily atmospherically derived carbon source, it would appear to be the right age. Contamination of samples can also be a problem, so if we preserve something in a carbon based preservative, then we will get a false age yet again - this has been observed in Mammoths preserved in formaldehyde and other preserving agents. Other interesting examples of problems can occur in underground nuclear sources which produce C14 in a similar way to atmospheric sources, so sometimes coal might be dated as under 50,000 years old if it is near a uranium deposit for example, since C14 will be produced from the radiation from the Uranium, again observation of the environment in which the material is found can eliminate these problems, since if you know there is contamination in some way, then you know your result is going to look strange.
I mentioned earlier that the amount of C14 under production in the upper atmosphere may change, and indeed it does. One criticism of C14 dating is that it relies on knowing how much C14 is produced, and of course nobody was measuring the Solar Wind 4000 years ago so how do we know how much was being produced. Maybe a lot less was being produced, making things look much older than they are, well we can test this also, and so I move on to the next section
(4) Correlating C14 Dates with independent measurements of age.
If the rate of C14 production changes, then how can we determine an age? We have to callibrate the amount of C14 according to the production rates, and this presents C14 dating with a problem, since one requires a well understood and accurate measure in order to determine how much C14 was produced in the first place. There are a number of available sources
(4a) Correlation with Tree Rings
There are a number of known trees which are thousands of years old and still alive. Each year, trees will deposit one layer of dead wood which makes up the trunk of the tree. The trunk's carbon source is atmospheric in nature and so will contain the sam proportions of C14 as the atmosphere, but once deposited, the wood is effectively "dead" and the C14 will decay out of equilibrium with the environment. Since we can see how old the tree is by looking at the numbers of rings, we can callibrate the amount of C14 and work out perturbations from the current value. We can match the amount of C14 in the living trees with dead trees and see where they overlap. Using this we can callibrate the C14 production rates back to about 9000 years or so. Occasionally there are additional rings or missed rings, however dendrochronologists can tell quite easily, and there is a tendency for missed rings rather than extra ones, and so trees are older than we think. Certain trees are less likely to miss or gain rings, and a knowledge of the trees can further improve accuracy.
(4b) Correlation with Lake Varves
Another type of seasonal deposition comes in the form of lake varves. In very calm lakes we find that there is a slow deposition of silt. In these lakes there also may be an abundance of algal and bacterial life living on the surface of the water (whose primary carbon source is atmospheric) which peaks during the summer and drops off during the winter. As these algae die, they also settle to the bottom of the lake. Since the silt is constantly being deposited and the dead organisms are periodic, then we see alternating dark and light bands. Each year, one of these bands is deposited, and these can form extremely thick layers consisting of thousands of bands. In the same way as the tree rings, we can analyse each of these bands and look at how much C14 is in them and correlate this with the number of bands. Using this technique we can correlate the amount of C14 in the atmosphere by tens of thousands of years (the most extreme perhaps is the Green River Formation in Wyoming, which has some 4,000,000 layers - these are all however too old for C14 dating). There are many of these sequences around the world, from Lake Sugietsu, Japan to Lake Gosciaz, Poland, The Cariaco Basin in Venezuela [3] lake Van in Turkey and others in Germany and Switzerland.
A criticism of this technique is that many varves may be deposited in a year. THe problem with that assertation is that this variation would have to be global in scale since we see correlation between the lakes all over the world.
The straight line is the assumption that C14 production rates have remained constant over the past few tens of thousands of years.
we see a slight drift from the C14 predicted dates and the predicted varve dates, due to the changing C14 production rate, but note that these variations correlate on a global scale - the graph includes points from Japan, Poland, Germany and Switzerland.
(4c) Correlation with Ice Cores[4]
Many polar regions are effectively deserts, seeing only a tiny amount of snowfall each year. During the summer months the snow is heated and melts slightly, and suring the winter it is deposited but not melted. Again this forms bands that are thousands of layers thick. Within this snow, bubbles of air containing a tiny sample of the atmosphere can be trapped. The Carbon in these bubbles can be analysed as normal, and the amount of C14 can be meaured. Since the layers are formed annually this can be callibrated with the amount of C14. As a slight aside, some of these ice cores are some three km thick, stretching back 740,000 years showing 8 ice ages which match with the obliquity cycle and the eccentricity cycle that occur every 41,000 and 100,000, confirming that these have a major impact on atmospheric conditions. So here we have ice cores matching up with astronomical evidence.
(5) Non C14 isotope dating.
As an additional note, there are a number of different types of radioisotope dating, using unstable elements other than C14, for which the lifetimes may be much longer. There are a number of methods of calculating the dates for these, from amount of material present through to ratios of parent and daughter products. Are there any alternate rulers to check these? Well these are much rarer, but here is one particularly exciting example.
Corals[5], much like trees, show varying deposition rates with the seasons. Corals are so sensitive however that we can study the weather at the time. In fact, to the extreme degree that corals have
daily bands. and using these bands we can measure the length of the day when the corals were alive. A study of the earth shows that its rotation is slowing at 0.000015 sec per day and that during the Devonian period some 360-410 million years ago, the day would have been a mere 21.8 hours in length. Using thorium 230 and protactinium 231 radiometric methods we have dated corals to this time period, and an analysis of the coral structure indeed demonstrates that the day length was indeed much shorter. In this case we have a callibration between astronomical events and decay rates.[6][7]
(6) Summary
One Criticism of these techniques is whether the alternate "rulers" are themselves accurate. Tree rings are pretty much undoubtedly accurate, and errors tend to be minor, observable and make the trees look younger than they really are. There is Global Correlation of Lake Varve ages and Ice core Ages, and what is more, all three different techniques agree with one another to a high degree of accuracy. The three, totally independent alternate "rulers" agree in terms of their C14 content, and all agree in terms of the fluctuations in C14 production rates over the entire useful lifetime of C14. While there may be criticisms of a particular technique, to date I have never seen a good criticism of the global and multi technique correlation of independent dating techniques.
(7) References and Bibliography
[1] Discussion of Semi-Empirical Mass Formula
http://www.phy.uct.ac.za/courses/phy300w/np/ch1/node22.html
[2]http://www.rlaha.ox.ac.uk/orau/sources.html
[3]http://www.ngdc.noaa.gov/paleo/pubs/hughen1998/cariaco.html
[4]
http://www.ngdc.noaa.gov/paleo/icecore/antarctica/vostok/vostok.html
[5]http://freepages.genealogy.rootsweb.com/~springport/geology/coral_growth.html
[6]Laurent Augustin, et al., Eight Glacial Cycles from an Antarctic Ice Core, Nature 429 (2004), 623-628.
[7]Jerry F. McManus, A Great Grand-Daddy of Ice Cores, Nature 429 (2004), 611-612.
nb: I may add a couple more graphs to this later.
