It is difficult to discuss the age of the earth without at some point referencing radiometric dating. I am going to give my best summary of the dating process itself because too often I have heard people dismiss radiometric dating offhand without even understanding the process. After that, I will discuss carbon dating more specifically.
All ordinary substances are made of atoms, and atoms are composed of protons, neutrons, and electrons. The type of element is determined by the number of protons. The number of neutrons in an atom of a certain element determines the isotope of that atom. This does not affect the chemical properties of the atom. However, if the atom has either too many or too few neutrons, then it is unstable, or radioactive. An atom of a radioactive isotope will at some unknown point in time undergo one of several types of radioactive decay, in which certain particles are ejected from the atom, resulting in the atom changing from one element to another.
Although it cannot be known when any particular atom will decay, it can be predicted with great accuracy when any given percentage of a radioactive sample will have decayed. Therefore, if we know how much of a radioactive isotope existed originally in something and how much is in it currently, then we can quite easily calculate its age.
Now the most obvious complication in this process is that the initial concentration of a radioactive isotope in an object typically is not immediately evident. However, there are ways in which it can be determined with confidence. Some of these are more straightforward than others.
One of the more straightforward methods of radiometric dating is carbon dating, which is used to find the age of once-living organisms or of materials made from them. Carbon-12 (6 protons, 6 neutrons) comprises most of the carbon on earth, but a small percentage is radioactive carbon-14 (6 protons, 8 neutrons). Because living things constantly exchange carbon with their environment, every living organism that takes in carbon primarily from an atmospheric source has the same ratio of carbon-14 to carbon-12 as that found in the atmosphere. After the organism dies, however, carbon is no longer exchanged with the environment, and the carbon-14 within it decays at a predictable rate, with half of the remaining carbon-14 decaying every 5730 years.
The historical levels of atmospheric carbon-14 have not been perfectly constant, but they can readily be determined by analyzing tree rings. The wood in the inner rings of a tree is as old as those rings themselves. For example, the innermost ring of a 1000-year-old tree is 1000 years old. By finding the relative amounts of carbon-12 and carbon-14 in this ring, knowing its age, it is a simple matter to determine the ratio of carbon-12 to carbon-14 in the ring (and thus in the atmosphere) when the ring was formed. This provides a reliable calibration for the carbon-dating process, enabling carbon dating to be performed with confidence. This calibration based on tree rings extends around 10,000 years into the past. Other methods exist for calibrating the carbon-14 record further into the past, but with significantly greater uncertainty.
It is certainly possible for carbon dating to be performed inappropriately. For example, marine organisms (or animals that eat primarily marine organisms) cannot be dated by this method because they obtain carbon from an oceanic source, which does not have the same level of carbon-14 as the atmosphere. Carbon dating a seal or a penguin, for instance, will yield a result far older than its actual age.
I have heard it argued that the carbon dating method cannot be reliable (or else that the earth must be young) because significant amounts of carbon-14 have been found in coal that supposedly is millions of years old, by which point virtually all of the carbon-14 should have decayed. This is true, but it is only half of the story. Some coal contains carbon-14, and some does not. The amount of carbon-14 varies greatly from one coal deposit to another, and there is a correlation between the amount of carbon-14 in the coal and the radioactive content of the surrounding rocks. This suggests that the carbon-14 may be produced in the coal by radiation emitted from nearby rocks. This is a subject of ongoing research.
Carbon dating has consistently been shown to be a reliable process. For example, it is used for dating biblical manuscripts and consistently yields dates in agreement with other methods (e.g., handwriting analysis). When used properly, carbon dating is a powerful tool for determining the ages of once-living things.
I should note that although I have had this article drafted for quite a while, it has taken me a long time to publish it. This is partly because my employer has been giving me more work (which is a good thing), partly because I have been occupied with other projects, and partly because I just wasn’t happy with the way it came out and could not improve it to my own satisfaction. However, I do have much more to say, so I will publish this and move on.