Reply to Bethgem's Questions.
"Note: the most accurate theory man has ever devised."
How do you know? I know little enough about this to be under the impression that it's only circumstantially experimentable (is that a word?). And mathematics indicates its veracity. Is that true?
Can you do a post, since you mentioned radioactive decay, dealing with carbon dating? I still don't quite understand how that works (or doesn't work). I know it's asking a lot...
Okay, I'm a moron. Obviously carbon isn't radioactive. Can you explain it anyway?
Replies to Bethgem. Esther, please read this! I'll tell you why later.
QED (Quantum Electrodynamics) is considered the most accurate theory man has ever devised. Why is that? Because the theory and experiment match up numerically to about nine or ten decimal places, which does not happen with any other theory.
You are right to call into question the veracity of science. As Gordon Clark was fond of saying, "Science is a collection of useful falsehoods." What he meant by that is that science is no means of arriving at truth. It can only give us approximations to the truth, and those approximations have predictive power, enough, as the engineers would say, for all practical purposes. Mathematics, on the other hand, I believe to be true in a manner quite beyond the capabilities of science. Mathematics is one gigantic "if-then." Start with these premises, come to those conclusions. Mathematics does not usually have as much to say about the premises as it does about the method of arriving at the conclusions from the premises. Mathematics is, among other things, the language of science.
About radioactivity. There are two major things going on here: the nuclear strong force, and the nuclear weak force. An atom is made up of protons, neutrons, and electrons. The protons and neutrons together form the core of the atom, known as the nucleus. The strong force tends to hold the nucleus together, and the weak force tends to split it apart. Both the strong and weak force get stronger the larger the nucleus. So for uranium, e.g., the strong and weak force are both stronger than for helium (a much smaller nucleus). However, the weak force gets stronger faster, with increased nucleus size, than the strong force gets stronger. Eventually, given a big enough nucleus, the weak force overcomes the strong force, and the nucleus splits. This is radioactivity.
Now carbon 14 dating works something like this. First of all, let me explain something about the elements. In an atom, if you vary the number of electrons, then you are talking about different ions. If you vary the number of protons, you get different elements. If you vary the number of neutrons, you get different isotopes. Most importantly, if I add some neutrons to an atom, I don't get a different element, but I do get a heavier nucleus, and thus the balance of the weak and strong force shifts more towards the weak force, thus tending to make the atom more unstable, or more radioactive.
Now about carbon. The usual isotope encountered in nature is Carbon 12. Now since we are talking about carbon, that means there are 6 protons. Carbon always has six protons, because if you recall, the number of protons determines the element. If we're talking about carbon 12, then there must be 12 - 6 = 6 neutrons. However, you also find carbon 14 in nature, which still has six protons, but now has 8 neutrons. With me so far? Now carbon 12 is stable, but carbon 14 is radioactive, though it takes a long time for the average carbon 14 atom to decay, on the order of a few thousand years I believe.
As it turns out, scientists have observed that the ratio of carbon 14 to carbon 12 in the atmosphere has remained quite constant ever since we started measuring. So, and here is the crucial step and highly problematic, we extrapolate backwards and assume the ratio was the same a few thousand years ago as it is today. Some scientists are willing to go even farther back.
The next item to consider is that living things today have the same ratio of carbon 14 to carbon 12 as does the atmosphere around them. However, when they die, they stop getting any carbon infused into their carcass. In time, the carbon 14 decays, leaving only the carbon 12. This changes the ratio of carbon 14 to carbon 12 in their bodies. Since we know generally how fast carbon 14 decays, we extrapolate backwards by measuring the current ratio in some fossil or carcass. This gives us some measure of the age of the fossil or carcass.
The mathematics involved in the theory here is not extremely complex: straight-forward freshman calculus. What's hard is measuring the carbon ratio in whatever sample you're examining. Incidentally, scientists can only perform carbon 14 dating on things that were once alive. Other dating methods are not so restricted.
Carbon 14 dating makes many assumptions, which are rightly challenged by many scientists today. I would not trust any carbon 14 dating if applied to anything older than, say, 4000 years. Scientists have shown that its accuracy is highly suspect outside the date range of maybe 1000-4000 years. They even dated a deer that was 27 days dead, and calculated it had been dead for millions of years!
There are other dating methods, all based on the same basic idea. Another notable such method is rubidium-strontium dating. They all make the same sort of assumptions, and are thus subject to the same source of error.
Ok, there's my explanation of carbon 14 dating. Now, Bethgem and Esther: you are both non-technical people. How clear was my explanation? I am passionately concerned about communicating science clearly and effectively to the general public. So any criticism (I thrive on criticism) of my explanation I would greatly appreciate.