Well, C-14 dating isn't really my thing, but I'll try to get the ball rolling.
First, it's hard to say that any one thing is "the biggest evidence" against young Earth creationism (YEC), because there's just so many widely varying and powerful lines of evidence that contradict YEC. But C-14 dating is one of those powerful lines of evidence.
Second, I'm not sure how much you do know, so I'll start real simple. Apologies if it's too simple.
The basic story is that cosmic rays hit nitrogen in the upper atmosphere and convert it to C-14, a radioactive isotope of carbon. This C-14 mixes throughout the atmosphere, plants take it in and incorporate it into their tissues, things that eat plants do the same, things that eat things that eat plants do the same, and all these things have the same percentage of C-14 in their bodies that is in the atmosphere at the time. When these organisms die, they stop taking in carbon of any kind, the C-14 slowly decays back to nitrogen, the non-radioactive C-12 stays as C-12, so the ratio of C-14 to C-12 slowly decreases. We can measure this ratio for things that are less than about 50,000 years old (any older than that and there's too little C-14 to measure).
But there are some potential problems.
First, if the dead organism ate or otherwise incorporated some carbon from a source with a different C-14 to C-12 ratio as there was in the atmosphere at the time, that throws things off. The classic example of this is marine organisms, such as clams, and things that eat marine organisms, such as seals. The marine organisms get a significant amount of their carbon from "old carbon", like dissolved limestone, which has no C-14 to speak of, and this makes their C-14 to C-2 ratio much smaller than it would be if they got their carbon from the atmosphere. There's no way around this problem; clams and seals and such cannot be dated by C-14. However, it's pretty easy to avoid trying to date such things. (Creationists love to parade examples of such dates as evidence of problems with C-14 dating in general, but the only source of such dates is scientists testing to make sure we really know what kinds of things to avoid trying to date). Dating dry-land plants and animals is pretty safe.
Another potential problem, and perhaps what you are talking about in the original post, is calibration. We can measure the ratio of C-14 to C-12 in an organic specimen today ... but we cannot
directly measure the C-14 to C12 ratio as it was when the organism died. For example, with totally made-up and unrealistic numbers, let's pretend that we measure a C-14 to C-12 ratio of a piece of wood, and it's 0.1. Let's also pretend that we magically know that the atmospheric C-14 to C-12 ratio when the tree died was 0.2. Then the sample has lost half its C-14 since it died, and it died one half-life ago (5,730 years ago).
But, of course, we
don't magically know the C-14 to C-12 ratio when the organism died! We
could (but we
do not) assume that the C-14 to C-12 ratio when the organism died was the same as it is in the atmosphere today; but that would lead to imprecise dates with errors of unknown size and other generally yucky situations that scientists don't like at all. So we
calibrate C-14 against other things that we can date more precisely. (Again, creationists love to criticise C-14 dating becasue of teh "assumption that the atmospheric C-14 to C12 ratio has remained the same", or because "the atmspheric C-14 concentration is not in equlibrium" ... but these criticisms are irrelevant because we don't assume that either of them are true or false).
Although there are some things that died at times we know from history and we can compare C-4 dating against, the really interesting stuff happened before reliable historical dates became available. So we have to compare C-14 dating to other methods of measuring the date of a sample of initially unknown age. And we do this with as many
different and
independent methods as we can think up, so as to have good confidence in the results.
The first comparison method is dendrochronology, or tree rings. Trees almost always grow one ring per year (and we have very strong evidence that there are an insignificant number of years in which they grow more than one ring). Let's go back to our piece of wood with a C-14 to C12 ratio of 0.1. That piece of wood happens to come from a bristlecone pine that was cut down in 1935, and had 5,147 rings. (Yes, some bristlecone pines really do have about that many rings, although I just made up that date and those numbers). We just dated material from the central ring, which is as old as the tree. We now know that, in 2004, that piece of wood was (2004 - 1935) + 5,147 = 5,216 years old (with perhaps a small error because the tree might have made two rings in a very few of those years). Now we know the c-14 to C-12 ratio of the sample today, and the actual age of the sample, and we can
calculate the atmospheric C-14 to C-12 ratio when the first ring was laid down!! We can repeat this for the other parts of our sample and get a calibration that tells us the atmospheric C-14 to C-12 for the last 5,000 years!
But we want to go farther back. Now we start collecting pieces of bristlecone pine that died long ago, and are lying around in the desert. We find one that has
exactly the same pattern in it outer 100 rings as our first sample has in its inner 100 rings! (Tree rings are wide or narrow depending on the weather in that year, and form a pattern over many years). This bristlecone pine died 100 years after our first bristlecone pine started growing! We can count its rings and test it for C-14 and extend our calibration farther back! And with other kinds of trees, and lots of overlapping patterns, we can extend that calibration back to about 11,000 - 12,000 years before the present.
Now we know the atmospheric C-14 to C12 ratio for about 11,000 years back, and we can measure the true age of any terrestrial sample that died in that period.
But that's not far enough, and we still want to verify our results from the trees; so we do uranium-thorium dating of corals from many different sites, and we count annual layers (called "varves") that are laid down in lots of lakes, and we look at pollen in ice cores, and we look at planctonic foraminifera in sediments, and we C-14 date these things, and they
all agree to within a percent or two ... and we get a rock-solid calibration of the atmospheric C-14 to C12 ratio for the last 24,000 years, and we can date any suitable sample that died in that period.
Then we find Lake Suigetsu in Japan with 45,000 varve layers, and we extend our calibration back to 45,000 years ago .. but we're not totally sure of it, because we don’t have corroborating data, so we don't trust our dates in the 24,000 to 45,000 year range as much as we do the dates in the 0 to 24,000 year range. However, we are sure that when we date a sample at 40,000 years it's pretty close to 40,000 years old.
Summarizing, C-14 dating is calibrated by multiple independent corroborating lines of evidence and, as long as suitable samples are chosen (which is usually easy), provides a reliable method of dating organic samples that are from 0 to 45,000 years old.
Some good sites with more detail:
Carbon Dating is short and not technical at all.
Radiocarbon Dating is a very good and not too technical site by
Dr. Gerald Aardsma, a former YEC formerly a member of ICR, still a creationist but too dedicated to truth to remain with the ICR.
A 45.000 YEAR VARVE CHRONOLOGY FROM JAPAN on the Lake Suigetsu varves.
You can see calibration curves for the last 4,000 years at
Typical Calibrated Ranges. A slightly more difficult to read curve for the last 10,00 years is at
CALIBRATION.
CALPAL 2004 January is the calibration curve for the last 45,000 years, too far reduced to see anything useful but you can get the general idea. You can use an online calculator based on that curve at
CalPal online.
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