Facts, issues and accuracy
A great deal of ancient history with regards to archaeology and orgins relies on results gained from Radiocarbon 14 dating. It is the attempt of this article to show explain the technique, and illustrate the "assumed component" as well as point out some of the clear and present risks in determining antiquity based upon this extremely commonly used measurement tool.

Exposing the Issues
This article does a far better job at illuminating the issues and assumptions regarding the carbon dating method than I could. I suggest it as a great primer for anyone who is interested in the validity of this dating method. Here is an excerpt and link:

Many of us are intimidated by science. Radiocarbon dating, a development in atomic physics, is a case in point. The importance of this scientific method, however, is far reaching, influencing a multitude of various and independent disciplines such as hydrology, geology, atmospheric science and archaeology to name but a few. However, we leave the actual task of understanding radiocarbon dating to the boffin elite - we accept their conclusions blindly, respect the precision of their equipment and admire their genius. (click title for link)
Marine Influence on Carbon Dating (from BBC website)
Here is a rare quote from the BBC website that actually admits to error to radiocarbon dating, error which specifically has been noted to drastically INCREASE the age results. In this article, modern shellfish have been dated to find that they are 400 years old!
"A related problem is that marine organisms have radiocarbon ages that are not comparable to organisms that live on land. Carbon that has been in the deep ocean for a long time, on the order of thousands of years, sometimes mixes with modern carbon and is taken in by marine animals and plants. Therefore, you get circumstances where radiocarbon dates on modern shellfish indicate they are actually 400 years old! This is because the shellfish have used modern as well as very old carbon, so their radiocarbon age is a mix of the two. Scientists are getting better information on exactly what corrections to apply to account for marine reservoir effects. However, currently, any dates on marine organisms, or indeed people who have eaten a lot of seafood, have to be viewed with some caution. "

And here is another illuminating admission about the issues of possible inacurracy with C14 dating:

"The use of these elements as chemical signatures indicating places of origin is very new. Researchers are still learning about how soil can contaminate bones, altering the original chemical signatures, as well as the amounts of variation in these chemical signatures within and between different environments and regions. Further work still needs to be done to ensure these factors do not affect test results. "
(Emphasis added)

Reasons to suspect?
It must be freely admitted to, that in the case of fossils and other archaeological artifacts, we simply were not there when the creature, plant, etc., was dead and buried. Therefore, it follows that we cannot know for certain (or even guess) the exact atmospheric conditions at that time. This is important because Radiocarbon Dating assumes to know the amount of 14C precent in the "object" at the time of death. Everything hangs on that. How can we then ascertain accuracy? The fact is, that there is a lot of guesswork and assumption as to the original conditions/amount of absorbed 14C. Here are some admissions that there are "possibilities" of error:

Carbon dating "might be wrong by 10,000 years"

"An Anglo-American team found large variations in levels of the carbon-14 isotope, used as the basis of carbon dating, preserved in a 19in stalagmite recovered from a submerged cave in the Blue Holes of the Bahamas, limestone caverns created when sea levels were nearly 330ft lower than today.

These findings suggested dramatic changes in the amount of radioactive carbon in Earth's atmosphere during the last Ice Age, much greater than previously thought, probably as a result of changes in the strength of the planet's magnetic field."

Bahamas find forces examination of carbon dating

"The ratio of carbon-14 to its stable cousin carbon-12 is used as the basis to carbon date items such as fossils. Any widespread variation in the balance at one point in history would confuse dating."

The Power and Pitfalls of Radiocarbon Dating

"Substantial errors can be contributed by geochemistry at the time the artifact was formed and, later, while it was buried. Living animals and plants can ingest or photosynthesize carbon that is not in equilibrium with the atmosphere at the time of formation. These age errors, termed “reservoir effects,” usually make an organic-carbon sample appear hundreds of years older than its time of origin."

Now, this is a very different picture than what you see or hear on TV. Radiocarbon dating is bulletproof in the opinion of many of the scientists who use it.

Hocus Pocus
And this quote is great too. It exposes the fact that in some cases, dates are "adjusted" due to what are basically assumptions about the time period, or the assumed history of the area! It does not take a genious to see that there is obviously some "fudging the numbers" going on here! (this is taken from DiscoveringArchaeology.Com):

"A final consideration is the conversion of radiocarbon years to calendar years. These corrections are needed because the amount of radiocarbon in the atmosphere — the baseline against which radioactive carbon-14 in the sample is measured — is not constant. However, the history of these atmospheric carbon-14 variations can be reconstructed. The result is that the real-time duration of paleontological or cultural processes can be lengthened or shortened depending upon the calendar correction."
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