There is a big difference between raidometric dating and carbon dating, and before considering this as a topic I suggest you read the existing threads in the Dates and Dating forum. You might want to begin with this one and then look at this one.
If, after you've read through them you still have questions post a reply here And I'll consider setting you up with someone who can walk you through dating issues.
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Science can only measure radioactivity by general measurement yearly. Whos to say that during the last several millions of years past back to and before the extinction of the dinosaurs as to the year by year, decade to decade, century to century, radioactivity that has transpired that there is any way to accurately date any fossil from previous ages? Is it all not a general science as to the radioactive amounts received from age to age? I am confused and bewildered. Does not also plant life and it's foilage also play a part in radioactivity dating? Do not weather climates and such things matter?
I think you should go to the threads that have discussed a lot of dating issues. When you have read them all then you may have more well-formed questions.
This one is the third continuation of an extensive topic on dating. It was bumped to bring it to your attention. It links back to the previous topics. If you honestly want to learn something I think the time spent reviewing all the posts will help you.
What one such as myself would need to know concerning other than old trees just how carbon dating works and if there are any scientists who disagree that carbon dating is an accurate means for dating fossils.
Fossils are not dated using carbon dating. Carbon dating is applicable only to organic remains, which describes very very few fossils, and applicable only to things less than 40,000 to 50,000 years old, which again describes very few fossils. (Older things will still have a little radioactive carbon in them, but the amount does not indicate the age). There's a very good description of the carbon dating method, by a creationist, at How does the radiocarbon dating method work?. Carbon dating is tremendously well validated by comparison with other methods, some involving other radioactive methods and some not involving radioactivity. THer's a nice discussion at Lake Varves.
Fossils are dated by using other radioactive methods. The most commonly used methods are U-Pb concordia-discordia methods, followed by Ar-Ar methods, followed by various isochron methods. Usually the fossils themselves cannot be dated, and usually the rocks (typically sedimentary) in which the fossils are encased cannot be dated. Mostly we date igneous or metamorphic rock above and/or below the fossil-bearing formation. Luckily there are lots of such circumstances, enough to put together a pretty comprehensive and cross-checked picture. There's a very good explanation of how radiometric dating methods weork at Radiometric Dating: A Christian Perspective.
But you seem to be asking why we think that the decay rate of radioactive material is constant. There are many reasons, both theoretical and experimental. See Re: summing up, & one more question for a brief list of the major lines of evidence. See Claim CF210 for a more detailed discussion with several references.
Sorry, Ned, I can't see how to restrict this to just carbon dating and still address his major question.
Have you read much of the research carried out by the RATE Project, in particular the investigation into C14 in diamonds?
Yes. They are either ignorant or deliberately misleading, and I think it's unlikely that they are ignorant.
14C is produced by high-energy particles ineracting with 14N. Most of it is produced in the upper atmosphere; the high-energy particles are cosmic rays. But it's also known that decay of uranium produces some appropriate particles. So, wherever there is 14N (and we know there's 14N in diamond) and uranium (which might well have been near or in the diamonds; we don't know for sure, but it's quite possible) there is going to be a little 14C.
Their claim that diamonds cannot be contaminated with modern carbon (" ...a diamond has remarkably powerful lattice bonds, so there is no way that subsequent biological contamination can be expected to find its way into the interior.") is not supported or reasonable; natural diamonds have flaws and cracks into which groundwater can intrude, no matter how powerful the atomic bonds.
The RATE group made no rational scientific estimate of how much 14C should be present in diamonds. I doubt that we have enough data on their history to do so, but I could be wrong. But the RATE guys assumed, without explicitly stating so, that the only source of 14C is the atmosphere; and we know that's not true. So their "study" is worthless, being based on an obviously faulty assumption that they didn't state.