How do you test that carbon dating is accurate back 4 billion years? We'd have to create a test which would prove the tests are accurate. We can't, and will never be able to. We assume the scale is linear, when we have no way to know for sure.
Here is what wiki says:
Carbon-14 has a relatively short half-life of 5730 years.
How do we know it is 5730 years? How did they determine this?
So in effect your point is:
"It doesn't make sense to me that science can accurately determine a half-life as long as 5730 years. My common sense tells me that in order to come up with a half-life that long scientists would need to wait 5730 years and then measure how much of the substance remained."
Or to put this another way,
"I'm ignorant about science. Therefore, what I don't understand cannot be true."
Are you even willing to acknowledge that such reasoning is highly irrational? I would venture to guess that you don't understand the vast bulk of scientific knowledge. But since most of this knowledge doesn't challenge your belief system, you have no problem accepting that it's true.
And yet, the measurement of a radioactive substance's half-life - even an extraordinary-long half life - is extremely simple, and can be accomplished in a very short period of time.
The "key" to the calculation is that even a very small mass of a substance contains vast numbers of atoms. For example, 1 gram of Carbon14 contains 4.3 x 10**22 atoms. Thus, over the half-life of the substance, half of those atoms will decay. Or to put this another way, one atom of Carbon14 is a "coin" that has a 50-50 chance of coming up heads (= decaying) over the course of the half-life. And more generally, the odds that an atom of Carbon14 will decay over a period of time, t, is:
1 - (1/2)**(t/H)
where H is the half-life of the material. Even for a very long half-life (for example, 1 billion years), we would expect 13.6 MILLION decays per second from a sample containing 4.3 x 10**22 atoms. Thus, by measuring the number of decays from a known sample in a known period of time, we can compute what the value of H is in the above equation. And this measurement is repeated many times during different experiments to achieve extremely high confidence in the accuracy of the result.
We don't even have to capture all of the decays. Since decay products will (on a random basis) be emitted in random directions, if we count the emissions in a fraction of the solid angle surrounding the sample, we can accurately extrapolate to the count over the entire solid-angle (4-pi steradians) surrounding the sample.
Facebook
Twitter