Monday, March 30, 2009

Mathematics and Theology - the Age of the Earth


Most science books who accept macro evolution teach that the earth is something like 4-5 Billion years old. Scientist typically arrive at this number using geologic dating of rocks and fossils on earth. Did you know that physics actually has a calculation that requires no more than simple algebra to arrive at a similar number for the age of the earth. The calculation depends on comparing on the relative concentration of Uranium isotopes in the earth's crust. The isotopes we used in my sophomore Physics class were U238 and U235. Both of these flavors or Uranium are radioactive. U235 is used in simple nuclear weapons like the bomb that was dropped on Hiroshima in 1945. U238 is used in our nuclear reactors. If we know about how many atoms of Uranium 235 and 238 are in the earth crust today and we know the half-life of both Isotopes then we should be able to figure out how old the earth is. The half-life of radioactive material is defined as the amount of time it takes for 1/2 of the material to decay into another kind of element. The equation we use to define the number of atoms (N) after time t, where is the half-life and Ni is the initial number of atoms:





So let's apply this idea for ration of U235 to U238. Remember that:


NU235 is the number of U235 atoms currently.
NU238 is the number of U238 atoms currently.
NiU235 is the number of U235 atoms initially.
NiU238 is the number of U238 atoms initially.
U235 is the half-life of U235 atoms. = years
U238 is the half-life of U238 atoms. = years




When I first got this problem in a problem set back in school I tripped out because they told me what the current ratio of U235 to U238 is: 0.0072516316. And I also had the numbers for the half-life. I knew I wanted to find t - the time it took for both isotopes to decay to the current ratio. So I tripped out. Got scared because I didn't know how much of each uranium isotope was in the earth's crust at the time the earth formed until I realized that I was supposed to assume that the earth had the same amount of each kind of Uranium in the beginning! what this means is that NiU235 = 0.0072516316 NiU238 and that means that you don't need to know the initial amounts of Uranium because those numbers cancel out - old algebra trick. When I plugged in all the numbers and solved the equation for t, I got 4 and half billion years back then.















Using the numbers I found off Wikipedia which slightly differ from the numbers I used in college and the scientific calculator add-on for Firefox I now get


years or years


4.18 Billion is close to 4.5 Billion (four-and-a-half) that I'm certain that I did the calculation accurately. Thank God!

A lot of people look at that and go...see the earth is as old as macro evolution shows that it should be. End of story. But this calculation depends on several assumptions that I never got proof that we should assume. I was just taught that the following assumptions were reasonable.

a. That the amounts of U235 and U238 were equal when the earth first formed. I mean other than it makes the math work out, I don't see why we need to assume that.
b. That half-life of U235 and U238 have always been constant. This one I'm willing to let them have as reasonable.
c. How did they determine that the ratio of U235 to U238 is 0.0072516316 in the earth's crust? How do we know it's the correct estimate?

I think that assumption "b" is reasonable, but "a" and "c" happen to seem convenient and I will need to do more research to really decide if they are reasonable. The best I can say is that it makes the math work out. When I was in school, I took their word for it and no proof was offered. Now, I think I would like to find out how they came up with their assumptions.

3 comments:

  1. You need to understand that the "assumptions" are not assumptions at all but refinements from cooperation with other disciplines that collectively verify the results. Science is a peer reviewed, self correcting process. There are many ways to date something (find its age), and since scientists are not interested in finding the answer that supports their belief system, they often throw their findings to contemporaries for cross discipline corroboration or rebuttal. You are looking for validation of a belief and therefore biased, but you know that.

    ReplyDelete
  2. No, I wasn't at all looking to validate any belief. This post reflects a calculation for the age of the earth based on empirical data. The set up for the calculations and assumptions made are from the textbook that was used in Physics 7C at UC Berkeley in Spring Semester 1995. Your comment adds nothing but shows how truly ignorant of physics you truly are.

    ReplyDelete
  3. Ignorant, exactly what I was thinking. Why, but for ignorance would you think on your most arrogant day that the worlds scientific community would falsify, invalidate, or even settle for sloppy dating practices. The reason we have tolerance bars in dating estimates is for the sake of accuracy among our colleges, so they may refine their finds to the most honest result and then get corroboration from everything from tree rings to C14 and Argon. It always amazes me that a methodology that produced everything you use and manned space flight, comes under attack from the arrogance of ignorance camp with nothing other than the, "it's not in my desert goat herder myth so it can't be right."
    We in the Scientific community do not guess, assume, or distort. We Hypothesize, experiment, test, verify and repeat. Then we let our rivals tear it apart and try to find any and all flaws. That is why your god is a failed Hypothesis.

    ReplyDelete