>
> I want to thank all those who responded to my question. However, it
> appears that some didn?t understand what I was trying to find out.
>
> For instance, George Murphy thought the question had to do with the
> constancy of radiometric decay, admitting that "we can't determine
> simply from laboratory measurements" that "the proportionality
> constant, & thus the half life, doesn't change on a geological time
> scale, so we have to make the assumption that Kulp mentions." But Kulp
> was saying that the fact of long term radiometric decay proved the old
> age of the earth, not that the decay rates were constant. ....................
> I hope the following illustration makes the point I?m trying to make
> more clear:
>
> Let?s say that we have been around for a very long time and have
> observed three different events which resulted in rocks being formed.
> Let?s say that we know that rock formation
>
> A is 25.5 billion years,
>
> B is 300 million years, and
>
> C is 125,000 years old.
>
> Now, Let?s suppose that some third party comes along who does not know
> us nor communicates with us, and begins to study the rocks using a
> measuring device capable of measuring at a maximum of 2.0 billion
> years. Other than possible physical relationship, the third party has
> no clue concerning the actual ages of nor the spread of the ages of
> the rocks. So the first thing that the third party must do is assume
> that each rock unit is old enough to be measured by his method. Now,
> we know that A is far older than he can measure, and that C is way to
> young. But he doesn?t know that, so he must assume that they are all
> measurable by his measuring method.
>
> He might be able to eventually obtain an age for the B rocks that
> agrees with what we know. However, he will never get the correct ages
> for A and C using his 2.0 billion year measuring device. In any case,
> whatever dates he may obtain are totally irrelevant, because he
> doesn?t know the true age. What is important is that he had to assume
> an old age for each of the rock units first and therefore he cannot
> later use whatever results he may obtain to prove that the rocks are
> old. And yet Kulp said, "only one assumption -- a uniform rate of
> radioactive disintegration [his measuring method]-- was necessary to
> prove a very old earth."
>
> Now if you assume an old universe, then you may, if you want, take the
> measurements and computed ages as valid. But you cannot use those
> computed ages as proof of the old age of the universe.
>
> Do you follow what I?m trying to say?
I'm not sure.
First, it isn't clear how your example might be realized. What sort of
measurement would be capable of measuring a _maximum_ of 2.0 billion (or whatever)
years? & why wouldn't it work for 125,000?
Suppose you were looking at abundances of a radioisotope with 1/2 life 2 billion
years. The abundance in your rock A would be down by a factor (1/2)^(25.5/2) ~
(1/2)^(13) ~ 1/8000 of its initial value. OTOH, the abundance in rock C would be
(1/2)^(.125/2) = (1/2)^(1/16) ~ .96 of its original value. Whether you could
distinguish 1/8000 from 0, or .96 from 1, would depend on how good your instrumentation
was. There are no _absolute_ limits, "too old" or "too young".
I don't think though that that gets at the basic question you're asking, which
has to do with the assumptions that need to be made in order for such measurements to
yield an age. We might, e.g., try to get an age for a rock by comparing the abundances
of relatively short-lived U-235 (700 million years) with U-238 (4.5 billion years) with
the assumption that the abundances when the rock was created were equal. We would also
assume (as I noted earlier) that the decay rates have been those measured in today's
laboratories as well as some other conditions (e.g., no preferential transport of one
isotope in or out). On the basis of these assumptions, measurements of the present
abundances of the isotopes would give us an age for the rock. We would _not_ have
assumed a priori that the rock was "old". Such a measurement would, in principle, work
with an artificial rock which someone had constructed with equal isotopic abundances in
1990 (though in this case the present ratio of abundances would be exceedingly close to
one).
The assumption about initial abundances can certainly be questioned, but it is
not equivalent to an assumption about any particular age, or range of ages, for the
sample.
In fact, the method I sketched can be applied not to a single rock but to the
whole solar system, thus giving (in principle) a time since the formation of the uranium
in the solar system. The initial abundances due to formation in a single supernova do
not have to be assumed arbitrarily to be unity but can be calculated from nuclear
theory: It turns out that the initial U235/U238 ratio would have been about 1.6. If
all the uranium in the solar sytem is due to a single supernova (or several closely
spaced in time) then an age of about 6.5 billion years is obtained.
Perhaps this is still not responding to your question about Kulp: I didn't save
your original post with his quote. But it does seem to me that I've sketched accurately
the basic assumptions that have to be made in order to use radiometric dating. The
method - like all techniques for age determination - is of course open to the "apparent
age" ploy - God made things recently but arranged them all - including isotopic
abundances - to look old. If someone calls rejection of that possibility an assumption
that the earth is old then so be it. I would call it an assumption that God isn't
trying to trick us.
Shalom,
George
George L. Murphy
gmurphy@raex.com
http://web.raex.com/~gmurphy/