Not consistent? Why would there not also be a lot of daughter material in materials?
I specifically mentioned ratios. Why would you have a direct relationship between the U/Pb and K/Ar ratios in the same stratum? Why would we consistently get the the same K/Ar ratio for a given U/Pb ratio in a same state past? Why would the relationship between those ratios also match up with the same state decay rates?
I was creating an example out of thin air since you seem incapable of providing one.
I have already provided examples. Why don't you use them?
Here is the standard equation that I am using, but with one difference:
The difference is that we are going to take
t out of the equation. Since you don't like it in there, let's take it out. Instead, let's replace
t with scientific observations. Let's have the U/Pb equation on one side of the equal sign, and the K/Ar on the other side of the equal sign. Just for clarification, we are using 235U and 40K which have observed decay constants of 9.846E-10 year and 5.540E-10 respectively. Again, these are the OBSERVED decay constants. No assumptions of long time periods are being used.
The equation will look like this:
[ln[1+(Pb/U)]]/9.84E-10=[ln[1+(Ar/K)]]/5.540E-10
If you have the U/Pb ratio, all you do is solve for K/Ar. In fact, I even graphed it so you can see it:
I plugged in a few different ratios if Pb/U in Excel, used the equation above with the decay constants, and voila. I got that chart with a trendline for you to follow.
That is the prediction. That line represents the ratios we should see if there is a same state past. This is a prediction that is made before any ratios are measured, and it makes no assumptions of billions of years of decay.
Now, can you tell us why a different state past could not produce a 1.5 ratio for Pb/U and a 0.1 ratio for Ar/K? That would be far away from the line and would falsify a same state past. So why shouldn't we see data points from real world data that falls all over that graph instead of along that line connecting the points?
[btw, if anyone finds any math errors I have made, please speak up. I used a polynomial regression for the trendline, in case anyone is wondering. This is the Excel formula I used:
(EXP((LN(1+A2))*($F$2/$E$2))-1)
Where A2 is the Pb/U ratio, F2 is the 235U decay constant, and E2 is the 40K decay constant. The formula can be drag copied in column B with Pb/U ratios in column A.]