some questions for optiongeek
A quick summary of the recent flurry of posts:
* application of the shell theorem shows that Mills' "orbitsphere" concept doesn't work, or has a fatal inconsistency (caveat: per markie's presentation of that here).
* the huge range of published results on a lot of "double slit" experiments is inconsistent with Mills' "classical physics (+quantum)" proposals (caveat: per markie's presentation of that here).
* Mills' published values for a single physical parameter for various ions (e.g. Li+) - derived from his published formulae - do not match, or are inconsistent with, the published experimental values (including the uncertainties).
* little, if any, of this is new to the thread (though some details may be); these same three things have been extensively discussed here before (including this thread's predecessor threads).
Is that about right?
That's about right.
With regard to your third point, we know the value for lithium that's given in Table 10.1 is not the value obtained from equation (10.25) as alleged in footnote f of that table. The other values in that table were allegedly obtained from equation (10.48). Having spent an hour or so of my life looking at Table 10.1 and those equations, I have some questions for
optiongeek.
I'm only posting here in the hopes that someone has something relevant to say about the GUTCP-based derivations for the spin flip and the 1 thru 20 electron ions that seem impossible according to QM. My concern is that I've missed something and therefore I no longer need to regard these as proof that Mills' math is superior to QM. So far, the discussion has simply confirmed that the equations are accurate.
As explained below, I don't think the highlighted statement is accurate.
As I've mentioned before, I've replicated Mills' 1 - 20 electron calculations in my own spreadsheet.
How did you replicate the value for lithium that's shown in Table 10.1? We know that value is different from the value Mills claimed in equation (10.25). When you were replicating Mills's calculations, how did you fail to notice that error in Table 10.1?
Equation (10.48), which is the alleged basis for all of the non-lithium values in Table 10.1, says: E(Ionization) = E(Electric) + E
T. I have three questions about that:
- I believe the ET term should be ΔET. Can you confirm that apparent error in equation (10.48)?
- The value of E(Electric) presumably comes from equation (10.43). Because of the minus sign that begins the right hand side of that equation, and the fact that all of the constants and variables mentioned in the fraction are positive, that equation says the value of E(Electric) must be negative. In equation (10.25), however, the minus sign is absent, so the corresponding term is positive. During your replication of Mills's results, you must have noticed that difference between the two equations. Based on your experience, are equations (10.25) and (10.43) both correct as written?
- Did you really type these equations into your spreadsheet exactly as they are shown in Mills's book?
I've searched for a set of computations based on QM theory that can rival the simplicity, compactness and universal predictability of GUTCP. I haven't found yet, nor has anyone on this thread been able to point me to one.
Allow me to explain how easy it is to come up with an equation that is far simpler than Mills's equation (10.48) and is slightly more accurate (assuming the values given in Table 10.1 really do come from equation (10.48), as you have repeatedly assured us they do).
First, let's note that equation (10.48) specifies the ionization energy as a function of Z. if you trace back through the equations giving the value of E(Electric), you'll find that Z not only appears linearly in equation (10.43) but also appears in equation (10.42), the equation for r
3, which appears in equation (10.43). You will notice that equation (10.43) is not a simple polynomial in Z; although the value of r
3 is an algebraic function of Z, that function is far more complex than a simple polynomial function of Z.
The following cubic function of Z is therefore a great deal simpler than the function given by equation (10.48):
f(Z) = 0.005035826300931423 Z3 + 3.2268883952560006 Z2 - 8.67775469504161 Z - 1.1090053331352037
Not only is that formula simpler than the formula given by Mills, it is slightly more accurate (as judged by the RMS relative error) for the ionization energies given in Table 10.1, excluding only the first two rows. (Mills used a different function for the first row, and got the value given in that row wrong, so I think it's fair for me to come up with a slightly different function for the first two rows.)
It's a simple test really. Show me a method that works as well as GUTCP does for 1 - 20 electron atoms/ions. In years of asking this question, no one has come close to answering it.
I can assure you that the method I used to come up with the cubic formula given above can be applied to all of the tables in Mills's Big Book of Boo-Boos. (Mills uses different formulas for each table, so it's only fair to let me come up with different formulas for each table.)
Please note that I am not claiming my formula is based on quantum mechanics, or that it has any scientific value. The only thing I'm trying to demonstrate here is that it's actually quite easy to improve upon the simplicity and accuracy of Mills's formulas.
That fact suggests you should bring other criteria to bear when you start to compare Mills's Big Book of Boo-Boos against quantum mechanics.
But what is better? QM methods that are 'accurate' only work as one-offs and depend on non-physical fudge factors.. QM methods that are general are many orders of magnitude less accurate than GUTCP.
Methinks you are not an authority on that. I suspect you are confusing generality with being in
closed form, which is a confusion Mills has gone to some trouble to foster.