Here's what my intuition tells me about the 1/137 level. An index label (the principal quantum number) has been confused for a physical constant. It has the aspect of a rookie error.
It's understandable on one level, because there's a lot going on before you get there. One can almost piece together what happened -- the paper that James pointed to was read (or a related one), the quantum number 137 was noted, and the need for a level below n=1 was deduced. How do you get there? Well, you can have fractional quantum numbers, as with spin, so let's make the principal quantum number a fraction, too. Now if we iterate over our index variable (the principal quantum number) far enough, and we get down to 1/137, and you feed the denominator into alpha(N), you get the fine structure constant (or something along these lines). Then if you squint your eyes, it's easy to imagine that an index label of the form 1/137 ~ alpha(N) = 1/137.035599, forgetting that the relationship between 137 and the output of alpha(N) was a decision made by the authors of the paper. It's sort of like taking a for loop and iterating over the indices, one by one, treating them like normal indices, and then treating the very last one like a physical constant. It's just not something one would normally think to do. There's a missing mapping somewhere. We have assigned an actual value to a pointer. We squinted our eyes too hard and saw what we wanted to see, forgetting what it was that we were doing. To the best of my knowledge, quantum numbers are index variables, not physical constants. They are the i's and j's that are used in iterative ∑ and ∏ operations. Not the concrete t's and x's that are used in integrations. None of this directly relates to the use of the fractional principal quantum numbers; only the equivalence of the most redundant level (1/137) and the fine structure constant is being called into question at the moment. I suspect not even Mills draws this equivalence and would tell the inquirer that there's a mapping step that is needed to get the latter, and that you shouldn't try to equate the two or use them interchangeably. I will try not to belabor the matter further. Eric On Sun, Jan 26, 2014 at 2:06 PM, David Roberson <[email protected]> wrote: > I guess that is what it boils down to Eric. I would much rather have the > series continue indefinitely as I have been discussing. i.e. > (1/2,1/3,...1/137,1/138...1/infinity) which would blend nicely with the > other integer portion that we all assume is real. If the total series is > found to be valid, then there is no special consideration needed for the > 1/137 term. > > But, we must abide by natural laws and most times they do not care what we > prefer. :( > > Dave >
