An Exact Value For The Fine Structure Constant.

[tetrahedron]

Sounds like some of you have been illegally snorting midiclorians again. I've warned you repeatedly about that. Next thing you know droids will be spray-painting themselves with them, and then where will we be? Force, Schwarz, Steroids- can't you boys just get with the program and act like the rest of the feminized male population of the US who understand who wears the pants? Princess Leia would have lived longer if young Anakin knew how to keep things light.

 

As Yoda might say- Fighting again I see- bad precedent this sets. Want you younglings to see? Drink gloog.

 

Jess Tauber (and as they used to say in the old Dark Ages curse, May the Norse be with you).

[Turtle]

Sounds like some of you have been illegally snorting midiclorians again. I've warned you repeatedly about that. Next thing you know droids will be spray-painting themselves with them, and then where will we be? Force, Schwarz, Steroids- can't you boys just get with the program and act like the rest of the feminized male population of the US who understand who wears the pants? Princess Leia would have lived longer if young Anakin knew how to keep things light.

 

As Yoda might say- Fighting again I see- bad precedent this sets. Want you younglings to see? Drink gloog.

 

Jess Tauber (and as they used to say in the old Dark Ages curse, May the Norse be with you).

 

anyway, bringing up the dark past, i'd like to ask you again to start a thread on numbers patterns in the periodic table. you have posted on it in several threads besides here, and keeping that interesting -to me at least- exploration and per se extollation here is just making fodder for collateral crossfire. oh yeah...the asking.

 

Pascal, will you please start a thread on Number Patterns in the Periodic Table of Elements ?

 

from what i can gather of your reported findings, these patterns have far more mathematical connections than the embattled fsc and per se bs.

 

now if you don't mind, i'm off to put on my kilt, gird my loins, (not necessarily in that order), and eat a quart of cheery yogurt with my light sword. will we ever see each other again?

[Don Blazys]

Quoting "turtle":

don, to quote clint reading a fiction writer's line, you are a legend in your own mind.

Fiction writers write fiction, but in reality, I am indeed a legend in my own mind!

 

Don.

[Don Blazys]

To: Jess Tauber (Pascal),

Quoting Jess:

Sorry to interrupt what I'm sure will turn out to be a a brilliantly bloody slugfest.

Slugfests are a waste of time. Boring too!

Hopefully, we can make some actual progress in answering some really tough and interesting questions.

 

Quoting Jess:

I'm wondering if anyone knows what the FSC would be, both for a Bohr atom,

and for the supposedly more accurate version based on a nucleus with an actual cross-section,

if Deuterium were used instead of Protium.

 

The fine structure constant gets larger as the energy scale increases.

 

At zero energy, the estimates range from: [math]\alpha^{-1}=137.036[/math] to: [math]\alpha^{-1}=137.03604(11)[/math]

 

At the lowest energy scale of the electron mass, it is [math]\alpha^{-1}=137.035999084(51)[/math]

 

At the high energy scale of the W boson, it is [math]\alpha^{-1}=128[/math]

 

and at unification energy, the estimates range rather wildly...

 

from:[math]\alpha^{-1}=42[/math](standard model) to: [math]\alpha^{-1}=25[/math](minimal supersymmetric standard model) to: [math]\alpha^{-1}=4*\pi[/math].

 

Don.

Edited April 27, 2012 by Don Blazys

[tetrahedron]

As the demigod Mercury used to say- 'If the shoe flits, I'm Mark Spitz'.

 

If you want ME to come out MY shell, in somewhat tortue-euse facion (I'm learning French, so pardonne), perhaps if you started the thread (les gens will actually read it), then I can weave it into something. Seeing how many postings you have put up, clearly the world really is turtles all the way down.

 

Jess Tauber

[Turtle]

As the demigod Mercury used to say- 'If the shoe flits, I'm Mark Spitz'.

 

If you [turtle] want ME to come out MY shell, in somewhat tortue-euse facion (I'm learning French, so pardonne), perhaps if you started the thread (les gens will actually read it), then I can weave it into something. Seeing how many postings you have put up, clearly the world really is turtles all the way down.

 

Jess Tauber

 

with all due kindness, non merci. je ne suis pas yurtle, je suis mack.

/forums/images/smilies/banana_sign.gif

[LBg]

...

You know my dear, last Christmas he e-mailed Lars Blomberg,

thanked him for all his help in the developement of the counting function

that you see in this thread, and asked his permission to thank him publicly

when he finally gets around to putting it on his website.

...

 

Don,

I have no website of my own and have no need create one either, sorry!

 

/LBg

[Don Blazys]

Hi Lars,

 

I'm sure that when our fictional MOTHER

said that to her equally fictional DAUGHTER,

she was talking about my website. :D

 

But seriously Lars, words cannot express the gratitude that I feel.

 

Thank you.

 

Don.

[tetrahedron]

So, I was looking for mathematical motivations for the atomic number positions of elements with anomalous ground state electronic configurations, some of which already relate strongly to number series based on the Golden Ratio, when something else suddenly popped out.

 

As I've written many times, every other alkaline earth position atomic number corresponds to every other Pascal Triangle tetrahedral number, and, counting backwards within Janet periods only, triangular numbers take you to the central positions of half-orbitals (which Valery Tsimmerman remembered were where quantum number ml=0).

 

In my tetrahedral models of the periodic system, using close-packed spheres (another innovation of Valery's), all mappings are such that the ml=0 positions are vertices of subtetrahedra.

 

What I noticed today was that whenever a period introduced a new l number, the ml=0 positions, when counting FROM the left RIGHTWARDS within the new block defined by the new l, were at positions defined by the Fibonacci series and its higher sisters:

 

0, 1, 1, 2, 3, 5, 8, 13, 21, 34....

1, 1, 2, 3, 5, 8, 13, 21, 34, 55....

2, 1, 3, 4, 7, 11, 18, 29, 47, 76....

3, 1, 4, 5, 9, 14, 23, 37, 60, 97....

4, 1, 5, 6, 11, 17, 28, 45, 73, 118....

 

and so on. For the new p block, the vertex positions are, counting right, 2 and 5; for the new d block, positions 3 and 8; for f, 4 and 11; g gets 5 and 14. Notice that these number come out of the fourth and sixth columns of the table of equations. Interestingly for the new s block with vertices at positions 1 and 2, we have to add a new Fibonacci series above the first, starting at -1, so -1, 1, 0, 1, 1, 2, 3... which just reproduces the Fib sequence later.

 

All these mappings work without exception so far as I can tell, and I looked at very high extensions of the Janet table. Whether there are related mappings in later blocks within periods has not been explored as yet.

 

Jess Tauber

[Don Blazys]

Quoting Jess:

All these mappings work without exception so far as I can tell,

and I looked at very high extensions of the Janet table.

Congratulations!

 

If those mappings do indeed work without exeption, then what you have discovered is

a pattern which may very well be the consequence of some underlying principle which

describes the entire system.

 

In and of itself, that pattern or "law" is as important as it allows us to make further predictions.

 

At some point, you should compile all your findings in one location, such as a website.

 

After all, it's a lot easier to put together a jig-saw puzzle if all the pieces

are on the table rather than scattered about in different rooms!

Edited April 29, 2012 by Don Blazys

[tetrahedron]

Thanks, Don. On reflection, I'm not sure how significant the finding is. It may simply be a consequence of the way one throws together squares and rhombi, in symmetrical fashion, so that the vertices aren't in arbitrary positions. My tetrahedral models are based on 'skew' rhombi, bent up along their minor diagonals and then stacked. But then the best rule is 'keep it simple, stupid', which the universe seems to cling to fundamentally. It would be far more interesting if some cumulation of periodic table features behaved as if they worked as a kind of 'control panel' (certain things do, but I'm still working on that...).

 

Other columns in the equations may have other functions in the system- then we would have to figure out whether the distribution of functions was random/arbitrary, or motivated, and if the latter, then would other configurations work in other 'universes'?

 

As for the last sentence in my post, the motifs recapitulate the earlier mappings, so that as one moves from the leftmost block in a period rightwards, the vertex/ml=0 assignments climb back up through each equation to the one starting with -1. That is, each row corresponds to a different quantum number l.

 

I'm wondering whether some of the more anomalous behaviors of the periodic system are caused by symmetrically altering the mapping rule, say shifting the columns, etc.

 

Jess Tauber

[LBg]

I have estimated the asymptotic behaviour of w(10^n) as n goes to infinity and found it to be

0.640362740055367 * 10^n.

 

See attachment for details.

 

/LBg

wAsymptotic.pdf

[tetrahedron]

Well, it turns out that the third column in fact gives the quantum number l value of the vertices in question. For s this is 0, for p its 1, d 2 and f 3 etc. So at least three columns have functions in defining the orbital structures. But because periods of the same length all appear paired, there doesn't seem immediately to be anything corresponding to the principle quantum number, unless I'm just looking at the system incorrectly (which has happened before- I'm not perfect- the first time I saw the triangular number differences between alkaline earth positions and the ml=0 numbers, it didn't 'click' in my mind that this was their ml value- it had to be pointed out to me by my research partner).

 

One of the few advantages of NOT publishing findings immediately is that you can backtrack and double-check your claims and results, or alter your interpretations as new things come in, or you learn more. At least I can disown things when I'm wrong and give a mea culpa.

 

Jess Tauber

[tetrahedron]

Three more column mappings since the first three. Don't know where this will end. So the family of Fibonacci sequences acts like a template for constructing the periodic table.

 

The nuclear periodic system, underlyingly, is built up from differently prioritized doubled Pascal-related numbers, for each nucleon type, which of course then have to be combined- evidence suggests that different Metal Means hold court over different parts of the nuclide curve (N vs. P)- I get the feeling that something similar might work in the electronic realm. This means combining numbers in different multiples, as with Pell numbers, but also may point to how to combine different Pascal sisters in fruitful ways. Can Pell and related numbers be summed out of an analogue of the Pascal triangle's shallow diagonals? Can we work out the shapes of those Pascal analogues? The columnar mappings I've outlined in the earlier posts are pure quantum-theoretical in nature, and don't take into account the actual surface properties of elements. As these mostly relativity-caused effects kick in, is what we see underlingly a shift between matrices of series from different Metal Means, along another dimension? Would such a trajectory be a straight one, dropping projections onto the matrix for Fib sisters?

 

Other folks have tried to come up with ways for dealing with properties of subatomic particles along vaguely similar number-theoretical lines. So I have to wonder whether by extension we can treat the FSC out of the same kind of sets, or some relations between them. The stab I made at this some month ago here might be worth exploring further.

 

If what I'm suggesting here works, it has implications in many other areas beyond just the periodic system, since we find the Golden Ratio all over the place, though the relation is often imperfect- because of possible shifting between Metal Means? One of my correspondents, who just finished his thesis dealing with Fib, Luc in syntax of living languages, suggests there are also Pascal numbers involved. Will this also be the case at other levels of material reality- how far does this go? And where different levels do use the same motifs, can we use this? For example get direct communication between such levels because of this? A kind of numerical resonance?

 

Jess Tauber

[Don Blazys]

Quoting LBg:

I have estimated the asymptotic behaviour of w(10^n) as n goes to infinity

and found it to be 0.640362740055367 * 10^n.

 

Looks really interesting.

Seems to match my results quite nicely.

Please stand by.

 

Don.

[Don Blazys]

Quoting Jess:

I'm wondering whether some of the more anomalous behaviors of the periodic system are

caused by symmetrically altering the mapping rule, say shifting the columns, etc.

It may be that those behaviors only appear anomolous because the entire system involves,

at its core, a sequence of numbers that is erratic and essentially unpredictable.

 

A while back, you mentioned string theory. Google searching phrases such as

"polygonal numbers in string theory" or "string theory polygons" shows that

polygonal numbers are not only at the very core of string theory, but ubiquitous throughout it,

so it should not be all that surprising that the fine structure constant should emerge naturally

when we try to develop an honest counting function for polygonal numbers of order >2.

 

Don.

Edited May 2, 2012 by Don Blazys

[tetrahedron]

I was looking again yesterday at discussions on the nature of quantum numbers and how they apply to atoms. The s orbitals, with quantum number l being zero, have electrons with no angular momentum. This means that they simply rise and fall (though from no particular direction over time) through the nucleus itself (which is why they can occasionally interact with nucleons). On average they spend most of their flight time at the nucleus than anywhere else particularly (which is NOT, however, how they are usually represented visually!).

 

And this might go to polygonal numbers. What would a polygon with 2 sides look like, or 1 side, or zero? A 2 sided polygon would have no area. Would this be analogous to the flight of an s electron? Something to think about....

 

Jess Tauber

[email protected]