View source for Why Some Particle Mass Ratios Nearly Equal Geometric Pattern Ratios

{{Infobox paper
| title = Why Some Particle Mass Ratios Nearly Equal Geometric Pattern Ratios
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_1005.pdf Link to paper]
| author = [[Carl R Littmann]]
| keywords = [[Elementary particles]], [[geometry]], [[mass]]
| published = 2008
| journal = [[Proceedings of the NPA]]
| volume = 5
| number = 1
| num_pages = 13
| pages = 130-136
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_1005.pdf here]

==Abstract==

Some volume ratios, in simple geometric patterns, are nearly equal to some important particle mass ratios in physics -- such as the proton to electron ratio.&nbsp; Those correlations were detailed by me in a widely read journal in 1995.&nbsp; However, I did not then suggest why such correlations arise.&nbsp; Unless the correlations are merely coincidental, an explanation is desirable; and now I attempt it!&nbsp; It involves these notions: Low density aether votices or spheres in space having a Planck's quantum of angular momentum; maximum nuclear densities (as in Bohr's liquid-drop model); some aether-related speed-of-light limitations imposed on nuclear densities ; and those small and large aether balls in space containing small and large energies, respectively.&nbsp; Those ethereal spheres are determined by what fits into neat, close-packed sphere patterns in space, and they share some energies and angular momentum with gross particles.

==Overview==

Carl R Littmann published a two-page note in the ''Journal of Chemical Information and Computer Sciences'' in 1995 pointing out that the volume ratios of certain elementary close-packed sphere patterns come very close to well-known particle [[Mass|mass]] ratios — most strikingly the [[Proton|proton]]-to-[[Electron|electron]] ratio of 1836. That paper stated the coincidence and stopped. The present 2008 NPA contribution is his attempt, thirteen years later, to say ''why''. The tone is unusually frank throughout: assumptions are flagged as assumptions, speculative passages are set in double parentheses and marked optional, and the closing self-assessment concedes that "rigorous dynamics were not presented".

The explanation offered is an [[Aether|aether]] one. Space is filled with spinning ethereal spheres or vortices, each carrying about ''h''/6.28 of angular momentum, of a typical radius near the [[Hydrogen Atom|Bohr]] radius, with smaller vortices filling the crevices between them and smaller ones again inside those. Which sizes become common is decided by combinatorics — the sizes that fit snugly into simple close-packed patterns are favoured and multiply. Ordinary matter cannot exceed nuclear density and cannot spin faster than roughly ''c'', so only a narrow band of "globs" can carry the required angular momentum; those that can, and that happen to match the energies of the combinatorially preferred aether spheres, become the stable particles. The mass ratios then reflect the volume ratios of the patterns, not because particles ''are'' spheres in those patterns, but because they exchange energy with aether spheres that are. Littmann is explicit on the point: "I think it is unlikely that one or three well-defined spherical electrons actually physically dwells within any nucleus."

==The argument==

===Origin: the tritium question===

The investigation began with a nuclear puzzle. Tritium — one proton, two [[Neutron|neutrons]] — is remarkably long-lived, and decays by emitting a beta particle. "Where did that small electron snugly fit, before being expelled from the presumed three-nucleon array?" Littmann's answer was a picture: three large spheres surrounding three small compressed charged spheres. That picture led him to compute the volume ratios of such arrangements, and the ratios turned out to match measured particle masses.

===The three patterns===

All spheres are taken perfectly round, coplanar and mutually touching.

* '''Case A''' — three equal large spheres surrounding one small central sphere. The geometry fixes ''R''/''r'' = 6.4641, giving a single-large-to-single-small volume ratio of 270.10. This is compared with the average of the three pion masses divided by the electron mass: ''&pi;''<sup>±</sup>/''e'' = 273.13, ''&pi;''<sup>0</sup>/''e'' = 264.14, average 270.13.
* '''Case B''' — three large spheres efficiently surrounding three small spheres. Here ''R''/''r'' = 9.89898 and the three-to-three volume ratio is 970.00, compared with the four-kaon average: ''K''<sup>0</sup><sub>S</sub>, ''K''<sup>0</sup><sub>L</sub>/''e'' = 973.92 and ''K''<sup>±</sup>/''e'' = 966.04, average 969.98.
* '''Cases B and C combined''' — the most efficient and the least efficient ways for three large spheres to surround three small ones, with ''R''<sub>1</sub>/''r'' = 9.89898 and ''R''<sub>2</sub>/''r'' = 13.9282. Averaging the two, (3''R''<sub>1</sub><sup>3</sup> + 3''R''<sub>2</sub><sup>3</sup>)/6''r''<sup>3</sup> = 1836.00, compared with the average of the four basic nucleon-to-electron ratios: proton 1836.15, neutron 1838.68, average 1837.42.

Littmann adds an observation about the residuals: where a particle departs further than its fellows from the pattern average, it tends to have the shorter half-life, and for the neutral pion "the magnitude of comparative offset, itself, seems to be 'quantized'."

===The aether assumptions===

Five assumptions carry the model. (i) A real dynamic aether of spinning spheres, each of radius roughly 0.5&times;10<sup>&minus;10</sup> m — about half the interatomic spacing in a crystal and about the Bohr radius — with spin near ''h''/6.28. Its density is put at roughly 10<sup>&minus;20</sup> kg/m<sup>3</sup>, its internal velocity at roughly 5&times;10<sup>26</sup> m/s, and its pressure at roughly 10<sup>33</sup> N/m<sup>2</sup>, which "helps prevent spinning protons from flying apart, since there are no so-called 'forces-of-attraction' in nature". (ii) These spheres do not fill space; smaller vortices occupy the crevices, recursively, each level at similar density, velocity and pressure but with less energy. (iii) Real matter cannot be compressed beyond roughly nuclear density, about 2.3&times;10<sup>17</sup> kg/m<sup>3</sup>, as in [[Niels Bohr|Bohr]]'s liquid-drop model, and a dense glob cannot spin faster than about one to two times ''c''.

===Assembling particles===

From these, the account runs: a glob of dense matter begins vibrating and spinning at roughly ''c'' under aether bombardment; most candidates lack the critical mass needed to carry ''h''/6.28 of angular momentum at maximum density without spreading out, and disintegrate. A successful candidate — the proton — reaches equipartition of energy with the surrounding aether spheres. Where a pair of ethereal spheres, one "too large" and one "too small", can form a snug geometric pattern, the pattern reinforces itself and the particle whose energy it matches; feedback then propagates the preferred sizes through space, and "almost all space 'forms up' along the patterns shown." The [[Electron|electron]] is the hard case, since it must supply the same angular momentum with far less mass and far lower density. Littmann's answer is that the numerous ''small'' aether spheres in the crevices interact with it constantly by equipartition, aided by a gyroscopic effect from its spread-out mass. He adopts [[Philipp M Kanarev|Kanarev]]'s toroidal, twisted-dough electron in preference to a "puff-ball", with handedness distinguishing electron from [[Positron|positron]], and endorses Kanarev's view that "the abstract algorism that we call 'charges' — are really fancy 'spins'."

===Optional sections===

The remainder is explicitly marked optional. Nuclear forces are attributed to strong Bernoulli suction from near-light-speed nuclear fluid; gravitational forces to weak Bernoulli effects in the very low density aether — a push-gravity picture Littmann traces to Query 21 of [[Isaac Newton|Newton]]'s 1717 ''Opticks'', differing from Newton's only in emphasising pressure rather than density gradients. Charge is argued not to be an intrinsic coating but a spin mode: a neutral, non-spinning kaon decays into spinning charged products, and "it seems very unlikely that the little mundane kaon has a hidden 'standby' miniature centrifuge inside it." He notes that his derivation of charge from [[Planck Constant|Planck's constant]] is the reverse of [[Petr Beckmann|Beckmann]]'s derivation of Planck's constant from charge, and closes with a superconducting-loop thought experiment from which he concludes "I think there is a preferred frame!"

==Assessment==

The geometry is exactly right, and that deserves saying plainly. Every ratio in the table reproduces on recomputation. Case A is the incircle of three mutually tangent circles: ''r''/''R'' = 2/&radic;3 &minus; 1, so ''R''/''r'' = 6.464102 and the cube is 270.09996. Case B satisfies (''R''/''r'')<sup>2</sup> &minus; 10(''R''/''r'') + 1 = 0, giving ''R''/''r'' = 5 + 2&radic;6 = 9.898979, cube 969.9990. Case C gives ''R''<sub>2</sub>/''r'' = 7 + 4&radic;3 = 13.928203, cube 2701.9996, and the average of the two nucleon patterns is 1835.9993. These are closed-form algebraic numbers that land within a few parts in 10<sup>5</sup> of 270.1, 970 and 1836 — a genuinely arresting fact, and the paper's real contribution. The physical story built on it is also more careful than most aether models: Littmann does not claim particles literally sit in the patterns, he gives his aether parameters explicitly enough to be checked (and they are internally consistent — ''&rho;v''<sup>2</sup> = 10<sup>&minus;20</sup> &times; (5&times;10<sup>26</sup>)<sup>2</sup> &asymp; 2.5&times;10<sup>33</sup> N/m<sup>2</sup>, matching his quoted pressure), and his nuclear density and Bohr radius figures are the standard ones.

The trouble is what the near-misses mean once the modern measurements are put beside them. The three-pion average is 270.136 against a pattern value of 270.100 — a discrepancy of 1.3&times;10<sup>&minus;4</sup>, while the pion masses themselves are known to a few parts in 10<sup>6</sup>. The four-nucleon average is 1837.418 against 1835.999, a discrepancy of 7.7&times;10<sup>&minus;4</sup>, while the proton-to-electron mass ratio is measured to about 3&times;10<sup>&minus;11</sup> — the gap is seven orders of magnitude larger than the experimental uncertainty. These are therefore not identities awaiting a small correction; they are coincidences at the third or fourth significant figure, and the model as it stands supplies no mechanism that would generate a residual of the observed size, nor any estimate of how large a residual it should tolerate.

The pattern of the residuals is also the wrong way round. The nucleon case is the one requiring the most construction freedom — two distinct patterns, one described as the "most efficient" and the other the "most inefficient" arrangement, averaged, with six small spheres — and it fits about six times worse than the pion case and fifteen times worse than the kaon case, which need only one pattern each. Ordinarily, extra fitting freedom buys a better fit. Here it buys a worse one, which is what one would expect if the underlying agreement is arithmetical accident rather than physics. Littmann is candid that his scheme "doesn't work" for shorter-lived particles, that some existing particles are not predicted and some predicted ones do not exist; the [[Muon|muon]] at 206.77 electron masses, one of the most conspicuous ratios in particle physics, has no pattern at all.

Several assumptions are asserted rather than derived, and one is in tension with the paper's own mechanism. The stated aether velocity of 5&times;10<sup>26</sup> m/s is about 1.7&times;10<sup>18</sup> times ''c'', in a paper whose central selection rule is that gross matter "must be limited to roughly ''c''" in its spin. No account is given of why the [[Speed of Light|speed-of-light]] ceiling binds ordinary matter but not the medium that is supposed to enforce it. Nor is it explained why an ambient pressure of 10<sup>33</sup> N/m<sup>2</sup> — some 10<sup>28</sup> atmospheres — leaves ordinary matter undisturbed. The requirement that particles carry "roughly ''h''/6.28" of angular momentum also sits awkwardly beside the measured intrinsic [[Spin|spin]] of the electron and proton, which is &#8463;/2 rather than &#8463;; Littmann's "roughly" absorbs a factor of two that his volume ratios would not tolerate anywhere else. Finally, the constituent-sphere intuition behind Case A and Case B is hard to reconcile with deep inelastic scattering, which resolves the proton's internal structure and finds a diffuse charge distribution of radius near 0.84 fm rather than a uniform hard sphere, and with the fact that pion and kaon masses are today calculated from quark and gluon dynamics rather than treated as free.

Read as a claim about nature, the paper is not established. Read as what its author says it is — an attempt to rationalise a striking numerical coincidence, offered with its assumptions on the table and its speculative parts labelled — it is honest work, and the coincidence itself remains unexplained by anyone else.

==See also==

* [[Carl R Littmann]]
* [[Aether]]
* [[Proton]]
* [[Electron]]
* [[Philipp M Kanarev]]
* [[Toroidal Ring]]
* [[Planck Constant]]
* [[Push Gravity]]
* [[Isaac Newton]]

[[Category:Scientific Paper|particle mass ratios nearly equal geometric pattern ratios]]

[[Category:Aether|particle mass ratios nearly equal geometric pattern ratios]]
[[Category:Particle Physics]]
[[Category:Structure]]
[[Category:Vortex Theory]]