Digressions on the mnp Model's Predecessors and Mathematics

Would investigation of geometries and symmetries lead to insight into the combinations of charge material that make up quarks and so support the posited six loops in coiled strands presented in the December blog entry? The short answer is no, that other geometries and and symmetries would also be supported, but the digression is interesting and provides reasons to look further at some of the predecessors of the mnp Model.

Digression on Topology, Combinations, and Geometry

What geometries and symmetries could lead to a specific number of combinations? The specific situation has six items with two candidates, four of one called "n" here and two of another, called "p." Investigating linear, 2-d, 3-d, more dimensions, circular, spherical combinations, and amorphous groups come to mind.

Group theory, topology, and maybe other combination/permutation studies seem to be involved.

Permutation groups, symmetry groups, and Cayley's theorem seem like candidates. The challenge seems to be to express geometries of symmetry, to enumerate symmetries, and perhaps most important, to be sure that all have been enumerated.

Thoughts so far:

For an amorphous (0 dimension) collection, only 1 possibility exists.

For a circular arrangement with symmetry, four of one kind and two of the other have three combinations. Currently the author's favorite

  d      d'     d''

 p p    p n    p n
n   n  n   p  n   n
 n n    n n    n p

Investigation yields other geometries that also yield three combinations, found below.

For 1 dimensions with linear symmetry where either direction is equivalent, do we have multiset permutations 6!/(4!2!) / 2? possibilities? Eight. Unlikely that physical arrangements within elementary particles would be linear, but if the six units are arranged concentrically, the four and two group would have 15 possible arrangements!

Things get complicated after that.

In two dimensions, many pictures can be drawn. Five in a circle around one in the center seems to yield 1) minority "p" in center 2) majority "n" in center, minority "p" together 3) majority "n" in center, minority "p" spaced by 1 on one side and two on the other side for three combinations.

  d      d'     d''

 p p    p n    p n
n n n  n p n  n n n
  n      n      p

Categorizing the possible pictures has probably been done. Having the six in some sort of proximity, that is to say, not at some distance approaching infinity, may keep the number of alternate pictures and geometries manageable.

In spherical geometry, with six items arranged at ends of three axes, there are two possibilities and not three as first thought. If we place minority "p" at top – the other minority "p" unit is opposite or adjacent.

Other arrangements of unevenly spaced items may exist. Are they treated like lattices? The term dual comes to mind.

In three or more dimensions, having only six items should limit the number of pictures or dimensions we need to examine.

The Physics Behind the Search for Combinations

Since these thoughts are related to a general model of small quarks and small leptons as six quantized units of charge material that sees the down quark as four negative plus two positive for -1/3 elementary charge, the arrangement of units may be relevant, even if that arrangement is hidden from us by scale or other dimensions.

The author's preferred image is of six quantized loops in a strand, coiling over the surface of the quark or lepton. That hides the structure, presents a uniform surface, has coil direction of two possible directions, puts the apparently uniform material at the particle's mass surface, and needs no extra dimensions.

That specific image leads to the suggestion that the up and anti-up quarks (five loops or one type and one of the other) have only one arrangement, but the down and anti-down quarks (four parts to two) have three arrangements. The author suggests the lopsided arrangement is down, the symmetrical arrangement is the strange quark, and the intermediate form a short lived version of down quark that should (but may not) survive long enough to be seen in the chaos of LEP and earlier experiments. Wild speculations: The author suggests charm may come in one form, but beauty/bottom in three that would show up as wider error bars if not as distinct particles at high energy. The top quark should be paired not with bottom but with an over-the-top quark that has +-1/3 charge and a few very minor variations.

But even if that third down (d') is accepted, that only makes the strand (circular symmetry) model possible, since other geometries yield the same number of combinations. The "five around one" model could be a strand. The spherical/three axis model would require that the axes be hidden in other dimensions since elementary particles do appear to us to be uniform, but that does not bother physicists.

Minor note: the linear arrangement can probably be ruled out since the five and one grouping would have six different arrangements, which are not confirmed by the single mass of up and anti-up quarks.

Further Mathematics Questions

Are there geometries that yield exactly two combinations? Two amorphous groups of three, where the choices would be 1 of the minority in each group or both of the minority in one group. Further thought leads to three amorphous groups of two in a logically circular pattern, where the choices would be 1 of the minority in two of the groups or both of the minority in one of the three groups.

Finding combinations of two is the fallback position if the down quark resoundingly does not have another variant. Physics' Standard Model of course sees down quarks in the first generation and strange quarks, though radically different in mass from charm quarks, as part of the second generation with charm. So orthodoxy so would prefer to see the quarks as an amorphous single group.

If extra dimensions, hidden or not, are involved then the possibilities expand. The next section, on predecessors to the mnp Model will touch on that issue. With only six items to combine (or three in the case of rishon model), few dimensions would seem necessary.

Digressions on Predecessors to the mnp Model and On Topology

To illustrate other, perhaps unspoken assumptions of topology, examine the rishon model (Harari-Schupe preon model from 1979). RM (if one may be so familiar) has an interesting “linear” combination of three preons – positive charge, negative charge, and neutral, all with 1/3, -1/3, and 0 of an elementary charge. The combinations are linear and order is important, determining color in quarks. The mnp Model is not concerned about color per se since it has other explanations for quark trios and since it deals in sixths rather than thirds. Yet the author recognizes the kinship of mnp with a model that sees electrons and positrons as unalloyed combinations of the same constituents as the quarks and suggests that bosuns such as W and Z are also combinations of the twice as many of the basic units as quarks.

Your author sees the conceptual rotation of three rishons as similar to the spin of quantum mechanics which needs to maintain its direction in its contact with four space so that in the rishon model TVV and VVT are different (colors). A number of geometric interpretations would be consistent. Travel order (which is encountered first in time by other particles interacting) could account for a linear first/last relation. Concentric spheres also exhibit “first” “last” and “linear” Rotating rings with a mandatory gap also exhibit linear ordering. Overlapping filaments with slightly different starting positions will also suffice – the three don't need to be completely discrete. Whether the linear assumption of having a beginning and an end was considered by the rishon model creators has not been investigated.

Others have recently proposed solutions. Piotr Zenczykowski in "The Harari-Shupe preon model and nonrelativistic quantum phase space" (http://dx.doi.org/10.1016%2Fj.physletb.2008.01.045 Physics Letters B 660 (5): 567–572 6March2008) proposes imposing “ordering” using “genuine rotations and reflections in [quantum] phase space.” Zenczykowski refers to this proposal as a minimal solution to realize the fundamental “ physico-philosophical idea” that the rishon model uses to represent quark color.

Bilson-Thompson actually uses the term topology in the arXiv article “A topological model of composite preons" (arxiv:hep-ph/0503213v2 2Feb2008 submitted 27Oct2006). He suggests, for any preon like model, “braids composed of three 'helons'” in positing a model of braided trios of “helons” where the braiding leads to stability.

Both articles ask why no 3/2 spin states and mention Cabibbo mixing (the quark mixing matrix) as an issue. Those questions are answered very differently in the mnp Model. A 3/2 spin nucleon would have no weak/strong interactions but would be held together very tenuously only by charge, in the mnp Model.

Four questions of "all preon models" that have not yet been answered (or translated) by the mnp Model are raised by Deutsch in D.Deutsch, The Fabric of Reality (Penguin Group, New York, 1997).

• adhoc CKM matrix elements
• Hofstadter's distribution of electric charge in nucleons (positive on the surface)
• EMC effect – bigger nuclei have less Fermi motion and presumably greater self-volume based on the uncertainty principle
• proton spin paradox – in the mnp Model, some of the loop may be loose in the nucleon and so some of the coils of the filament loops are out away from the quarks themselves. This is related to residual strong force effects, which are not yet satisfactorily explained.

David Bohm and pilot waves get a mention from Deutsch, with the conclusion that pilot waves are more complicated than parallel universes (p.93). At least pilot waves are on the field and considered a competitor rather than being behind 28-6. Lights out.

Of course, the mnp Model is even more ambitious than the rishon model in attempting to explain both particles and fields as built of the same low level entities. In attempting universal explanation, the mnp Model is more akin to quantum loop gravity, though mnp chooses a much more limited base of three entities with three interactions.

Adventures Await.

2013-05-20 Edits - The term spin is no longer being used to refer to the coils of filaments or strands and the direction of that clockwise or counter-clockwise coiling with respect to the particle's or shell's center. In the mnp Model, the movement of the entities making up filaments and strands are moving at the speed of light, so direction is important and leads to the measurable spin. To avoid confusion, the term spin is reserved for its quantum mechanical and modern (twentieth century) classical meanings.