Binary mechanics (BM) defined 8 elementary particles based only on three binary digits, namely modulo 2 parity (0 or 1) of each position coordinate in 3 quantized spatial dimensions (Table 1 in [1]). These parities defined 8 adjacent location types, named spots [2], based on a pair of relativistic Dirac spinor equations of opposite handedness. Each spot was associated with one of these 8 elementary particles (Tables 1 to 3; Table 3 updated in [1]). A spot was composed of 3 smaller spatial objects, named spot units. In 2014, the 8 BM fundamental particles were found to be not as elementary as previously thought, but rather were themselves composed of only 4 types of spot units [3]. This article itemizes how 62 Standard Model (SM) "elementary" quarks and leptons may be built from the 8 original BM particles. In sum, 62 Standard Model quark and lepton particles may be entirely composed of only 4 types of spot unit, the most elemental objects known in physics [3].
Methods and Results
Legend: L, left; R, right. r, red; g, green; b; blue. Neutrinos and anti-neutrinos by Majorana concept.
With quantized space, spot location is expressed with integer coordinates. The spot XYZ position modulo 2 parities (0 or 1) entirely determine a number of properties of the associated particle including charge (Q), color (r, g, b), handedness (L or R), spot unit direction (L or R), the particle vs anti-particle status (matter vs antimatter) attribute and membership in either the proton or electron bit cycles [4]. Over the decades, many very bright and discerning physicists have managed to summarize an enormous amount of data providing current SM lepton and quark particle types [5]. Properties of these SM particles were examined to find one or more BM particles with appropriate properties which could be the underlying components of the SM particles accounting for their corresponding properties (items marked X in Tables 1 to 3).
In this analysis, the short list of SM leptons and quarks was expanded to include color variations and anti-particles. In some cases, more than one selection of BM particles could account for a SM particle (e.g., crR1 and crR2 in Table 2). For leptons, the positively charged particle is generally seen as the anti-particle of the negatively charged particle -- e.g., the positron (e+R) is the anti-particle of the electron (e-L) in Table 1. Neutrinos were not expanded by color from any d quark pairs summing to zero color, but instead listed more simply as a particle and an anti-particle of opposite helicity (L or R) for each particle generation [6]. Neutrino rows are blank reflecting their 0-state bit definition; namely, the neutrino field is thought to be the ones bit complement of the 1-state bit field (the X's). SM particle composition is presented according to the number of down (d) quarks (0 to 5) required to match BM and SM particle attributes (Tables 1 to 3). Finally, nucleon and meson hadrons will be treated in future papers, noting that the baryon and meson groups include SIX-d members, not required to represent SM leptons and quarks.
Table 1 shows a simple mapping of BM elementary particles to SM particles in the ZERO-d and ONE-d groups, and introduces the format used in Tables 2 and 3 for multiple d quark particles.
The electron (e-L) and electron anti-neutrino (/VeR) have opposite handedness (L and R). BM predicts an association between these two particles based on the opposite helicity of 1- and 0-state bit motion in primary force action [7]. Specifically, motion of a 1-state bit to a 0-state locus, in effect, exchanges the positions of the two bits. That is, 0-state bits moves "backwards" in the opposite direction as 1-state bit motion with a primary force effect (examples in [8]). For example, in the electron bit cycle, 0-state neutrino bits circulate in the opposite direction as 1-state electron bits and therefore must represent 1-bit R-handed anti-neutrinos.
Now consider beta decay
where the electron spot in a neutron looses 1-state bits to form an electron at another electron spot. The neutron becomes a proton. Where do we look for the electron anti-neutrino? In the "vacated" electron spot in the previous neutron (now proton) location, of course. Why an anti-neutrino? Because that specifies the circulation direction a 0-state bit would have in an electron spot. In sum, Fermi's 1934 conception of beta decay [6] is predicted by, or at least is consistent with, BM postulates and resulting BM elementary particle specifications. Fermi's insight some 80 years ago is breath-taking and fully conforms to BM mathematical formalism for the primary forces [7] and nucleon representation [2]. Incidentally, BM predicts that probably most beta decay in higher Z atomic nuclei might not result in detectable beta radiation since it would simply shuffle which nucleons are protons or neutrons never leaving the atomic nucleus, which might explain to some extent the "reactor antineutrino anomaly" [9].
With the simple procedures above, a major result is that the main flavors and three generations of SM leptons and quarks emerge, perhaps remarkably, from only three spot position parity input values.
Legend: L, left; R, right. r, red; g, green; b; blue. Neutrinos and anti-neutrinos by Majorana concept.
With SM TWO-d leptons and THREE-d quarks (Table 2), more permutations of the 8 BM particles could build individual SM particles. For the leptons, three configurations may build a negative muon or its anti-particle depending on which d quark color is used. For example, red (+1) and anti-red (-1) sum to the defining lepton color value of zero. The question of possible d quark content in the muon neutrinos is presently left open. For each quark and anti-quark particle with 3 BM d quark components, the defining non-zero quark color may be obtained in twice as many permutations (1 and 2, Table 2), for both the charm and strange types.
Legend: L, left; R, right. r, red; g, green; b; blue. Neutrinos and anti-neutrinos by Majorana concept.
The third generation Table 3 tabulates results for SM FOUR-d leptons and FIVE-d quarks. Leaving the question of tau neutrino d quark content aside, the tau lepton and top and bottom quarks and their anti-particles all may be constructed in three different component configurations depending on the defining zero (leptons) or non-zero (quarks) color attribute.
In sum, Tables 1 to 3 list permutations of 8 BM particle components in 62 SM so-called "elementary" particles.
Discussion
Location, location and location. With the simple analytic procedures described, the main flavors and three generations of SM leptons and quarks emerged, perhaps remarkably, from only three spot position parity input values. This result may begin to address the question: why quantize space? Set aside, for the moment, that continuous space in classical and SM physics presently has no known justification other than tradition and superstition. Space quantization led to definition of spatial objects called spots. Then the modulo 2 parities of integer spot coordinates in three spatial dimensions led to definition of 8 and only 8 BM elementary particles (Table 1 in [1]) and a boat load of their physical properties listed above. Further, the information presented argues that some 62 SM lepton and quark so-called "elementary" particles might be represented in terms of the 8 BM particle components. All from three little numbers (0 or 1). As in real estate, almost everything boils down to "location, location and location".
"He Ain't Heavy He's My Brother" (The Hollies). Experimental physicists have done an outstanding job in estimating rest mass of the SM lepton and quark particles based on empirical data. As predicted by BM, the rest mass increases as the number of d quark components increase because (1) all 6 BM d quark particles and anti-particles are located in the proton (hadron) bit cycle and (2) proton rest mass is about 1836 times greater than the rest mass of the electron with its own much smaller bit cycle [4].
The Occam-o-meter. Occam-o-meters measure the scientific principle of parsimony as economy of explanation in conformity with Occam's razor. For example, when this device is placed close to a periodic chart, untold millions of chemical compounds composed from this listing of a relatively small number of elements cause the Occam-o-meter needle to rise to the "physicists happy" level. In the present case, 62 SM particles appear to be composed of only 8 BM particles. This meter reading of 7.75 (62 / 8) is in the "physicists riot" range. The finding that the 8 BM elementary particles may be built from only 4 spot unit types [3] doubles this reading to 15.5, in the off-the-charts, red-alert "physicists revolt" zone. The 62 SM particles arose from just 3 integer spot coordinate modulo 2 parities or a 20.6 (62 / 3) reading beyond the scale of hand-held Occam-o-meters, in the "Standard Model apocalypse" range.
Caution is warranted if the device is also close to the additional BM quantized parameters of time and energy; the Occam-o-meter may be irreparably damaged.
Out-sourcing laboratory services. With the 15.5 to 20.6 payoff from space quantization, imagine. If time and energy quantization (independent of the time factor in Planck's constant) were added (they have been), then breakthroughs in many physics sub-specialties might figuratively "rain from the sky". At Binary Mechanics Lab, it's been "pouring" advances in physics for several years now. The "deluge" has required that many research projects be out-sourced. Hence, at present, knowingly or unwittingly, many of the largest or most prestigious physics research labs in the world staffed with some of the best physicists have conducted and continue to conduct key "out-sourced" projects, thus far all confirming BM predictions, to be listed with gratitude in an upcoming article [Keene, in preparation].
Editor's note: The results in Tables 1 to 3, minus the neutrino rows, were written in the 1994 "Binary mechanics" paper, time-stamped by notarization and other methods, then shelved due to other pursuits and finally dusted off and published in 2010 [1] with its Table 3 now updated with Table 1 to 3 above.
References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[3] Keene, J. J. "Spot unit components of elementary particles" J. Bin. Mech. October, 2014.
[4] Keene, J. J. "Proton and electron bit cycles" J. Bin. Mech. April, 2015.
[5] Wikipedia. "Standard Model" January, 2016.
[6] Wikipedia. "Neutrino" January, 2016.
[7] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[8] Keene, J. J. "Faster than light" J. Bin. Mech. January, 2016.
[9] An, F.P. et al. (Daya Bay Collaboration) "Measurement of the reactor antineutrino flux and spectrum at Daya Bay", February, 2016.
© 2016 James J Keene
