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Our best understanding of how the known elementary particles and three of the forces (electromagnetic, weak and strong) are related to each other and explain the nature and behavior of matter is encapsulated in the Standard Model of particle physics. However, the Standard Model is incomplete as it fails to explain a number of phenomena. The Standard Model relies on a set of elementary particles which are also known to be incomplete. This paper presents a complete set of elementary particles to serve as the basis for an expanded Standard Model. The set of elementary particles contains all known elementary particles and 6 extra elementary particles which relate only to mass and gravity. They include the graviton, a Higgs-like particle (but 6.13 times heavier than the Higgs), 2 heavy dark matter particles and 2 light dark matter particles for a total of 22 elementary particles (the W and Z bosons are seen as manifestations of a single entity).

It is widely accepted by the scientific community that everything in the universe is made from several elementary particles and is governed by four fundamental forces. Our best understanding of how the known elementary particles and three of the fundamental forces (electromagnetic, weak and strong) are related to each other and explain the nature and behavior of matter is encapsulated in the Standard Model of particle physics.

As successful as the Standard Model is, we know it’s incomplete in several areas. For example: the Standard Model does not incorporate gravity, it does not deal with dark matter, it does not explain why there are three levels of matter particles and it fails to provide a relationship between at least 18 parameters [

As the Large Hadron Collider (LHC) continues to produce more results we expect to see physics expand beyond the Standard Model. In fact, in late 2015 it’s possible that a new particle in the 750 GeV range was observed [

As the Standard Model sheds little light on the elementary particle masses, we have little guidance as to where to look for new particles.

This paper proposes a model for a complete set of elementary particles, including those not dealt with by the Standard Model. The Standard Model has 12 matter particles (that come in three generations of 6 quarks and 6 leptons), 4 force carrier particles (2 for the weak force), and the Higgs. The proposed set of elementary particles presented in this paper includes these particles, in addition to 6 other particles that relate only to mass and gravity. These 6 other particles include: the graviton (thought to be the force carrier for gravity), a Higgs-like particle (but 6.13 times heavier than the Higgs), 2 heavy dark matter particles and 2 light dark matter particles, for a total of 22 particles (as will be shown in this proposed model the W and Z bosons governing the weak interaction are seen as manifestations of a single entity).

The complete set of 22 elementary particles is derived from a manuscript [

The author understands that it is unacceptable to use these kinds of manuscripts in order to motivate new theories. Nonetheless, the manuscript does shed much light on what is already known and does predict additional particles and their masses not found in the Standard Model. In addition, most of the extensions of the Standard Model are motivated by a belief in unification and simplicity, also without any scientific source; but in fact, in agreement with the source text of the manuscript relied upon herein.

The complete set of 22 elementary particles in the proposed model is shown in

7 vertical connections. In total, the connections represent the 22 building blocks of nature (which correspond to the 22 Hebrew letters).

We note the following characteristics of the 22-particle proposed model depicted in

1) There are 3 letters along horizontal lines (horizontal particles), there are 12 letters along diagonal lines (diagonal particles), and there are 7 letters along vertical lines (vertical particles).

2) Horizontal particles. The 3 horizontal particles [

Name | Alef | Bet | Gimel | Dalet | Hey | Vav | Zayin | Het |
---|---|---|---|---|---|---|---|---|

Symbol | א | ב | ג | ד | ה | ו | ז | ח |

Value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Simple value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Name | Tet | Yud | Kaf | Lamed | Mem | Nun | Samesh | Ayin |

Symbol | ט | י | כ | ל | מ | נ | ס | ע |

Value | 9 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |

Simple value | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

Name | Pe | Tzadi | Kuf | Resh | Shin | Tav | ||

Symbol | פ | צ | ק | ר | ש | ת | ||

Value | 80 | 90 | 100 | 200 | 300 | 400 | ||

Simple value | 17 | 18 | 19 | 20 | 21 | 22 |

Memמ , the strong force. These non-gravitational forces do not interact with the vertical particles, only with the diagonal particles. Note that the Alephא is a composite of two letters (corresponding to the W and Z bosons) as will be explained in section 3, entitled Letter Shapes and Particles.

3) Diagonal particles. There are 12 diagonal particles [

4) Vertical particles. There are 7 vertical particles [

5) Horizontal and vertical axis are independent. Thus, vertical particles do not interact via horizontal particles, i.e., via the 3 non-gravitational forces, they only interact with the force of gravity. Diagonal particles interact with horizontal and vertical forces, i.e., all forces and also vertical mass particles in the middle pillar (Higgs and Higgs-like).

6) The right-side, left-side and middle pillars are associated with the pillar’s numbers of 248, 365 and 613, respectively (these numbers correspond to the positive biblical commandments, negative commandments and total commandments).^{1}

7) Each energy level has a particular scale factor which, when multiplied by the Hebrew letter value, determines the particle’s mass, as will be shown in section 4, entitled Particle Masses―Some Predictions. a) To determine the scale factor of a higher energy level one multiplies the scale factor of the lower energy level by the associated pillar number then divides by 2, e.g., by 365/2 for the left-side pillar. b) To correlate scale factors at the lowest level on the right-side with the left-side pillars one simply multiplies the scale factor by the ratio of the pillar numbers; thus to go from the scale factor on the right-side pillar to the scale factor on the left-side pillar one multiplies by 365/248. c) To correlate the scale factors at the lowest level on the middle pillar with the right-side pillar one multiplies the right-side pillar lowest level scale factor by 40; the value of the letter Mem מ connecting the lowest levels.

8) Each Hebrew letter shape reveals an underlying reality and will be illustrated in section 3, entitled Letter Shapes and Particles.

9) Under this reality [

The Hebrew alphabet consists of 22 letters. Each Hebrew letter has 3 modalities; a pictogram, a letter and a number. Each of these modalities provides underlying information about it as a building block of nature. We examine the three horizontal force particles and their associated letter shapes, for illustration purposes.

1) Electromagnetic force: The Shinש has 3 heads and is actually pronounced differently when a dot is placed over the rightmost or leftmost head. These two ways to pronounce the letter Shin ש correlate to polarizations of the photon.

2) The strong force: The Mem מ actually comes in 2 shapes―the 1st shape (shown in ^{nd} Mem shape ם, (which is close to a simple square) is used when the letter Mem appears at the end of a word. Thus, one Mem ם consists of four lines (sides of a square) and the other Mem מ consists of 2 lines at the right and bottom and 2 modified lines at the top and left. In total the Mem consists of 8 components (6 identical and 2 slightly different). These 8 components correspond to the 8 gluons (6 of which have mathematically symmetrical characterizations).

3) The weak force: The Aleph א is actually a composite of 3 letters; on the top right and bottom left are 2 identical Yuds י, and separating them is 1 diagonal Vav ו. The 2 Yuds clearly represent the ±W boson, and the Vav represents the Z boson.

The letter’s numerical value is a measure of its energy and can thus be used to calculate the particle’s mass. Measured particle masses versus predicted particle masses are illustrated in

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|

Particle | Letter | Letter value | Scale factor | Predicted mass (MeV/c2) | Measured mass (MeV/c2) | Measurement Error/range | Comment |

up quark | lamed | 30 | 0.0752 | 2.26 | 2.16 | +0.49, −0.26 | <1 sigma |

down quark | samesh | 60 | 0.0752 | 4.51 | 4.67 | +0.48, −0.17 | <1 sigma |

charm quark | tzadi | 90 | 13.7254 | 1235.28 | 1270.0 | ±20 | <2.1 sigma |

strange quark | zayin | 7 | 13.7254 | 96.08 | 93.0 | +11, −5 | <1 sigma |

top quark | ayin | 70 | 2504.8800 | 175,341.60 | 172,760.0 | ±700 | <3 sigma |

bottom quark | vav | 6 | 2504.8800 | 15,029.28 | 4180.0 | +30, −20 | Out of range |

electron | yud | 10 | 0.0511 | 0.51 | 0.51 | Control | |

muon | kuf | 100 | 1.0561 | 105.61 | 105.66 | ±0.0000024 | Out of range |

tau | hey | 5 | 355.4411 | 1777.21 | 1776.86 | ±0.12 | Out of range |

dark 1 | pe | 80 | 6.9003 | 552.02 | |||

dark 2 | gimel | 3 | 1259.3027 | 3777.91 | |||

dark 3 | kaf | 20 | 0.5536 | 11.07 | |||

dark 4 | bet | 2 | 178.2486 | 356.50 | |||

Higgs boson | resh | 200 | 626.4847 | 125,296.94 | 125,100.00 | ±140 | <1.4 sigma |

Higgs-like | dalet | 4 | 192,017.5630 | 768,070.25 | |||

Z boson | alef-yud | 1000 | 91,187.60 | 91,187.60 | ±2.1 | Control | |

W boson | alef-vav | 0.8831 | 80,524.53 | 80,379.00 | ±12 | Out of range |

1 | 2 | 3 | 4 | 5 | 6 | Note |
---|---|---|---|---|---|---|

Particle | Letter | Letter value | Scale factor | Predicted wavelength (m) | Calculated wavelength (m) | |

photon | shin | 300 | 2845.0734 | 1.616255E−35 | 1.616255E−35 | Planck length |

gluon | mem | 40 | 0.1263 | 2.731E−30 | ||

graviton | tav | 400 | 2.0440 | 1.687E−32 |

Column 1 of

1) Matter particles: The electron, with its well-defined mass, is used as the control factor to compute the matter particle masses. The electron corresponds to the letter Yud י, whose value is 10. The scale factor for level 1 (lowest energy) on the right-side pillar is the electron mass divided by 10 or 0.0511. To obtain the scale factor for level 1 on the left-side pillar we multiply by the pillar ratio 365/248 and obtain 0.0752. Then to obtain level 2 scale factor on the left-side pillar we multiply level 1 scale factor by 365/2 and again to obtain the level 3 scale factor we multiply the level 2 scale factor by 365/2. To obtain the predicted mass for any given particle we multiply the letter value by the scale factor by (Column 3 times Column 4). All results for quarks (rows above the electron on

2) Dark particles: These same scale factors derived above are used to predict dark particle masses. Since these occur between energy levels the average of the scale factor of the level above and below are used. One obtains a heavy dark matter particle around 552 MeV and a light dark matter partner at about 11 MeV, with corresponding higher energy pairs at 3.78 GeV and 357 MeV. As expected, from the vertical particles’ discussion in section 2, the left-side dark particles are heavier and the right-side dark particles are lighter.

3) Higgs-like particle: The scale factor for level 1 (lowest energy) on the right-side pillar is 0.0511. To obtain the scale factor for level 1 on the middle pillar we multiply by 40 and obtain 2.044. Then to obtain level 2 scale factor on the middle pillar we multiply level 1 scale factor by 613/2 and again to obtain the level 3 scale factor we multiply the level 2 scale factor by 613/2. To obtain the predicted mass for any given particle we multiply the letter value by the scale factor (Column 3 times Column 4). The Higgs’s (a level 2 particle) predicted mass is within measurement error. Its higher mass cousin, at exactly 6.13 times the Higgs mass or 768 GeV, compares well with preliminary observations of a potential particle at around 750 GeV (750 and 760 respectively for ATLAS and CMS) [

4) Weak force particles: Intuitively the horizontal particles would be expected to have zero mass. We know, however, that the weak force particles have mass due to symmetry breaking. And one can see in

In the case of massless particles, like the photon, one can still calculate an energy and since the particle is massless the energy can be converted to a wavelength. To obtain the scale factor for the photon we sum the right- and left-hand side scale factors for the level 3 which the photon connects and subtract the sum the right- and left-hand side scale factors for level 2 and 1. By multiplying this scale factor by the letter’s numerical value, we obtain an energy (and thus a wavelength) for the photon. See

The Standard Model is a triumph of physics. However, it is incomplete in several areas. In particular, it does not incorporate gravity, it does not deal with dark matter particles, it does not explain why there are three levels of matter particles, and it fails to provide a relationship between the masses of most of the particles. An ancient manuscript contains a model for all building blocks of the physical world that is more complete. This model consists of 22 particles at 3 energy levels. It includes both matter particles, force particles and several gravity/mass particles which do not interact with the known forces other than with gravity. It also provides a means to calculate particle masses. Such a model sheds some light on where we might look to find more particles. Among the model’s predictions are 1) a heavier Higgs-like particle at 6.13 times the Higgs mass, 2) heavy dark matter particles at about 0.55 and 3.8 GeV, and 3) light dark matter particles at around 11 and 357 MeV. The model also yields a photon wavelength very close to the Planck length derived using only the electron mass and without any knowledge of the gravitational constant.