Introduction

What could possibly be in common between the Standard Model of particle physics with some biblical accounts of Israelites’ travels in the Sinai desert, or with Kabbalistic doctrines related to the unfolding of spiritual worlds, or with the arrangement of the letter in the Name of G‑d? To suspect any connection or parallel between such different concepts may sound farfetched indeed. However, this is exactly what we are going to do in this essay.

Remember that in structural analysis, we do not concern ourselves with the specifics or the nature of the objects at hand—we are only interested in the interrelationship between the objects, the high-level structure, or the storyline. So, let us not worry that particle physics speaks of… well, particles, whereas the Torah speaks of the arrangement of Jewish tribes around the Tabernacle in the desert—topics as distant as they could be. What interests us is the interrelationship between the particle or between the tribes. We will be looking for parallels in the structure, no matter how distinct the objects of this structure may be.

The encampment of the Jewish people in the desert, as described in detail in the Torah portion of Bamidbar (Numbers 1), exhibits remarkable structural resemblance to the arrangement of the elementary particles in the Standard Model. We will explore this and other structural parallels and their significance in this essay.

Jewish Encampment in the Desert

The encampment of the Israelites during their journeys through the wilderness of the Sinai desert was highly ordered. At the center of the camp was the Tabernacle (Mishkan), a portable sanctuary where the divine presence dwelled. It housed the Ark of the Covenant (Aron HaKodesh), which contained the tablets with the Ten Commandments (Luchot) as well as the Torah Scroll written by Moses. The Tabernacle was a vital part of divine worship, and its central location signified the importance of G‑d in the life of the community.

Surrounding the Tabernacle were the tents of the Levites, the tribe tasked with the care and transportation of the Tabernacle. The Levites were divided into three families (Numbers 3:17): the family of Gershon—the Gershonites, who camped behind the Tabernacle (Numbers 3:21-26); the family of Kohat—the Kohathites, who camped along the south side of the Tabernacle (Numbers 3:27-31); and the family of Merari—the Merarites, camped along the north side of the Tabernacle (Numbers 3:33-37), each with specific duties related to different parts of the Tabernacle. Moses, Aaron, and his sons camped on the east side, towards the entrance of the Tabernacle (Numbers 3:38). Moses and Aaron were also descendants of Levi and, in this sense, may be considered as one of Levites families, their elevated status notwithstanding. Therefore, we can say that the Tabernacle was surrounded by four families of Levites.

Beyond the Levites, the twelve tribes of Israel were encamped, three tribes in each direction (north, south, east, and west). Each tribe had a designated leader and a tribal standard—a flag or banner—with its unique emblem. The tribes were arranged as follows (Numbers 2:2-31):

1. The Camp of Judah on the East: Judah (leader), Issachar, and Zebulun;
2. The Camp of Reuben on the South: Reuben (leader), Simeon, and Gad;
3. The Camp of Ephraim on the West: Ephraim (leader), Manasseh, and Benjamin;
4. The Camp of Dan in the North: Dan (leader), Asher, and Naphtali.

Let us arrange these tribes and families in a table as follows:

Now, let us recall the arrangement of elementary particles in the standard model.

The Standard Model

The Standard Model of particle physics is the theoretical framework describing all known elementary particles and their interactions, except for gravity. This model is based on quantum mechanics and quantum field theory and includes both matter particles (fermions) and force-carrying particles (bosons).

Fermions: There are twelve elementary particles that make up matter. All fermions have spin ½.^[1] Fermions obey the Pauli exclusion principle, according to which two or more identical particles with half-integer spins (i.e., fermions) cannot occupy the same quantum state within a quantum system simultaneously.^[2] Fermions are divided into two main categories—six quarks and six leptons:

• Quarks: These come in six ‘flavors’: up (u), down (d), charm (c), strange (s), top (t), and bottom (b).^[3] Up and down quarks are the lightest and most common, making up protons and neutrons (a proton is made of two up quarks and one down quark, whereas a neutron is made of two down quarks and one up quark). The other four types are heavier and unstable. Quarks are unique because they carry a fractional electric charge and engage in strong interactions—they are kept together or “glued” by the strong nuclear force.
• Leptons: These also come in six types. The electron (e) is the most familiar, along with its two heavier counterparts, the muon (µ) and the tau (τ) particle. Each of these has an associated neutrino (ν) (electron neutrino ν_e, muon neutrino ν_µ, and tau neutrino ν_τ). Neutrinos are elusive particles that interact very weakly with matter.

Bosons: These particles mediate the fundamental forces and are responsible for particle interactions. They are also quanta of the three fundamental fields—electromagnetic, strong nuclear, and weak nuclear forces (gravity is not included in the standard model).

• Gluons: These mediate the strong nuclear force, the force responsible for holding quarks together within protons and neutrons, and holding protons and neutrons together within atomic nuclei.
• Photons: These are particles of light; photons mediate the electromagnetic force, which governs interactions between electrically charged particles.
• W and Z bosons: These mediate the weak nuclear force responsible for beta decay.
• Higgs boson: This particle is associated with the Higgs field, a field of energy permeating all space that gives other particles their mass.

The particles in the Standard Model are arranged according to their properties, including their masses, charges, and the ways they interact. It resembles the periodic table of elements but for elementary particles.

The Standard Model is remarkably successful. All particles predicted by the Standard Model have been found.

The First Parallel

Although Torah speaks of the encampment of the Israelites in the Sinai desert, whereas the Standard Model speaks of elementary particle—concepts far removed from one another—nevertheless, as mentioned above, in structural analysis, what matters is the relationship between objects, not the objects per se. Indeed, the Israelites’ encampment in the wilderness exhibits surprising structural parallels with the Standard model. Here are some of these parallels:

1. There are sixteen elementary particles in the Standard Model. And there are sixteen groups of the Israelites.
2. The sixteen elementary particles are comprised of twelve fermions (the particles of matter) and four bosons (the force-carrier particles). Similarly, the sixteen units of Israelites are comprised of twelve tribes of Israel and four families of the Levites (including the family of Moses, Aaron and his children).
3. According to the Standard Model, all elementary particles are arranged in a four-by-four table.

So too, the Israelites camping in the desert are arranged in a four-by-four formation:

Interestingly, the Standard Model does not explain this four-by-four arrangement. We know why there are four rows in the table—the equation dictates that if there is one particle, there must be three more. However, we have no idea why that table has four columns. The four-by-four encampment arrangement of Israelites has an explanation in Jewish mysticism, where everything is rooted in the four letters of the Tetragrammaton—the proper name of G‑d.

This realization—that everything is rooted in the four letters of the Tetragrammaton—leads us to another incredible parallel. As mentioned above, all fermions (particles of nature) are divided into two families—quarks and leptons. The first generation of fermions (shown in the first column of Table 2) has two quarks and two leptons—four particles altogether. These four particles correspond to four letters of the Tetragrammaton. But where do we see the division of these four particles into two families—quarks and leptons? Sure enough, Tetragrammaton is also divided into two units, two letters each—Yud and Heh (Y‑H),^[4] and Waw and Heh (W‑H), so the parallel still holds.

 
But it doesn’t stop here. As it is explained in Kabbalah, the first group, Y‑H, represents the hidden world (alma d’itkassia). The second group, W‑H, represents the revealed world (alma d’itgalia).^[5] And this is exactly how it plays out in the material world of elementary particles. Quarks are hidden; they have never been observed because they only exist in combinations, such as in protons or neutrons. They cannot be observed directly—they are hidden—alma d’itkassia (“hidden world”). Electrons and neutrinos, on the other hand, are ordinary particles observed in nature—alma d’itgalia (the “revealed world”).

The parallel goes even deeper. So far, we have established that in our parallel, quarks correspond to the name Kah, made of two letters, Yud and Heh. In Kabbalah, the name Kah generally corresponds to the sefirah of Chokhmah (“wisdom”). However, more particularly, the letter Yud corresponds to Chokhmah, and the letter Heh corresponds to Binah (“understanding”). In Kabbalah, these two sefirot—Chokhmah and Binah are called “two companions that never part.” When it comes to elementary particles, quarks are also companions that never part. Quarks have a fractional electric charge—an up quark has a charge of +2/3, and a down quark has a charge of -1/3. Quarks always combine so that the resulting charge is an integer. For example, a proton is made of two up quarks and one down quark. If we add their charges (+2/3 +2/3 -1/3 = +1) we find that the proton has a positive electric charge of +1. A neutron is made of two down quarks and one up quark. If we do the math (-1/3 -1/3 +2/3 = 0) we find that the neutron has an electric charge 0 – it is a neutral particle. Just as Chokhmah and Binah, up and down quarks never part each other’s company.

We also notice that just as among bosons, the Higgs Boson, the so-called G‑d’s Particle,⁴ stands out, so too among Levites, the Aaronites. stand out as priests.

The problem with the Standard Model

The search for basic building blocks of matter can be traced back to antiquity. Ancient Greek atomists saw all matter made of four basic elements—fire, water, air, and earth. Other cultures produced similar ideas. By the Nineteenth Century, chemists believed all matter was made of 100 or indivisible atoms. Now we know better. We know that atoms are made of nuclei and electrons orbiting around the nuclei, which, in turn, are made of protons and neutrons. But, as it turned out, this was not the last word in this story. According to the Standard Model, even protons and neutrons are not elementary (indivisible) particles but are comprised of quarks. Quarks, along with electrons, are indeed elementary—that is, indivisible—particles. Later, neutrinos were discovered—very light neutral particles that weakly interact with matter.

When speaking of four elements, after all, Greek atomists got something right—the number of the basic building blocks of our ordinary matter turned out to be four—up quark, down, quark, electron, and neutrino—the elementary particles that occupy the first column of Table 2.

But what about the rest of the fermions? The charm quark is a replica of the top quark with one difference—it is heavier than its sibling. So is the strange quark, which is a replica of the down quark but heavier; and muon, which is an exact but heavier replica of the electron; and muon neutrino, which is an exact but heavier replica of the neutrino (also called the electron neutrino). These particles occupying the second column in the fermion table are much heavier than their counterparts in the first column, and are unstable—they quickly decay into their stable siblings. These particles are called second-generation fermions. The next column in the table to the right is occupied by third-generation fermions. The strange phenomenon of heavier clones replays itself here as well: these particles are identical to their ordinary siblings from the first column, but incredibly heavier and even more unstable. Second and third-generation particles do not form atoms and are not found in the universe except cosmic rays and particle accelerators. They exist for split moments only to quickly decay into ordinary quarks, electrons, and neutrinos—the first-generation particles. We don’t have a clue as to why nature would produce second and third-generation clones, which seemingly play little, if any, role in the universe.

The Jewish esoteric doctrine of Kabbalah may help shed some light on this mystery.

The Second Parallel in the Seder Hishtalshelut

Jewish philosophers and mystics also spoke of four elements—aish (“fire”), ru’ach (“air”), mayim (“water”), and afar (“dust”).^[6] While the names may have been borrowed from Ancient Greeks, the meaning was quite different. To call them “elements” is a misnomer. In Hebrew, they are called arba yesodot, (“four foundations”). Instead of indivisible elements (atoms) of matter, in these four elements, Jewish mystics saw four spiritual energies corresponding to four letters of the Tetragrammaton—Yud-Heh-Waw-Heh (Y-H-W-H): fire corresponds to the letter Yud (Y), air—to the first letter Heh (H), water—to Waw (W), and dust to the second Heh (H).^[7] All matter would ultimately emerge from these four foundational energies or what contemporary physicists would call fields.^[8]

According to Arizal, the universe of Tikkun is made of four worlds—Atzilut (the World of “Emanation”), Beriyah (the World of “Creation”), Yetzirah (the World of “Formation”), and Assiyah (the World of “Action”). This hierarchical structure is called Seder Hishtalshelut (ontological chain-like order of creation). Each of these four worlds corresponds to one of the four letters of the Tetragrammaton (Y-H-W-H): Atzilut (the world of “Emanation”) corresponds to Yud (Y), Beriyah (the world of “Creation”) —to the first Heh (H), Yetzirah (the world of “Formation”) —to Waw (W), and Assiyah (the world of “Action”) —to the second Heh (H). Let us summarize these correspondences in a table:

The four foundations (elements) are present in each of the four worlds. We have, therefore, a primeval hierarchy of spiritual energies or fields organized in a four-by-four table:

Structurally, this table is a mirror reflection of Table 2 of the Standard Model—the first column in Table 5 corresponds to the fourth column in Table 2; the second column in Table 5 corresponds to the third column in Table 2; the third column in Table 5 corresponds to the second column in Table 2; and the fourth column in Table 5 corresponds to the first column in Table 2. If we read Table 2 right-to-left, as we read Hebrew, two tables are structurally identical. This establishes a clear structural parallel between the arrangement of elementary particles in the Standard Model and the arrangement of four elements (foundations) in the four worlds of Seder Hishtalshelut.

One does not need to be a person of faith or a spiritual person to see this parallel—however surprising, it is undeniable. One can also understand it in a metaphorical sense. But for a spiritual person, this is more than a parallel or a metaphor. The spiritual structure summarized in Table 5 may be seen as the primordial spiritual source of the Standard Model. The first column represents the spiritual source of the bosons—quanta of fundamental fields. The world of Atzilut precedes the creation—it is the world of pure emanation, the world of spiritual energies, which correspond to fundamental fields:  Aish of Atzilut is the source of photons, Ru’ach of Atzilut is the source of gluons, Mayim of Atzilut is the source of W and Z bosons, and Afar of Atzilut is the sours of the Higgs Bosons.^[9]

The world of Beriyah is the world of Creation. It is in this world that the spiritual source of matter is first created. Aish of Beriyah can, therefore, be seen as the source of the top quark, Ru’ach of Beriyah—as the source of the bottom quark, Mayim of Beriyah—as the source of tau, and Afar of Beriyah—as the source of tau neutrinos. What we call in the Standard Model the third generation of particles is actually the first generation of proto-particles. In quantum field theory, mass is measured in electron-volts—the units of energy. The world of Beriyah is the first created world—the rarefied world of high energy. This may help understand why corresponding third-generation particles are so heavy (that is, high-energy) and unstable—there is no place for coarse matter in Beriyah. The source of the second generation of particles—charm quark, strange quark, muon, and muon neutrino—are proto-particles of the world of Yetzirah. Only the proto-particles of the lowest world—Assiyah—give rise to stable matter: up and down quarks, electrons, and neutrinos—relatively light particles appropriate for the relatively low energy of Assiyah—the only world in which matter can exist.

The structural parallel between the Seder Hishtalshelut (“chain-like” ontological order of creation) and the Standard model sheds light on the mystery of the second and third generation of particles.^[10]

Conclusion

Structural parallels are not just an exercise in curiosity—they often offer rich metaphors and symbols that help advance our understanding or provide intuitive insight into what otherwise appears as a highly abstract mathematical model. An amazing parallel between the Standard model on the one hand, and the encampment of Israelites in the Sinai desert, the arrangement of the four elements in the four spiritual worlds, and the structure of the Tetragrammaton on the other are nothing short of amazing. They enrich our understanding of the Standard Model, at least on a qualitative level, and provide powerful intuition into the mathematics of particle physics.

Endnotes

[1] Spin is a quantum-mechanical analog of angular momentum.

[2] This principle was formulated in 1925 by Jewish-Austrian physicist Wolfgang Pauli.

[3] The top quark (t) sometimes is called “truth,” and the bottom quark (b) sometimes is called “beauty.” Note that the names of quarks are completely arbitrary and do not represent any real properties of quarks. There is no up or down in the quantum world.

[4] This is a distinct name of G‑d, pronounces as “Kah.” We frequently find this name in Psalms For example, “Extol He Who rides upon the highest heavens with His Name, ‘Kah’.” (Psalms, 68:5) The book of Psalms end with the verse, “Let every thing that hath breath praise the Lord (Kah). Hallelujah (praise-Kah).” (Psalms 150:6)

[5] Rabbi Schneur Zalman of Liadi, Tanya, Likutei Amarim, 26.

[6] Midrash Rabba, Numbers, 14:12.

[7] Zohar Vayera 23.

[8] Sha’ar HaGilgulim (Gate of  Reincarnations) 18:4. (See also “The Four Elementals,” Chabad.org, https://www.chabad.org/kabbalah/article_cdo/aid/1372760/jewish/The-Four-Elementals-184.htm, retrieved December 5, 2021.)

[9] On an intuitive level, this taxonomy offers an insight into why Higgs bosons endow other particles with mass. As we see in our parallel, Higgs bosons correspond to the element of afar (“dust” or “earth”). This element corresponds to the sefirah of Malchut also associated with the planet Earth. Intuitively, we associate mass with earth, because mass is proportionate to weight (Principle of Equivalence, which is one of the cornerstones of Einstein’s General Theory of Relativity), and weight of an object is the measure of the gravitational attraction of this object to Earth. Thus, it is fitting that Higgs bosons, which are parallel to afar, are responsible for the mass of all elementary particles.

[10] On a more speculative basis, we should note a possible parallel between the division of all elementary particles into two groups—bosons and fermions—on the one hand, and the division of the Tetragrammaton into two groups of letters on the other. All elementary particles possess an important characteristic—spin—the quantum analog of classical angular momentum. Thanks to spin, electrons act as little magnets, as if they were spinning around their axes. In reality, electrons do not spin, but they do possess a magnetic field. The nature of the spin is not relevant to the present discussion. Suffice it is to say, all bosons have integer spin (e.g., photons, gluons, and W/Z bosons have spin 1, Higgs bosons have spin 0, and hypothetical gravitons—spin 2), but all fermions have spin ½. Recall that in our model, the spiritual source bosons is in Atzilut—the wholesome world of perfection and unity. There are no halves they—everything is whole. Fermions, on the other hand originate in the three worlds of BiYA (Beriyah, Yetzirah, and Assiyah. These worlds, where the divine light gets progressively diminished, are characterized by fragmentation and “halfness.” This is, for example, where the concept of half-coin (machtzet hashekel) originates. It is, therefore, fitting that the particles originating from these lower worlds would have their spin of one-half.