In the first installment on the Standard Model, we uncovered a curious parallel between the arrangement of the elementary particles in the Standard Model (a.k.a. quantum field theory) and the biblical description of the encampment of the Jewish people in the wilderness of the Sinai Desert. We further demonstrated an even more surprising parallel between the standard model and Seder Hishtalshelut—the chainlike ontological order of creation—a central doctrine of the Lurianic Kabbalah. In this second installment, we will explore the difference between leptons (particles of matter) and bosons (quanta of fields) and discover an intuition for why bosons (except for Higgs) transcend space and time. Finally, we will find a spiritual parallel for the antimatter in the words of Ecclesiastes.

Bosons vs Leptons—Transcending Space and Time

The parallel between the four worlds on the one hand and three generations of matter and fundamental forces on the other opens up another parallel. What mainly separates bosons (carriers of forces) from fermions (particles of matter) is that whereas fermions occupy space, bosons do not. The reason fermions occupy space is that they have spin of ½ and, therefore, 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.[1] It is because of the exclusion principle that atoms occupy exclusive space—two atoms cannot occupy the same space. Consequently, all matter occupies space. Bosons, whose spins are full rather than half integers, do not obey the exclusion principle, and two bosons can happily coexist in the same space. Indeed, bosons are quanta of fields (electromagnetic, gravitational, strong, and weak), which spread through all of space and overlay each other. We see this from our daily experience: radio waves (which are waves in the electromagnetic field) propagate over the same space “occupied” by the gravitational field. While fermions are limited by space, bosons are not. In some sense, bosons almost transcend space.[2]

This fits very well with our model. Recall that the fourth column in the grid of the Standard Model—the column occupied by bosons—corresponds to the world of Atzilut—the world of Emanation. This world transcends space and time. Kabbalah and Chassidic philosophy teach that space and time (or their spiritual archetypes) first appear in the Malchut (the lowest sefirah) of Atzilut. Thus, space and time (albeit spiritual) are felt only in the worlds of BiYA—Beriyah, Yetzirah, and Assiyah. The appearance of spatial limitations in the worlds of BiYA parallels the fermions, which appear in the first three columns of the grid of the Standard Model corresponding to the three worlds of BiYA.

A somewhat similar parallel involves time. As mentioned above, there is no time in Atzilut; time is first created in the Malchut of Atzilut and felt only in the lower worlds of BiYA. Similarly, fermions that inhabit the first three columns of the grid, which correspond to the three worlds of BiYA, are limited by time. The bosons, however, inhabit the fourth column that corresponds to Atzilut, where there is no time. We should expect to see bosons transcending time, at least in some sense. Indeed, photons, gluons, and W and Z bosons have zero rest mass, and all move at the speed of light. As we know from Einstein’s special theory of relativity, the faster an object moves, the slower time flows—a phenomenon known as relativistic time dilation. At velocities close to the speed of light, time slows almost to a standstill. At the limit, when the object’s velocity equals the speed of light, time stops. That is why a photon, which always travels at the speed of light, does not “experience” time—it transcends it. So too other three bosons—gluons and the Z and W bosons—all move at the speed of light and do not “experience” time. That is what we would expect from the particles that correspond to the timeless worlds of Atzilut. 

The only exception from this beautiful parallel is the Higgs boson, which has a rest mass and does not move at the speed of light—it is a creature of time. But the Higgs boson is an oddball in many respects,[3] so perhaps, we should not be surprised that it breaks the otherwise perfect parallel. Presumably, the Higgs boson does not belong in the fourth column of the grid—this place should really be occupied by the graviton—a hypothetical quantum of the gravitational field. If we did make this substitution, we would restore the parallel, because the graviton is supposed to have zero rest mass, travels at the speed of light, and does not “experience” time. For now, so long as the Standard Model does not include gravity, many prefer to place the Higgs boson in a fifth column, as in this diagram:

Antimatter

Our parallel would not be complete if we didn’t address antimatter. According to the Standard Model, as mentioned earlier, every fermion has an evil twin—an antiparticle, which has all of the same properties as the fermion except having an opposite charge. For example, the antiparticle of an electron is a positron—a particle identical to an electron except for having a +1 charge, instead of the -1 charge of the electron. Every other fermion has an antimatter partner. Is there a parallel to antimatter in the spiritual realm? As it turns out, there is.

As Kabbalah teaches, there are two domains in spiritual worlds—the domain of holiness (sitra d’kedushah) and the domain of the unholy (sitra achara—the “other side”). Indeed, Ecclesiastes says, “G‑d has made ze l’uma zeh” (“this opposite of that”).[4] Two domains are mirror reflections of each other. As I have suggested elsewhere,[5] the unholy klippot (“husks”) are parallel to antimatter.  

Conclusion

As the parallel deepens, we are left to wonder, are spiritual worlds metaphors or the precursors of the physical reality?

Endnotes:

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

[2] Bosons only “transcend” space insofar as they don’t carve out exclusive space but rather fill the entire space and not confined to spatial limitations. They can also coexist in the same space. On the other hand bosons do not completely transcend space, because they are quanta of fields that are defined as functions on space.

[3] Whereas all other bozons are guge bosons, Higgs is not—it is a scalar boson. We don’t know how Higgs boson acquires its mass. Higgs mechanism is responsible to giving mass to all ferions. But can Higgs boson give mass to itself? These are just some of many oddities of the Higgs boson.

[4] Ecclesiastes 7:14.

[5] Counting Days and Weeks, footnote 14. (See online https://quantumtorah.com/counting-weeks-and-days/.)