Korach’s Revolt: a Tale of Symmetry

Korach Revolt

Korach, the proto‑egalitarian, cried:

All the community are holy… so why do you exalt yourselves? (Numbers 16:3).

Chassidut explains that holiness is indeed everyone’s birthright, yet its light must be channeled through distinct roles—kohanim (priests), levi’im (levites), yisraelim (Israelites). Korach’s rejection of this divinely-ordained hierarchy and demand of undifferentiated equality challenged the boundaries, shattered those channels, and ruptured the very ground he stood on: the earth itself—symbol of structure and boundaries—opened to swallow him and his dream of boundless sameness.

The equality that Korach craved can be described as symmetry. Imagine a perfectly symmetrical object, like a perfectly round ball. You can rotate it in any direction, and it will always look the same. In the language of mathematics, such “sameness” under a transformation (in our example, a rotation) is called symmetry.

Higgs Field

1.   The Symmetric Universe: A Massless Beginning

Shortly after the Big Bang, the early universe was also perfectly symmetrical. In this primordial state, the fundamental forces of nature, including the electromagnetic force (responsible for light) and the weak nuclear force (responsible for radioactive decay), were unified into a single “electroweak” force. The equations describing this unified force possessed a high degree of symmetry, known as electroweak symmetry.

A key consequence of this perfect symmetry was that all elementary particles were massless. Just as all points on the surface of the symmetrical ball are indistinguishable, all particles in this highly symmetric universe behaved identically, zipping around at the speed of light. In a perfectly symmetric world governed by the electroweak force, there was no inherent difference between a photon (the particle of light) and the W and Z bosons (the carriers of the weak force).

2.   The Higgs Field: The Agent of Symmetry Breaking

This is where the Higgs field comes into play. The ubiquitous Higgs field is a quantum field that permeates all of space. The quantum of this field, the Higgs boson, has been dubbed “God’s particle.” Unlike other fields, the Higgs field has a unique and crucial characteristic: its lowest energy state, or “vacuum state,” is not zero. This non-zero vacuum expectation value is the key to breaking the electroweak symmetry.

To visualize this, consider a classic analogy: a perfectly symmetrical, circular sombrero placed on a table. A ball placed precariously at the very center would be in a symmetric but unstable position. Any tiny perturbation would cause the ball to roll down into the brim of the sombrero, settling at a random point in the circular trough. This is the shape of so-called Goldstone’s “sombrero” potential.

In this analogy:

• The initial position at the center represents the high-energy, symmetric state of the early universe, where the electroweak force was unified and particles were massless.
• The sombrero-shaped potential represents the potential energy of the Higgs field.
• The circular brim represents the lowest energy state (vacuum) of the Higgs field.
• The ball rolling down signifies the universe cooling and settling into its lowest energy state.

When the universe cooled and expanded, the Higgs field “settled” into its lowest energy state, much like the ball rolling into the brim of the sombrero. This process is known as spontaneous symmetry breaking. The underlying laws of physics (the shape of the sombrero) remain symmetric, but the state of the universe  (the position of the ball in the brim) is no longer symmetric. The universe has chosen a specific, arbitrary direction in the abstract “Higgs space.”

3.   The Consequence of Broken Symmetry: The Emergence of Mass

The breaking of the electroweak symmetry by the Higgs field has a profound consequence: it endows elementary particles with mass. Particles that interact with the Higgs field acquire mass through traction (or friction) with the field, while those that do not remain massless.

The strength of the interaction with the Higgs field determines the mass of the particle. The more a particle “drags” through the Higgs field, the more massive it becomes. These create three categories of particles:

• W and Z Bosons: These carriers of the weak force interact strongly with the Higgs field and therefore become very massive. This is why the weak force has a very short range.
• Quarks and Leptons (such as electrons): These particles also interact with the Higgs field, acquiring their respective masses.
• Photon (and hypothetical graviton): The carriers of the electromagnetic force (and gravitations force) do not interact with the Higgs field at all. As a result, they remain massless and travel at the speed of light.

The Higgs field is the fundamental ingredient that disrupts the perfect symmetry of the early universe. Through the process of spontaneous symmetry breaking, the Higgs field provides a mechanism for elementary particles to acquire mass, transforming a universe of massless particles into the complex and diverse cosmos we observe today. Without that symmetry breaking of the Higgs potential, atoms could never form. Diversity, chemistry, life—all sprang from that single decision of the cosmos to let symmetry surrender to purpose.

The discovery of the Higgs boson at the Large Hadron Collider in 2012 was a monumental confirmation of this beautiful and intricate picture of our universe’s fundamental workings.

Conclusion

Korach craved a cosmos stuck in pre-Higgs sameness: perfect, but sterile. True creation blossoms only after a subtle asymmetry installs purpose and direction. Just as the symmetry breaking in the early universe created three lineages of particles, the spiritual “symmetry breaking” that Korach challenged grouped twelve tribes into three lineages: kohanim, levi’im, yisraelim. Spiritual “mass” emerges the same way as physical mass—by traction with purpose. Only when a soul accepts a distinct mission does its light slow down enough to be expressed.

The priestly service is the Torah analogue of the Higgs mechanism, which breaks symmetry and endows each soul with its unique mission, while knitting the tribes into one organism.

Vive la différence!