The Entangled Twins

Entanglement is often called the most baffling and quintessential phenomenon in quantum mechanics. What is entanglement, in a nutshell? Two particles born from one reaction (or two particles that interact through collision) remain connected, no matter how distant from each other. A change in the state of one particle instantaneously causes a change in the state of the other particle. Einstein called it “spooky action at a distance.”

Entanglement is often associated with certain symmetries and corresponding conservation laws. For example, the law of conservation of angular momentum requires that the spin (the quantum-mechanical analog of angular momentum) of two entangled particles always points in opposite directions. This means that if two entangled particles have their spins in a state of superposition of Up (↑) and Down (↓) and we collapse the wavefunction of one of these particles thereby fixing its spin, in, say, the Down (↓) direction, the wavefunction of the other particle is immediately collapses as well, fixing its spin in the opposite, Up (↑), direction. The entangled particles act like twins, instantaneously reacting to each other’s moods. One difference between entangled particles and twins is that entangled particles do not always resemble each other as identical twins do. More often than not, they mirror each other (exhibiting the opposite property: if one has spin ↑, the other has spin ↓)—a consequence of the underlying symmetry.

The Torah portion Toldot centers on one set of biological twins who, like our entangled particles, were complete opposites. Speaking of Rebecca’s difficult pregnancy, the Torah says:

And the children struggled within her… And the Lord said to her: “Two nations are in your womb, and two kingdoms will separate from your innards, and one kingdom will become mightier than the other kingdom, and the elder will serve the younger… and behold, there were twins in her womb. (Genesis 25:22-24)

Two twin brothers are born, Esau and Jacob. The twins share many characteristics of entangled quantum-mechanical objects. The Torah hints at the entanglement of the twins in a later verse:

…[H]is brother [i.e., Jacob] emerged, and his hand was grasping Esau’s heel. (Gen. 25:26)

Twins, as the entangled particles, remain connected. Their oppositeness becomes even more pronounced as they mature:

And the youths grew up, and Esau was a man skilled in hunting, a man of the field, whereas Jacob was an innocent man, dwelling in tents. (Genesis 25:27)

There is an apparent symmetry here—as twins, they can be swapped with no change to the sum—there would still be two sons born to Rebecca, one, Jacob, and the other, Esau, one righteous and one wicked. It is this symmetry that allows Jacob later to exploit the interchangeability by pretending to be Esau to obtain his father’s blessing.

Conservation laws are at play here as well. For example, Esau sells his birthright to Jacob. He cannot just gift it to Jacob; he must receive compensation for his birthright to satisfy the conservation principle. As a result of the transaction, Esau loses his birthright and Jacob gains it—the symmetry is preserved!

As another example, after Isaac blesses Jacob (who was pretending to be Esau), and the real Esau belatedly demands his blessing, Isaac tells him:

Your brother came with cunning and took your blessing. (Genesis 27:35)

And here we encounter an astonishing manifestation of true entanglement. Just as with the entangled particles, if one has the spin Up (↑), the other must assume the spin Down (↓), or vice versa, Isaac tells his son, Esau:

Behold, I made him a master over you… and you shall serve your brother, and it will be, when you grieve, that you will break his yoke off your neck. (Gen. 27:37-40)

When the fortune of Jacob is up (↑), he is a master over his brother, Esau, and Esau’s fortune is down (↓). But if Jacob misbehaves and loses his merit to have the blessing, their fortunes reverse, with Esau’s fortune turning up (↑), thereby making Jacob subservient to him and bringing Jacob’s fortune down (↓). We have seen this played out repeatedly throughout Jewish history.

This story concludes with a puzzling statement from Rebecca, who tells Jacob:

Behold, your brother Esau regrets [his relationship] to you [and wishes] to kill you…Why should I be bereft of both of you on one day? (Gen. 27:42-45)

This seems paradoxical. If Esau were to kill Jacob, Rebecca would lose only one son, as she would still have Esau. Why would she be “bereft of both”? Quantum mechanics offers an intriguing perspective. One particle can destroy another particle, with which it is entangled, only if it is its antiparticle, say, an electron and a positron. The collision of a particle and an antiparticle causes the annihilation of both particles. Indeed, evil Esau was an “antiparticle” to righteous Jacob. Was Rebecca contemplating Esau’s murderous plans to kill Jacob as a kind of mutual destruction with both twins simultaneously killing each other?

To be sure, I don’t mean to imply that Jacob and Esau were literally entangled in a quantum-mechanical way—Jacob and Esau were human beings, not quantum-mechanical particles. But it is more than a poetic metaphor. The structural parallel is remarkable.

Symmetry and Spondateous Symmetry Breaking

Symmetry plays a vital role in physics, particularly in quantum mechanics. However, symmetry breaking is even more significant in quantum field theory and the Standard Model. In a particular type of symmetry breaking, called spontaneous symmetry breaking, the underlying laws remain invariant (i.e., unchanged) under symmetry transformation, but the resulting system is asymmetrical. It is spontaneous symmetry breaking that underlies the Higgs mechanism and Higgs boson, the so-called “G‑d Particle,” that endows particles with mass. In Toldot, we have an example of such spontaneous symmetry breaking.

The Haftorah (weekly reading of the Prophets) connected to this Torah portion begins with the following paragraph:

I loved you, said the Lord, and you said, “How have You loved us?” Was not Esau a brother to Jacob? says the Lord. And I loved Jacob. And I hated Esau… (Malachi 1:2-3)

This beautifully illustrates spontaneous symmetry breaking. The underlying laws of family relations are symmetrical—”Was not Esau a brother to Jacob?” Yet, ultimately, G‑d “spontaneously” chooses Jacob, breaking the symmetry.

This concept plays out explicitly on Purim. Haman, who sought to destroy the Jewish people, dared not attack them directly—he knew full well that the G‑d of the Hebrews would protect them. He devised an ingenious plan: to reach the spiritual level where Jacob and Esau were brothers and there was no difference before G‑d between Jews and Gentiles, or so he thought. “Was not Esau a brother to Jacob?” He crafted symmetrical dice (in Hebrew, “pur“—hence Purim) to cast lots to determine the month and day of the attack.

Apparently, Haman had not studied quantum field theory. He knew nothing about symmetry breaking—”And I loved Jacob. And I hated Esau”—and this miscalculation ultimately caused his downfall. The moral of the story: it pays to study physics!