In my last year’s post “Balak – Interference of Souls,” I suggested that Balak needed Balaam (Bilam) to cause constructive interference to make the curse more powerful. This year, while reading this Torah portion last Shabbat, I realized that there was another reason for which Balak needed Balaam – the entanglement.

As I wrote last year, both Balak and Balaam received evil aspects of the souls of Cain and Abel (Havel) but in different proportions: Balak was primarily a reincarnation (gilgul) of the evil aspect of Cain (although he also received some smaller portion of the evil aspect of the soul of Abel) and Balaam was primarily a reincarnation of the evil aspect of Abel (although he also received some smaller portion of the evil aspect of the soul of Cain).

Let us now take a detour into physics and recall that in classical physics a system can only be in a single state. For example, a spinning top can only spin clockwise or counterclockwise. However, in Quantum Mechanics, a system can be in a superposition of two states at the same time. For example, an electron can be in a state of superposition of having its spin up (i.e., spinning clockwise) and down (i.e., spinning counterclockwise). In Quantum Mechanics, it is customary to use Dirac’s bra-ket notations consisting of a left part, 〈A| called the “bra” and the right part, |A〉 called the “ket”. For example, the state of an electron with a spin up, is written in bra-ket notations as |↑〉 and a state of an electron with a spin down is written as |↓〉. When an electron is in a state of superposition of having spin up and down, this state can be described as a vector sum of two state vectors:
|↑↓〉 = |↑〉 + i |↓〉.

Since Balak received evil aspects of the souls of Cain and Abel, he can be described as being in a state of superposition

|Balak〉 = |Cain〉 + i |Abel〉.

Similarly, since Balaam received evil aspects of the souls of Abel and Cain, he can be described as being in a state of superposition

|Balaam〉 = |Abel〉 + i|Cain〉.

Now, let’s recall that two electrons can be entangled. This means that their states are correlated. Say, two entangled electrons are each in a state of superposition of spin up and down. If we measure the state of one electron thereby collapsing its wavefunction into a single state, say “up” |↑〉, then the state of the other electron when measured will necessarily turn up to be “down” |↓〉.

Cain killed his brother Abel. This interaction caused their souls to entangle. Consequently, Balak and Balaam, who were reincarnations of Cain and Abel, were entangled with each other. But each of them was in a state of superposition of being reincarnations of Cain and Abel. The entanglement dictates that these states are now correlated. If one assumes the identity of Cain, the other is forced to assume the identity of Abel and vice-versa.

The story of Balak and Balaam translated into the language of Quantum Mechanics now reads as follows:

Balak, the reincarnation of (the evil aspect of the soul of) Cain, sees the nation of Israel lead by Moses across his border. He knows that Moses is a reincarnation of (the holly aspect of the soul of) Abel and, having killed Abel in the earlier gilgul, now expects retribution. He is terrified of Moses and hates him. He manifests the identity of Cain and his state is now |Cain〉. Balak needs his entangled partner, Balaam, to curse the nation of Israel. Balak sends messengers to Balaam. The latter, who finds himself in the state of superposition of being a reincarnation of Abel and Cain, |Abel〉 + i|Cain〉, is unsure. He tells the messengers to rest overnight while he would inquire of G‑d whether he is to act as the incarnation of Abel or the incarnation of Cain. By acting as the incarnation of Cain, Balak collapses his state of superposition into the state |Cain〉, thereby forcing his entangled partner, Balaam into the state |Abel〉. Therefore, the first time around, Balaam feels more Abel-like. Knowing that Moses is also a reincarnation of Abel, he feels a kinship to Moses and is reluctant to go against him. The second time, when Balak sends messengers, Balaam repeats the procedure – he tells the messengers again to rest overnight while he would inquire of G‑d whether he is to act as in the incarnation of Abel or the incarnation of Cain. This time, however, he feels more like Cain and agrees to come. He saddles his donkey and gets on his way.

This donkey is no ordinary donkey. The Midrash tells us, it was created on bein hashmashot – during twilight, which is neither day nor night but is the state of superposition of day and night. (See my earlier blog “Secret of the Talking Ass“). The donkey in Hebrew is “hamor” – a word that can also mean matter. This tells us that this particular donkey symbolizes matter in the state of superposition, which is what Balaam was.

Why did G‑d send an angel to stop Balaam? Because Balaam was about to violate the laws of “physics” – he was acting as Cain while his entangled partner, Balak was also acting as Cain, thereby violating the correlation of their states dictated by their entanglement. Only after Balaam agrees to obey the word of G‑d, i.e., to obey the laws of entanglement he is allowed to proceed. No wonder that when he meets his entangled partner, Balak, he is forced to assume the identity of Abel and bless the nation of Israel led by Moses – the incarnation of the holy soul of Abel.