“The law of unity is all-embracing. Everything in the universe is One, the difference is only of scale; in the infinitely small we shall find the same laws as in the infinitely great. As above, so below.”

| -G.I. Gurdjieff

The human mind is made to desire the ending of every started action. In certain circumstances, as long as it doesn’t know the ending and neither the moment of the ending, it becomes restless and curious, prisoner of the time between the beginning and the end of an action. From the psychological view, the triggered and unfulfilled desire represents the basis of the so-called ‘Zeigarnik‘ effect (look it up), something well studied in psychology and used in advertising.

|-Mattei, L. (2019). The Attraction to Endlessness. Revista Transilvania. Google Scholar.

“You should know that before the emanations were emanated and the creations created, a most supreme, simple light filled the whole of existence. There was no vacant place, no aspect of empty space or void, but everything was filled by that simple, infinite light. It had no aspect of beginning or end, but was all one pure, completely uniform light, and this is what is called the light of the Infinite. When it arose in His pure will to create worlds and to emit emanations, to bring out the perfection of His actions, His names, and His attributes—for this was the reason that the worlds were created, as we explained, then the Infinite contracted itself at its midpoint, in the exact center of its light.”

|~Chayyim Vital, ”Kabbalah Denudata”

Perhaps [this space] can be viewed as a potential phase space of the universe to be created, in which every possible state of the future universe is represented by a unique point. However, since the universe has not yet been created, and each potential state in the future is a superposition of all possible states, this requires a phase space of infinite dimensions. Consequently, this space may be viewed as a Hilbert space (“an abstract vector space possessing the structure of an inner product that allows length and angle to be measured”). Armed with this understanding, we can now proceed to analyze the process of the tzimtzum (“contraction of the Infinite”) that led to the creation of this space.

The tzimtzum resulted in the creation of abstract space—a potential phase space—where each possible state of the future universe would be represented by a unique point. As was mentioned above, in any conceptual space, two contradictory ideas, such as statement A and its negation, non-A, would be represented by two points infinitely far apart from each other. However, God is the ultimate self-referential and self-contradictory construct. God is the master of all possibilities—nothing is impossible for God. He can be in state A and state non-A at the same time. God is infinite and perfect, and therefore He lacks nothing. It follows that absolute infinity and perfection require that He does not lack finitude. In other words, as Omnipontent, He possesses the powers of infinity and of finitude. A contradiction!

God can be in any state and the opposite state at the same time. He can be in all states, because nothing is impossible for God. The sages termed this self-contradictory aspect of God as nimna hanimna’ot (literally “restricting [all] restrictions”), that is, the “paradox of paradoxes.” This enigmatic state of nimna hanimna’ot, of being in contradictory states A and not-A, is reminiscent of what is called in quantum mechanics the “superposition of states.” Indeed, God, as Infinite Being, can be and is in a superposition of all states. God is the ultimate paradox. This paradoxical nature of Ein Sof  (“Endlessness”) extends to the Divine emanation, Ohr Ein Sof (“Light of the Endless”), as God manifests His powers of infinitude and finitude together.

So long as God’s emanation filled all of the existence, there could not be any conceptual space where two contradictory ideas may not occupy the same point but are infinitely far from each other. Thus, before the conceptual space could be created, God had to conceal the self-contradictory nature of His Light—Ohr Ein Sof (which reflects the self-contradictory nature of Ein Sof), that is, He had to separate His ko’ah hagvul (powers of finitude) from His ko’ah bli gvul (powers of infinitude) to hide the paradoxical aspect of nimna hanimna’ot. Without such concealment, no conceptual space, no abstract space, let alone creation, would be possible. The necessity to restrict the contradictions in order to create a conceptual space makes tzimtzum necessary. In a manner of speech, tzimtzum is God’s way of sweeping the contradictions under the proverbial rug.

Tzimtzum is thus somewhat akin to the collapse of the wave function in quantum mechanics. Before the collapse, a particle may be in a superposition of two contradictory states. For example, an electron can be in a superposition of both the spin-up |↑〉 and the spin-down |↓〉 states, which, in classical physics, is analogous to a particle rotating clockwise and counterclockwise at the same time. A popular example of this paradoxical situation is the Schrödinger cat, which is in a state of superposition of being alive and dead at the same time. The collapse of the wave function resolves the ambiguity and the contradiction, resulting in a definitive state (spin-up or spin-down, or being alive or dead, as the case may be). The collapse of the wave function limits or contracts the plurality of possible states to a single actual state. Similarly, if before tzimtzum, godliness, that is, the idea of God, was in a state of superposition of all possible states, tzimtzum may be viewed allegorically as the collapse of the “wave function” of godliness, as it were, resulting in resolving contradictory states. Moreover, as earlier proposed, it may be preferable to translate the word tzimtzum as “collapse” rather than as “contraction.” Indeed, the collapse of the wave function removes all uncertainties about the state of the system. As noted earlier in footnote, the Talmudic dispute whether efshar l’tzamtzem—whether it is possible to remove uncertainty—uses the word l’tzamtzem in exactly the same way (“to remove uncertainty”) as in the collapse of the wave function.

Just as the wave function collapse is relative to the observer, so too is tzimtzum. In the Wigner’s Friend thought experiment, from the point of view of the friend in a  laboratory who performed the experiment and observed the system in question, the wave function is collapsed, whereas for Wigner, who stepped outside the laboratory during the experiment, the system is still in the state of superposition. This experiment demonstrates the relative nature of the collapse of the wave function. The sages of the Kabbalah, as well as Chasidic masters, stress that the tzimtzum occurred only relative to us (sc., it so appears from our frame of reference), whereas for God, no tzimtzum ever took place. Based on this understanding of tzimtzum, they call it “illusory.” Calling it “relative,” as we do here, means the same thing—tzimtzum happened only from our perspective—but it allows us to employ fruitful metaphors of relativism in physics and further strengthens the analogy between tzimtzum and the collapse of the wave function.

As it happens, the quantum-mechanical wave function also defines a Hilbert space. So, the conclusion at which we previously arrived that makom panui—the abstract space created by tzimtzum is also a Hilbert space may not be coincidental after all.

-Alexander I. Poltorak (2020), The Times of Israel, ‘Physics of Tzimtzum II—Collapse of the Wave Function‘