Collapse and Revelation

The Splitting of the Sea as a Metaphor for the Collapse of the Wave Function in Quantum Mechanics

And lift thou up thy rod, and stretch out thy hand over the sea, and divide it; and the children of Israel shall go into the midst of the sea on dry ground. . . . And Moses stretched out his hand over the sea; and the Eternal caused the sea to go back by a strong east wind all the night, and made the sea dry land, and the waters were divided.

Exodus 14:16, 21

Sometimes, the Torah offers new insights into the most perplexing paradoxes of physics. The Measurement Problem, also known as the wave function collapse, is one such paradox that proved to be quite intractable. Much ink has been spilled debating the nature of the Measurement Problem giving rise to competing interpretations of Quantum Mechanics.  We shall endeavor to show here how Chasidic thought and Kabbalah shed light on this challenging problem.^[1]

The wave function

In Quantum Mechanics, a state of a physical system (e.g., a particle, an ensemble of particles, or a field) is described by a wave function (or wavefunction) ψ. The square amplitude of the wave function is the probability^[2], that is, a chance of finding the system in a particular state—for example, finding a particle at a certain point.  This is called the Born Rule.

The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states. However, any actual measurement always finds a physical system in a definite state (rather than in a blurred state of superposition). This phenomenon is called the measurement problem or the collapse of the wave function. The measurement problem in quantum mechanics is the problem, in part, because it does not follow from the Schrödinger equation and is added ad hoc. It is a random event not predicted by this deterministic equation. The questions are why and how the wave function collapse occurs.^[3]

Quantum superposition

Quantum superposition is a fundamental principle of quantum mechanics. Two (or more) quantum states can be added together (“superposed”), and the result is another valid quantum state.  Mathematically, this is the result of the linearity of the Schrödinger equation. As we know from algebra, any linear combination of solutions of a linear equation is also a solution of this equation. In fact, this is the definition of a linear equation. Since the Schrödinger equation is linear, any linear combination of solutions is also a solution.^[4] Therefore, any linear combination of states is also a permissible state in quantum mechanics. A system, which is in a state that is a combination of states, is said to be in a state of superposition.

The collapse of the wave function

Whenever we measure or observe a physical system that is in a state of superposition of multiple states, its wave function collapses into a single state, that is, the plurality of probabilities collapses into a single value. In essence, this is called the collapse of the wave function. The wave function can be visualized as a cloud of droplets, where each droplet represents a probability value. The wave function collapse can be visualized as this cloud suddenly condensing into a single droplet—a single random value.

Why is this a problem? The wave function is deterministic. That means that the Schrödinger equation determines the wave function at any point in time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict the precise results of the measurements, but only their probabilities? How can one establish a correspondence between quantum and classical reality?

The Collapse of the Wave Function in Talmudic Thought

We find a hint at the collapse of the wave function in Babylonian Talmud ^[5]:

Rabbi Yitzchak says, “Blessing is found in a matter concealed from the eye, as it is stated, ‘The Lord will command blessing with you in your storehouses.’ (Deuteronomy 28:8) (where the grain is concealed).” The school of Rabbi Yishmael taught, blessing is found only in a matter over which the eye has no dominion.

The Sages taught, one who goes to measure the grain on his trashing floor recites: May it be Your will, O Lord, our G‑d, that you send blessing upon the product of our hands. If one began to measure the grain, he says: Blessed is He who sends blessing upon this pile of grain. If one measured and afterward recited the blessing, this is a prayer made in vain, because blessing is found neither in a matter that is measured, not in a matter that is counted. Rather it found in a matter concealed from the eye, as it is stated, The Lord will command blessing with you in your storehouses.’”

Baba Mitzia 42a

Let us try to understand what Talmudic Sages are teaching us here. Before one begins measuring one’s grain, there may be more or less of the grain in his silo. In other words, the amount of grain in the silo is in a “state of superposition” of being more or less, metaphorically speaking.^[6] At this point, it is still appropriate to pray that one finds more grain rather than less. But how could that be? Isn’t the amount of grain in the silo fixed at the time the silo was filled with grain? According to the Talmudic Sages, the amount is not fixed until measured (or counted), at which time the “wave function” of the grain is “collapsed.” In other words, one is instructed to pray that he collapses the wave function “the right way.” Once he measures his grain, such prayer would be in vain, because the wave function is collapsed, and the result is determined.

The Collapse of the Wave Function in Kabbalah and Chasidic Philosophy

Quantum mechanics in Schrödinger’s formulation is called the “wave mechanics.” It is not a coincidence. Let us look at the parting sea waves—Kri’at  Yam Suf (“Splitting of the Sea of Reeds”).

The Hebrew word for “nature” is teva (טבע). This word shares the root tet–bet–ayin (ט-ב-ע) with the word tub’u (טבעו)—“sunk,” as in Tub’u b’yam Suf—“sunk in Sea of Reeds.”^[7] Chasidic philosophy teaches that godliness is “sunk” in nature i.e., just as an object sunk in the sea. Nature covered godliness like water covers the seabed and makes it invisible.

The esoteric wisdom of Kabbalah speaks of two worlds, Alma d’Iskasya (“concealed world”) and Alma d’Isgalya (“revealed world”).^[8] The Zohar refers to the Partzuf Leah (sub-partzuf of Nukva d’Z”A) as Alma d’Iskasya, because Leah symbolizes the World of Thought (Olam HaMachshavah), which is the concealed world. After all, thoughts are not revealed until spoken. Partzuf Rachel (another sub-partzuf of Nukva d’Z”A) is referred to in the Zohar as Alma d’Isgalya, because Rachel symbolizes the World of Speech (Olam HaDibur), which reveals hidden thoughts.

Alma d’Iskasya (the hidden world) is symbolized by the yam (“sea”). Although the sea is teeming with life and is full of fish, plants, and other sea creatures, all this remains invisible to an observed looking at the surface of the sea. Alma d’Isgalya (the revealed world), on the other hand, is symbolized by dry land where everything is on the surface and is revealed to an observer.

Kri’at Yam Suf (the “Splitting of the Sea of Reeds”) symbolizes the process of revelation. That which was hidden under the sea becomes exposed and revealed. It is as if curtains are pulled wide open revealing the scene of the play.

Similarly, the collapse of the wave function is the process of revealing hidden possibilities. Reducing uncertainty reveals information. Until the wave function is collapsed, the system is in an uncertain state—the state of superposition. The measurement that causes the collapse of the wave function eliminates this uncertainty revealing the state of the system. The collapse occurs as the result of an experiment or observation. It is the discovery of the state of the system. The process of discovery—revelation—in the terminology of Kabbalah—is the process of revealing Alma d’Isgalya from Alma d’Iskasya. This is why the splitting of the sea can be seen as an allegory of the collapse of the wave function.

Endnotes:

[1] This essay is based on the lecture given at the annual meeting of the Association of Orthodox Jewish Scientists in August 2017.

[2] More precisely, probability density.

[3] Many physicists mistakenly believe that the collapse of the wave function is caused by quantum decoherence (loss of coherence, i.e., definite phase relation between different states due to the loss of information into the environment). The fallacy of this belief has been clearly demonstrated. See, for example, Schlosshauer, Maximilian, “Decoherence, the measurement problem, and interpretations of quantum mechanics,” Rev. Mod. Phys. (2005) 76 (4): 1267–1305; Wojciech H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Reviews of Modern Physics, (2003) 75: 715; or Adler, Stephen L., “Why decoherence has not solved the measurement problem: a response to P.W. Anderson,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, (2003).

[4] If a system can be in a state A or state B then the system can be in a superposition state C, which is a linear combination of A and B: C = k₁∙A + k₂∙B, where Prob (A) = |k₁|², and Prob (B) = |k₂|².

[5] Talmud, Baba Mitzia 42a.

[6] Needless to say, the state of superposition is a quantum-mechanical concept, not something we normally apply to macroscopic objects we encounter in our daily life. We are using this term here metaphorically rather than literally as we are exploring structural parallels between quantum mechanics and Talmudic thought.

[7] Exodus 15:4

[8] See, for example, my earlier essays, “Entangled Sisters” and “On Rachel, Leah, and Dark Energy.”