Cartesian dualism, or mind-body dualism, formulated by the French scientist, mathematician, and philosopher René Descartes (1596–1650), holds that the body and the mind (which he equated with consciousness, or the soul) are two distinct ontological substances with nothing in common. They exist in different worlds and do not interact or communicate with each other. This position presents a serious problem—if the two have nothing in common, how can they have the causal connections they seem to have? How, for example, can the mind causally direct the body? And, vice versa, how can the body communicate sensations, such as pain, to the mind? This valid criticism proved fatal for Cartesian dualism, which has been all but relegated to the dustbin of history.
The Jewish theosophical doctrine of Kabbalah takes a very different approach. It is based on the doctrine of seder hishtalshelut—a chainlike ontological order of the unfolding (or descent or evolution) of the worlds in the creation process. According to this doctrine, the creation took shape gradually through the consecutive ever-more-diminished emanation of the divine light broadly classified as four “worlds”—the World of Emanation (Olam HaAtzilut), the World of Creation (Olam HaBeriyah), the World of Formation (Olam HaYetzirah), and the World of Action (Olam HaAsiyah). The first three worlds, Atzilut, Beriyah, and Yetzirah, are purely spiritual. However, the godly consciousness is progressively diminished, concealed, and displaced by self-consciousness, which is the hallmark of creation—recognition of oneself as an entity separate from and, to a progressively greater degree, independent of G‑d. The lowest world in this hierarchical structure is the World of Action, Olam HaAsiyah. This world is further subdivided into two strata—an intermediate stratum called the spiritual stratum of the World of Action (Olam HaAsiyah Ruchni) and the purely physical world we inhabit, the physical stratum of the World of Action (Olam HaAsiyah Gashmi).
Since the unfolding of the worlds is a continuous process, how do the spiritual and the physical strata of the World of Action connect? Kabbalah’s answer is simple: the lower (furthest from the source) spiritual world has some physical aspects to it (gashmiyut sheb’ruchniyut) that interlock with the spiritual aspect of the physical (ruchniyut sheb’gashmiyut). This is why the ontological unfolding of creation is called the “chain”—when links of the chain interlock, the lowest portion of an upper link is lower than the highest portion of the link below it.
This approach also explains how the soul interacts with the body it inhabits. The soul is spiritual, whereas the body is physical. Yet, in Kabbalistic and Chasidic sources, the soul is said to inhabit the body and causally interact with it. How? Because the physical-in-the-spiritual aspect of the soul is sewn from the same cloth as the spiritual-in-the-physical aspect of the body, they can interlock and interact. Unfortunately, these sources provide no explanation for how exactly this intermeshing works and what these mysterious entities—the “physical in the spiritual” (gashmiyut sheb’ruchniyut) and the “spiritual in the physical” (ruchniyut sheb’gashmiyut)—are.
I tend to think that both are wave functions. The wave function (or the psi-function), traditionally denoted by the Greek letter ψ or Ψ (psi or Psi), is an abstract mathematical object that describes what we know about a physical object or system. Specifically, the “physical in the spiritual” is the wave function of the soul (or, more broadly, of the spiritual realm), and the “spiritual in the physical” is the wave function of the body (or, more generally, of physical objects).
It is entirely uncontroversial to say that all physical objects, not only subatomic particles, have wave functions associated with them. One can define wave functions for one’s body, house, the planet Earth, and the entire universe. In fact, American physicists John Wheeler and Bryce DeWitt did just that—they defined a wave function for the universe and formulated their eponymous Wheeler–DeWitt equation that forms the foundation of quantum cosmology. The wave function has no physical meaning. It is an abstract mathematical object that provides a recipe for calculating the probability of finding an object in a particular physical state. The wave function satisfies all indicia for what Kabbalists call the “spiritual in the physical.” “Spiritual” simply means “not physical,” and the wave function certainly is not physical. Yet, it is bound to the physical object and provides information about its state. I can think of no better example of the spiritual-in-the-physical concept than the wave function.
My suggestion that the “physical in the spiritual” is also a wave function is less intuitive and needs some justification. What does defining a wave function for a nonphysical (that is, “spiritual”) entity mean? Let us note that every physical or nonphysical entity can be described as having coordinates in some abstract multidimensional space. For physical objects, we use six-dimensional phase space. For nonphysical entities, various so-called conceptual or parametric spaces have been used. For example, color can be encoded as a point in a color space where each dimension represents one of the primary colors. In artificial intelligence, transformer neural networks encode words or images as a point in multidimensional abstract spaces. Whatever the nonphysical entity is, we can encode it in an abstract multidimensional space whose dimensions represent the properties or characteristics of that entity. Indeed, the oldest book of Kabbalah, Sefer Yetzirah (the “Book of Formation”), describes spirituality in terms of multidimensional space. Kabbalists took pains to explain that whenever they use words such as “higher” or “lower,” we are to understand them in terms of conceptual similarity to divine attributes. For example, when one angel is said to be “higher” than another angel, it means that this angel is more similar in his attributes to the divine attributes than the other angel. Similarly, if someone is said to be closer to G‑d, it is to be understood in terms of the person’s character traits’ similarity to divine attributes. The notion that distance could be equated with similarity allows us to define a conceptual space where the metric (“distance”) is defined in terms of conceptual similarity.
Although nonphysical (spiritual) entities do not exist in space (that is, they are not constrained by spatial limitations), they do exist in time—they evolve. In the language of physics, this means they have various states and can evolve from one state to another. The state of a nonphysical entity can be described as a vector in a Hilbert space. But this is exactly how we define a wave function of a physical object—as a function on Hilbert space. Thus, nothing stops us from formulating a wave function that provides information about the state of a nonphysical (spiritual) entity.
Lest someone object to the application of quantum mechanics to the macroworld, the world of larger objects, let alone to the spiritual world, let me address this issue head-on. First, quantum mechanics is applicable not only to the microworld (the world of subatomic particles, such as photons, electrons, protons, neutrons, and quarks) but equally to the macroworld—the world of people, cars, cats, cannonballs, planets, and stars. Quantum mechanics is the most fundamental theory of nature we have, and it applies to every material object, no matter its size. We use classical physics in the macroworld, rather than quantum mechanics, as a matter of convenience—you don’t use cannons to shoot a bird. Classical physics is simple and requires no advanced math. Any high-school student can solve many physics problems related to ordinary objects using classical (Newtonian) physics. Quantum mechanics, on the other hand, requires more advanced math and is not taught till college. Furthermore, Newtonian physics is a special case of quantum mechanics—an approximation. In our day-to-day life, the predictions of Newtonian mechanics are good enough. We could use quantum mechanics to calculate the time it takes to get from New York to Boston by car. However, the incremental improvement in the precision of calculation would be drowned in the margin of error due to our inability to measure the position and the velocity of the car with the precision that quantum mechanics requires. We simply would not see the difference. So why use complicated math when we can use high school physics to solve most everyday problems? Another and more fundamental reason is that in the noisy, hot environment of the macroworld, information would quickly dissipate into the environment, leading to decoherence of the wave function. Regardless of whether we can observe quantum effects in the macroworld or whether it is convenient for computations, in principle, quantum mechanics can be used to describe the macroworld.
As far as applying quantum mechanics to describe the nonphysical (spiritual) world goes, I am not suggesting it. I only suggest that we can define a wave function that describes the state of a given nonphysical entity whose properties are encoded in an abstract multidimensional conceptual space. This can be done outside of the quantum-mechanical context. The use of “quantum mechanics” in the title of this essay notwithstanding, there is nothing intrinsically quantum-mechanical in a wave function, besides that it owes its origin and its fame to quantum mechanics. In the context of a nonphysical entity, the wave function is simply an abstract mathematical object that contains information about the state of that nonphysical entity.
A properly defined wave function describing the state of a nonphysical entity, at the end of the day, is the same mathematical function as the wave function describing physical objects. Consequently, they can be added together to form a combined wave function.
Let us consider Cartesian mind-body dualism, for example. Let us define the wave function of the body ψbody and the wave function of the mind (that is, consciousness or soul) ψsoul. Then the total wave function of body and mind (consciousness or soul) can be thought of as the sum of two wave functions— ψbody and ψsoul. Each of these functions yields a number—a probability of finding the respective entity in a given state. We started with two ontologically distinct entities—matter and spirit—which seemingly had nothing to do with each other. By associating a wave function with each of them, we now have two numbers—two probabilities. We are no longer comparing apples and oranges; we are comparing two numbers. Now that matter and spirit are on the same wavelength, they can communicate. This allows direct interaction and causal connection between body and soul (or mind) or between the physical and the nonphysical (the spiritual).
My proposal to interpret Kabbalistic notions of the “spiritual in the physical” (ruchniyut sheb’gashmiyut) and the “physical in the spiritual” (gashmiyut sheb’ruchniyut) as the respective wave functions of the physical and nonphysical entities allows us to resolve the principal fault of Cartesian dualism by providing for a causal mechanism for two distinct ontological entities—matter and spirit (the nonphysical) to communicate and interact with each other.
 In the philosophy of mind, this view is called substantive dualism.
 In some contexts, Kabbalah sources discuss five worlds starting with Adam Kadmon (A”K) (“Primordial Man”), followed by the four worlds discussed above.
 To be more precise, the square amplitude of the wave function gives us the probability of finding a particle in a given volume of the phase space.
 See footnote 2 above.
 Hilbert space is a multidimensional vector space that preserves the inner product. It is a generalization of the familiar Euclidean space.
 To be precise, it is a complex-valued function.
 To say that quantum mechanics describes spiritual phenomena or a nonphysical entity would be to say that their wave function satisfies Schrödinger’s equation, which is far from obvious. The immediate problem is that the Schrödinger equation is linear, whereas not every phenomenon is linear. In the physical domain, gravity is nonlinear. This is one of the conceptual problems of marrying Einstein’s general relativity with quantum field theory. Brain and consciousness are also nonlinear. For example, humans have metacognition—the ability to think about one’s thoughts. Self-reflection and metacognition are, in mathematical language, nonlinear. In the nonphysical domain, consciousness is highly nonlinear. Thus, applying Schrödinger’s equation across the board does not seem to be possible. Consequently, it would be incorrect to say that quantum mechanics can describe the spiritual domain.
 As mentioned above, a wave function is a complex-valued function defined across a Hilbert space.
 It is enticing to define the total wave function of body and mind (consciousness or soul) as simply the sum of two respective wave functions: Ψtotal defined as Ψtotal = ψbody + ψsoul. One must bear in mind, however, that each wave function is defined on a different Hilbert space (H1 and and H2) and cannot be simply added together. Imagine a function f1(x,y) defined on a two-dimensional space R2 (a plane) and another function f2(z) defined on a one-dimensional space R (a line). To add these two functions together, one needs to combine the two spaces RxR2. Now we can redefine the two functions as f1(x,y,z) and f2(x,y,z) and add them together f1(x,y,z) + f2(x,y,z). Remarkably, this is exactly the approach of the ancient book of Kabbalah, Sefer Yetzirah (the “Book of Formation”), which adds the fifth spiritual dimension to four-dimensional spacetime.
Dear Alex, thank you for fascinating post. I like it very much.