And the History of Physics in Two
The history of creation can be expressed in three words (not even words but mere conjunctions): “and,” “or,” and “and/or,” whereas the history of physics can be expressed in two of them: “or” and “and/or.” Although it will take slightly more than three words to make the connections—my apologies—allow me to explain.
The History of Creation
The history of creation began with . . . well, the Creator, of course. Most people, including Jewish mystics, believe that the most characteristic and unique property of G‑d is His infinity. Thus, the Kabbalists call G‑d Ein Sof—literally, “without end,” or “infinite.” This property is unique to the Creator insofar as we do not find infinity in nature—nothing physical can be infinite.
However, in mathematics, infinities are ubiquitous, and mathematicians are very comfortable dealing with them. We can make some nontrivial observations about infinities and even compare them. There are infinitely many natural numbers (positive integers like 1, 2, 3,…) and infinitely many real numbers (points on a line, say, between 0 and 1). However, there are infinitely more real numbers than natural numbers, because between any two natural numbers we can fit infinitely many real numbers. The mathematician Georg Cantor introduced new transfinite numbers (that are greater than any finite number but not necessarily infinite), which are a generalization of the number of elements in the set (cardinality of the set) on infinite sets. These numbers are traditionally denoted by the letter aleph (א) with a subscript.
Some Christian theologians attacked Cantor’s mathematics for challenging G‑d’s unique infinity. But the use of infinity in mathematics does not pose a challenge to Judaism. The most characteristic and truly unique property of G‑d is not infinity but His self-referential and self-contradictory nature. Or, looking at this from another angle, the self-contradictory nature of G-d stems from His absolute perfection (shelemut), because He lacks nothing.
The First “And”
The self-contradictory nature of G‑d can be expressed by the coordinating conjunction “and.” For any thesis A and antithesis not-A, G‑d can be said to possess both A and not-A, because He lacks neither A nor not-A. Thus He has the potential for both infinitude (ko’ach bli gvul) and finitude (ko’ach hagvul), because He cannot be limited by anything, including by His infinitude. As a perfect being, G-d lacks neither infinitude nor finitude. The most mind-bending statement about G‑d is that He exists and “does not exist,” as it were, at the same time, because He is not limited by His existence. G‑d can be in any state and its opposite state, because He lacks neither state. And He can be in a superposition of all states because nothing is impossible for G‑d. The sages termed this self-contradictory aspect of G‑d as nimna hanimna’ot(literally “restricting [all] restrictions”), that is, the “paradox of paradoxes.” God is the ultimate paradox. This paradoxical ability of G‑d to be in any state and its opposite state is summed up by the coordinating conjunction “and.”
As it arose in the mind of G‑d to create this world, He desired to manifest Himself and His attributes in the lower worlds (tachtonim). The tachtonim (lower created worlds) are characterized by the gevulim (“finiteness,” or “finite measures”), as well as by their false sense of independence. There is nothing infinite in the created worlds. Therefore, there is no room for paradoxes in the lower worlds. Any thesis excludes its antithesis and vice versa: it is either the thesis or the antithesis.
This physical world cannot endure any paradoxes. One way to avoid paradoxes is to create time so that two contradictory things happen at different times without canceling each other out. That’s how the doorbell works—its electrical circuit is self-referential and self-contradictory, but it works because the contradictory elements occur one after another, not simultaneously. At any given moment in time, only one of two contradictory statements can be true, but never both. So, at each moment, it is either one or the other. Therefore, this physical world is characterized by the correlative conjunction “or.”
The Psalmists said:
How manifold are Thy works, O Lord.Psalms 104:24
The fundamental question regarding creation is, How did such an incredible variety of forms of life and matter come from one G‑d? By way of analogy, just as a pure white light after traveling through a prism splits into seven rainbow colors, so too, when Infinite G‑d, who is unlimited and is so-to-say in a superposition of all possible (and impossible) states, wishes to manifest Himself in a finite (lower) world, each of these states has to have its own embodiment, because a limited world cannot contain contradictions. Thus, contradictory states must be realized either at different times, in different places, or be embodied by different objects.
This world reflects its divine source. However, unlike its divine source, it cannot combine contradictory states—it’s either one or the other. For this reason, we label this stage in the creation by the correlative conjunction “or.”
This world is not intended to remain in the same state forever. Any purposeful project must have an end goal, which represents the fulfillment of the purpose. A purposeful creation also has an end goal—what is called the messianic era (a.k.a. the world-to-come or the hereafter). According to the Lurianic Kabbalah, in the present pre-messianic state of the creation, the Light of the Infinite (Or Ein Sof) shins through the limited vessels (kelim), which greatly screen, diminish, and conceal the godly light. Thus, we receive only a dim glimmer of that infinite light. This is necessary, because the limited vessels of the physical world could not withstand infinite light and would burn up if not for the intense contraction and screening of the light.
In the messianic era, the Light of the Infinite will be able to manifest itself in the full measure of its unmitigated infinitude despite the vessels that remain finite. How is this possible? As we discussed above, G-d possesses the potential of infinitude and finitude. The main characteristic of the messianic era is the revelation of G-d’s essence, which contains the potential of infinitude and finitude. It follows that this paradoxical aspect will be revealed and both infinitude and finitude will be manifest in this physical world. That means that the physical world will remain physical and limited as it is now, but after being purified and rectified, its vessels will be able to withhold—and, indeed, benefit from—the infinite light. This is the ultimate contradiction and a miracle of the messianic time, reflecting the contradictory nature of the Creator, who possesses the power of infinitude as well as finitude.
The unnatural (and self-contradictory) combination of the Light of the Infinite (Or Ein Sof), symbolized by the coordinating conjunction “and,” on the one hand, and limited vessels (kelim), symbolized by the correlative conjunction “or” on the other hand, creates an unusual combination of “and” and “or,” which we are going to represent as “and/or.”
The History of Physics
The history of physics begins with Isaac Newton, who formulated the first rigorous scientific theories of physics—mechanics, optics, and the universal law of gravity, which are still used today in science and engineering. In Newtonian physics, any physical system (a collection of physical objects) is characterized by a state. And by “state,” we do not mean classical states of matter—solid, liquid, and gas (and plasma); by “state,” we mean a set of values of all measurable properties of the physical system. For example, a single particle has two primary properties—its coordinates and its momentum. The values of the coordinates and the momentum of the particle at a particular time define the state of that particle. A system of several particles will have a state defined by the values of the coordinates and the momenta of all particles in the system. Thermodynamical systems have other primary characteristics, such as volume, pressure, and temperature. The values of these characteristics define the state of the thermodynamical system at a particular time. A spinning top has angular momentum as its primary characteristic. Its angular momentum shows which direction the top is spinning (clockwise or counterclockwise) and the angular velocity of rotation. And so on.
The fundamental principle of classical physics is that no system can be in two different states simultaneously. Thus, a particle cannot be here and there—in two different locations in space—at the same time. A gas cannot have two different values of its temperature at the same time. And a top cannot spin clockwise and counterclockwise at the same time—it can spin either clockwise or counterclockwise. For this reason, we shall represent this stage of physics development by the correlative conjunction “or.”
As it turned out, Newtonian physics is only accurate for ordinary objects we encounter in our daily lives. When it comes to the microworld of atoms and subatomic particles, Newtonian physics gives way to quantum mechanics—the most fundamental and accurate theory of science known to date.
Quantum physics is where our intuition goes to die. This theory is famous for its weirdness and mind-bending concepts, but it never fails to predict the results of the experiment. It is the most tested theory in all of science, and we can rely on it to correctly describe subatomic physics as well as molecular chemistry, which is based on it. The weirdness of quantum mechanics comes from the fact that a physical system can be in more than one state at a time. In fact, it can be in a superposition of many states (some of which can be mutually exclusive). In quantum mechanics, a top can spin clockwise and counterclockwise simultaneously, and a cat can be simultaneously dead and alive. This fundamental property of quantum mechanics led one science writer to aptly say, “The pleasure and pain of quantum theory began when an “or” became an “and.”
In quantum mechanics, a physical system is described by a wave function that obeys the Schrödinger equation. This equation is linear. As we know from high school algebra, a linear combination of solutions to such an equation is also a solution (in fact, this property defines a linear equation). Therefore, any linear combination of states is also an allowed state in quantum mechanics. This mathematical fact leads to a possibility of a quantum particle having its spin up and down at the same time (a quantum equivalent to a classical top spinning clockwise and counterclockwise simultaneously). This mind-bending property was enigmatically captured by Ervin Schrödinger in his famous thought experiment with the eponymous cat locked in a box with radioactive material that can randomly decay, killing the cat. In that experiment, the cat in a box (until looked at) is in the state of superposition of being dead and being alive. This strange phenomenon can be classified using the coordinating conjunction “and.” However, any act of measurement collapses the wave function of the system, which is always found either in one state or the other—a phenomenon described by the correlative conjunction “or.” Indeed, when we open the box and look inside, we find the poor feline either dead or alive, but never both. This contradiction is called “the measurement problem.” We are going to denote this state by the “and/or” moniker.
If you haven’t noticed the parallel yet, here it is, staring straight at us:
|Before Creation||First Stage||Ultimate Stage|
|The history of Creation:||and||or||and/or|
|The history of physics:||or||and/or|
The history of physics tracks the history of creation precisely, with one exception—the initial “and” is missing. But this is fully expected because the initial “and” in the history of creation characterizes the Creator. Physics doesn’t study the Creator (the subject of theological inquiry); it studies the world as it was created. Far from coincidental, this parallel is highly significant. We would expect to see progress in science tracking the development of the creation, and indeed it does.
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 an Infinite Being, can be and is in a superposition of all states.
The enigmatic state of nimna hanimna’ot would manifest itself only in miracles that violate the laws of nature. A well-documented example of such a miracle is found in the description of the measurements of the Bet HaMikdash (the Holy Temple in Jerusalem) recorded in the Talmud. Aron HaBrit—the “Ark of the Covenant”—was the golden box containing the tablets (Luchot) with the Ten Commandments, placed in the Holy of Holies—the innermost sanctum of the Bet HaMikdash (the “Holy Temple” in Jerusalem). According to the Talmud, the Ark did not occupy any space. The Holy of Holies measured twenty cubits by twenty cubits. The Ark itself measured two-and-a-half cubits. When measured from the south wall to the nearest side of the Ark, the distance was ten cubits. When measured from the side of the Ark to the northern wall, the distance was also ten cubits. It appears that the Ark occupied no space, although its width was 2.5 cubits.
This miraculous state of affairs will once again be found in the messianic era. While we can expect and accept miracles in the hereafter, we cannot accept miracles in physics here and now. The fact that we still do not understand the nature of the collapse of the wave function—the measurement problem—is indeed a problem indicative of the fact that the messianic age has not fully arrived yet, albeit very close. The measurement problem is what separates us from the hereafter. When this problem is resolved, this will herald redemption, at least on the intellectual level.
In the meantime, on a social level, the bunker mentality “me against them” or “us against them” tribalism expressed by the correlative “or” (it is either them or us) is distinctly un-messianic. While physicists are hard at work hastening the redemption by trying to understand the nature of the measurement problem, the rest of us have to do our part by shifting the mode of our personal relationships from the attitude expressed by the correlative conjunction “or” to the attitude symbolized by the coordinating conjunction “and”—from “I or you” to “I and you.” Only together—you and I—can we bring about redemption.
 Georg Ferdinand Ludwig Philipp Cantor (1845–1918), a German mathematician, the founder of the branch of mathematics called set theory.
 The “non-existence” of G-d is only relative to our existence. It simply means that His existence, which according to Maimonides is a necessary existence, is of an entirely different nature and cannot be compared to our existence in any way. When using such expressions as “at the same time” with respect to G‑d, we must remember that G‑d transcends time, which He created, and such expressions are meaningless and are used only as a figure of speech. Moreover, our existence is necessarily temporal. A divine being that transcends time cannot be said to exist because the word “exist” necessarily means to exist in time.
 Responsa of the Rashba (Shu”t HaRashb”a), vol. I, sec. 418; see also Sefer HaChakirah by the Tzemach Tzedek, p. 34b ff.
 See more on this in my essay, “Physics of Tzimtzum II — Collapse of the Wave Function” (2020), available at https://quantumtorah.com/tzimtzum-ii-collapse-of-the-wave-function/.
 This concept called dira b’tachtonim (a “dwelling place” [for G‑d]), based on the Midrash Tanhuma, Naso, is the cornerstone of the theology of Chasidism.
 See my essay “On the Nature of Time and the Age of the Universe” (2005), available at https://quantumtorah.com/on-the-nature-of-time-and-the-age-of-the-universe/.
 In classical logic, this is called an exclusive disjunction.
 And/or is not used here as a conjunction that indicates that two words or expressions are to be taken together or individually, as it is normally used in the English language. We are using “and/or” here merely as an emblem of an unusual combination of two metaphysical concepts symbolized respectively by “and” and “or.”
 Richard Webb, “What Makes Quantum Theory So Strange?” in “Quantum Frontiers,” New Scientist, August 28, 2021.
 See footnote 7 above. As there, our use of “and/or” here is not intended as a conjunction, but as an emblem of a paradoxical clash of two incompatible situations—a superposition of states before measurement denoted as “and” vs. the collapsed state after measurement denoted by “or.”
 A quantum mechanical system can be in a superposition of all possible states. G-d, on the other hand, can be “in superposition” of all states, possible and “impossible,” because nothing is impossible for God. Moreover, we must not forget that this is just a crude allegory—G-d is not in any state that we can think of, as it says, “I am G-d and I do not change” (Malachi 3:6). Only our idea of G-d can be in different states—He can be angry and forgiving at the same time, for example.
 See Talmud, Yoma 21a; Megillah 10b; Bava Batra 99a. As the sages explained, this is an example of G‑d’s presence occupying and not occupying physical space—nimna hanimna’ot. See Rabbi Menachem M. Schneerson, Maamar Gadol Yiheyeh Kavod HaBayis HaZeh. See also Sefer HaMa’amarim 5643, p. 100; and loc. cit. 5665 p. 185.