Abel and Cain Conflict — Wave-Particle Duality

Cain and Abel, 16th-century painting by Titian (public domain)

…And Abel was a keeper of sheep, but Cain was a tiller of the ground. And in process of time it came to pass, that Cain brought of the fruit of the ground an offering unto the Eternal. And Abel, he also brought of the firstlings of his flock and of the fat thereof. And the Eternal had respect unto Abel and to his offering; but unto Cain and to his offering He had not respect. And Cain was very wroth, and his countenance fell. And the Eternal said unto Cain: “Why art thou wroth? and why is thy countenance fallen? If thou doest well, shall it not be lifted up? and if thou doest not well, sin coucheth at the door; and unto thee is its desire, but thou mayest rule over it.” And Cain spoke unto Abel his brother. And it came to pass, when they were in the field, that Cain rose up against Abel his brother, and slew him.  (Genesis 4:2–8)

As we mentioned before, the story of creation is the story of many coming from one. So, too, within the creation, the tension between the overarching principles of klal (general, the whole) and prat (particulars, details) continue to play out. This dichotomy was symbolized by the two trees planted in the Garden of Eden—the Tree of Life (representing the principle of klal) and the Tree of Knowledge (representing the principle of prat). The primordial serpent, being a dogmatic atomist, espoused the principle of prat to the exclusion of klal. And now, the klalprat dynamic plays out in the struggle between the first two sons of Adam and Eve—Cain (Qayin) and Abel (Hevel).

The dynamic of klal and prat is at the center of Torah hermeneutics. Any concept, object, or biblical verse could be analyzed as a whole, from a more general, holistic perspective, or it could be viewed as the sum total of its parts, in which case the focus is on the details and the particulars. The Oral Torah provides thirteen rules for biblical exegesis. These rules were formulated by Rabbi Yishmael in the Baraita as the introduction to Sifra, the halahic midrash to Leviticus. Of the thirteen principles, eight principles (numbers 4–11) involve the dynamics of klal and prat. One might say klal and prat are the central themes of Torah exegesis. It is this dialectic tension between klal and prat, between general and particular, that is responsible in no small measure for the body of Oral Torah as expounded in Mishna and the Talmud.

In physics, we find a similar tension between klal and prat, between the general and the particular. It is wave-particle duality. It is no coincidence that, in the English language, the words “particle” and “particular” share the same root, in that both come from the Latin particula, meaning a “little bit” or a “part.”

In quantum physics, every object could be viewed as a wave or as a particle. In our everyday life, we encounter particles and waves separately. Some objects can be idealized as pointlike objects or particles. In contrast, when we look at the surface of a lake or an ocean, we see waves, which are spread in space. These familiar concepts of particles and waves fail us when applied to the microworld of subatomic particles. Notions of “wave” and “particle” by themselves are inadequate for describing the reality of subatomic objects, which are neither particles nor waves but rather possess properties of both. Only wave-particle duality, where the concepts of “wave” and “particle” are taken together, produces the correct description of subatomic particles. Einstein said it best: “We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”[1]

The debate about the nature of matter goes back to antiquity. According to the atomist school of thought (whose most prominent figures were Leucippus,[2] Democritus,[3] Epicurus,[4] Lucretius[5]), matter is composed of particles or atoms (corpuscula).

Whereas atoms were believed to be indivisible, corpuscles could in principle be divided. Close to two thousand years later, in the seventeenth century, this ancient theory became highly influential among many of the great minds of the era, who further developed the theory into corpuscularianism, a physical theory postulating that all things are composed of minute particles (corpuscula). The main developers of this theory were Thomas Hobbes, René Descartes, Pierre Gassendi, Robert Boyle, Isaac Newton, and John Locke.

The corpuscularians, although in agreement on the particle basis of matter, did not concur on everything. For example, Newton,[6] like Alhazen[7] in the tenth and eleventh centuries, believed that light too was also made of particles – the corpuscular theory of light developed first by Alhazen and then further developed by Newton.

In contrast, a competing school of thought that included Rene Descartes[8] and Christiaan Huygens,[9] and later Thomas Young[10] and James Clerk Maxwell,[11] believed that light is made of waves.

Years later, at the dawn of the twentieth century, Albert Einstein played a unique role on both sides of this debate.

On the one hand, he provided the atomic theory with much needed theoretical foundation in his 1905 paper on Brownian motion. Einstein also conceptualized light not as a wave but as a collection of discrete wave packets, photons. This allowed him to explain the photoelectric effect, for which he was awarded the 1921 Nobel Prize in Physics. On the other, in the process of developing the theory of the photoelectric effect, Einstein proposed that even discrete quanta of light, i.e., photons, can have wavelike properties such as frequency and wavelength. After the theory of relativity, this was the beginning of the next revolution in physics.

In 1924, the French physicist Louis de Broglie[12] realized that all particles, not just quanta of light, possess wave properties such as frequency and wavelength. He extended the wave theory of light to all matter, postulating every object has a wavelength inversely proportional to the momentum of the object: λ=h/p, where λ is the wavelength, p is momentum, and h is the Planck constant.

Accepting de Broglie’s view, Niels Bohr[13] came to view quantum-mechanical objects as both waves and particles. This concept became known as wave-particle duality. The apparent contradiction didn’t bother him a bit. In fact, he saw it as another manifestation of his principle of complementarity. His motto was contraria sunt complementa—“opposites are complementary.”[14] Bohr felt that a quantum-mechanical object can be described in terms of contradictory properties depending on the choice of the experiment.

Our conceptions of “particles” and “waves,” however, are merely classical approximations. Truth be told, a quantum-mechanical object is neither a wave nor a particle. Subatomic particles simply do not fit into a classical mold. Quantum-mechanical objects have both characteristics, which play up in different circumstances. When the wavelength of an object is very short and, consequently, is well localized in space, it is natural to view the object as a particle, even if this is only an approximation. Similarly, when the wavelength of an object is relatively long (i.e., the object is not well-localized, but is spread in space), it is only natural to view this object as a wave, which, again, is only a classical approximation. Arthur Eddington[15] called quantum-mechanical objects “wavicles” that have idealized approximations on the opposite sides of the spectrum, where they behave more like waves or more like particles.

Modern quantum field theory takes the view that objects are excitations of the quantized field, which, depending on the shape of the excitation, can appear more like a particle or more like a wave. Wave-particle duality inevitably leads to Heisenberg’s Uncertainty Principle.

The conceptual connection of the quantum-mechanical wave-particle dualism with the dynamics of klal and prat is easy to see. We associate waves with klal because they are spread out in space. Therefore, one cannot see a wave by focusing on any particular spot.  To see waves, one needs to take a broad and expansive view of the wave as a whole (at least, one whole cycle of the wave from one crest to the next crest, or from one trough to the next trough). On the other hand, particles are localized in space. One can zoom in on a particle to investigate its properties disregarding the global picture. That is why particles represent the prat aspect of the klal–prat dynamics. One might say that wave-particle duality is a special case of klal-prat duality.

Returning to Cain and Abel, their story is quite puzzling. One brother kills another brother. What was the reason for the first murder in human history? The literal reading of the text leaves a clear impression that Cain killed Abel because he was envious of his brother—God looked favorably upon Abel’s offering but rejected Cain’s. Jealousy and envy are all too familiar human vanities. According to tradition, even before the incident, Cain was jealous of Abel’s twin sister, whom he wanted for himself. Both brothers were born with twin sisters—Cain had one, but Abel had two. Cain was envious of Abel’s extra twin, whom he wanted as his wife.[16] Cherchez la femme! These simple explanations notwithstanding, one cannot shed the feeling that there is something much deeper in this biblical story, which is positioned so prominently in the story of the creation.

As the Mitteler Rebbe[17] explains, Abel personified the klal principle in klal-prat duality, whereas Cain represented the prat principle. We see that in their occupations and in their offerings to God.[18]

As the verse tells us, “Abel was a keeper of sheep,”[19] i.e., he was a shepherd. Sheep tend to congregate together and move as a flock. A shepherd tends the herd as a whole. The job of a shepherd is primarily to keep the flock together. This hints at the principle of klal. The lifestyle of a shepherd is wholesome, uncomplicated, and pastoral. This also hints at klal. The soul of Abel was rooted in the sefirah of Chesed—kindness, which also hints at the principle of klal.

“Cain was a tiller of the ground,” i.e., he was a farmer (Genesis 4:2). Farming requires diversity and involves many details. A farmer plants a variety of different crops and vegetables. This multiplicity hints at the principle of prat. As a tiller of the ground, Cain was involved with the earth. The earth is a metaphor for multiplicity as it sprouts forth a great variety of vegetation, and this, of course, hints at the principle of prat. Agriculture requires detailed knowledge where and when to seed particular crops, how to care for them, and when to harvest them. This hints at the connection with the Tree of Knowledge and also at the principle of prat, as discussed earlier.

Moreover, farming is hard work. This hints at the sefirah of Gevurah (power, judgment) and at the principle of prat. Indeed, the soul of Cain was rooted in the sefirah of Gevurah.

The offerings brought by Abel and Cain also hint at the klal-prat duality. Abel offered the firstborn sheep as a sacrifice to God. A whole animal hints at the principle of klal, and so does the concept of “firstborn,” which is rooted in the sefirah of Keter (crown)—the first sefirah. Cain, on the other hand, offered plants: “Cain brought of the fruit of the ground an offering unto the Eternal” (Genesis 4:3). “Fruits of the ground” is a euphemism for picked vegetables. The plurality of such picks hints at the principle of prat.

According to tradition, Cain killed Abel with a stone. Stone is an allegory of an atom—a small quantum of matter—and hints at the prat principle. There is an opinion that Cain was born from the illicit union of Eve with the Nachash—the primordial serpent.[20] While it may be challenging to understand literally, metaphorically, it means that Cain was a spiritual heir of the Nachash and inherited his atomist philosophy (see chapter “The Serpent—An Incurable Atomist”). By spilling his brother’s blood, Cain manifested his nature rooted in Gevurah—the power to break.

The biblical story of Abel and Cain, parallel to the story of the Tree of Life and the Tree of Knowledge, further unfolds and deepens the klal-prat duality and serves as an allegory for wave-particle duality.

The murder of Abel by Cain is a stern reminder of the danger of the naked atomism which, albeit necessary, always threatens underlying unity. The development of modern science is in no small measure due to atomism, for which it is rightfully celebrated. However, the spectacular advances in scientific knowledge came at the price of undermining the faith in God and the unity of creation. This why God cautions Cain, in Genesis 4:7, that “sin coucheth at the door.” The present push toward the grand unified theory (GUT) is a clear sign of the tendency to restore the balance between klal and prat, when we will see the unity of Creation and, indeed, see God in all scientific details of nature. As the Psalmist sang:

How manifold are Thy work O God! In wisdom hast Thou made them all; the earth is full of Thy creatures! (Psalms, 104:24)

This realization will be Abel’s ultimate revenge.


[1] Albert Einstein and Leopold Infeld, The Evolution of Physics: The Growth of Ideas From Early Concepts to Relativity and Quanta (Cambridge University Press, 1938), p. 278.

[2] Leucippus (Leuikippos of Miletos, fifth century BCE)—a pre-Socratic Greek philosopher who, according to Aristotle and Theophrastus, invented atomism.

[3] Democritus (c. 460–c. 370 BCE)— a pre-Socratic Greek philosopher, a student of Leucippus, who further developed atomic theory. Democritus is called by many the father of atomism and by some the father of science.

[4] Epicurus (341–270 BCE)—an ancient Greek philosopher who founded the philosophical school of Epicurianism. Influenced by Democritus, he taught that the universe is made of invisible and indivisible particles known as atoms.

[5] Lucretius (Titus Lucretius Carus, c. 99 BCE–c. 55 BCE), a Roman poet and philosopher and author of the philosophical poem, De rerum natura (On the Nature of Things, c. 60 BCE), which taught Epicurian atomism and even described Brownian motion (in verses 113–140 from Book II), which he used (as later Einstein did in his famous paper of 1905 on Brownian motion) as proof of the existence of atoms.

[6] Isaac Newton (1642–1726)—English mathematician, physicist, astronomer, and theologian, who is considered one of the greatest scientists of all time. In his magnum opus, Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy,” 1687), he developed the foundations of classical mechanics and theoretical physics.

[7] Alhazen (Ḥasan Ibn al-Haytham, c. 965 – c. 1040)—Arab mathematician, astronomer, and physicist, the father of modern optics was an early adopter of a similar theory, some centuries before Newton.

[8] René Descartes (1596–1650), a French philosopher, scientist, and mathematician. He was one of the founders of modern philosophy best known for his saying, cogito ergo sum (I think, therefore I am). His contribution to optics was the discovery of the laws of refraction and reflection.

[9] Christiaan Huygens (1629–1695)—Dutch physicist, astronomer, mathematician, and inventor, who made groundbreaking contributions to optics, astronomy. First to use mathematics to describe the laws of physics, Huygens is called the first theoretical physicist. He also improved the design of the telescope and invented the first pendulum clock. The developed the wave theory of light (1678).

[10] Thomas Young (1773–1829) an English polymath and physician who developed the wave theory of light and is most famous for his double-slit experiment, in which he demonstrated interference as the proof of the wave nature of light.

[11] James Clerk Maxwell (1831–1879)—a Scottish theoretical physicist who developed the theory of electromagnetism unifying electric and magnetic fields as one physical phenomenon. This was called the “second great unification in physics,” after Newton’s first unification.

[12] Louis Victor Pierre Raymond de Broglie (1892–1987)—French physicist who made an important contribution to quantum theory, for which he won the 1929 Nobel Price in physics.

[13] Niels Henrik David Bohr (1885–1962)—Danish physicist and philosopher, the founder of atomic physics and the head of the Copenhagen school, where quantum mechanics was largely formulated. Bohr received the Nobel Prize in Physics in 1922 for his contributions to the atomic structure and quantum theory.

[14] Contraria sunt complementa was the motto Niels Bohr chose for his coat of arms when he was confirmed as a member of the Order of the Elephant (Danish order of chivalry, and Denmark’s highest honor).

[15] Sir Arthur Stanley Eddington OM FRS (1882–1944) was an English astronomer, physicist, mathematician, and philosopher. In 1920, he discovered the mechanism of nuclear fusion processes in stars. He also provided the earliest experimental confirmation of the general theory of relativity when he confirmed that the sun did, indeed, bend the light around it during May 29, 1919, total eclipse of the sun. This proved the mind-bending prediction of general theory of relativity that mass curves spacetime causing the ray of light to bend around the sun.

[16] See Bereishit Rabbah 22.

[17] Rabbi Dovber Schneuri (1773–1827), known as the Mitteler Rebbe, was the second Rebbe of the Chabad Hasidic movement. He was the son of Rabbi Schneur Zalman of Liadi, the Baal HaTanya—the founder of the Chabad movement.

[18] See Torat Chayim, Shemot, parshaht Yitro. I am grateful to Rabbi Yossi Krasnjanski and to my son-in-law D. Maimon Kirschenbaum for their help with this reference.

[19] Genesis 4:2.

[20] See, for example, Pirkei de-Rabbi Eliezer 21, Targum Pseudo-Jonathan on Gen.4:1, Philo 61:5–10.

Originally published on QuantumTorah.com.

About the Author
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.
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