Tag Archives: Impurity

Red Cow: Quantum Physics in the Torah

This week’s parasha, Chukat, begins with the laws of the Red Cow (or “Red Heifer”). The Torah describes in detail the Red Cow ritual, starting with the production of a special mixture which alone had the power to remove the greatest of impurities, the impurity of death. (Because we lack this mixture today, everyone is considered ritually impure at all times, and this is one reason why most Orthodox authorities discourage Jews from ascending the Temple Mount in Jerusalem.) First, the Torah requires finding a perfectly red calf. The Sages elaborate that even two non-red hairs invalidate a cow. The calf must also be entirely unblemished, and in perfect health. It must not have ever been used for any kind of labour. The simple act of putting a yoke on the cow—even if just for a moment—immediately disqualifies it.

Rabbis inspect a red cow in Israel (Courtesy: Temple Institute). Jewish tradition maintains there have only been nine red cows used in history. The tenth will come in the time of Mashiach.

Once such a cow is found, it is taken to the Temple and appropriately slaughtered. The High Priest takes some of its blood and sprinkles it towards the Holy of Holies (or the “Tent of Meeting”). The cow is then entirely consumed in flames, with the added ingredients of cedar wood, hyssop, and crimson wool. At this point, the High Priest has become impure himself, and must go to the mikveh. Another priest (who is pure) must gather the ashes to be used to make the purifying solution. This person, too, becomes impure. Finally, the third pure person who actually prepares the mixture and sprinkles it on the impure people also becomes impure in the process. Perplexingly, the act of purifying others instantly makes the purifier himself impure.

This strange Red Cow ritual puzzled the ancient Sages. They went so far as to say that even King Solomon—the wisest of all men—could not understand the Red Cow (Yoma 14a). The Sages base themselves on Solomon’s own words (Ecclesiastes 7:23): “All this have I tried by wisdom… but it was far from me.” Solomon had all the wisdom, yet there was one thing that was too “far” for him to grasp, and that was the Red Cow. (The Midrash, meanwhile, comments on Solomon’s words in Proverbs 30:18—“Three things are wondrous to me, and four I do not know”—to mean that Solomon didn’t know seven more things.  The three things wondrous to him were the secrets of the Pesach offering, matzah, and maror; and the four he didn’t know were the mysteries of the four species of Sukkot. See Vayikra Rabbah 30:14)

The Sages conclude that the Red Cow has no human logic and is, as the Torah states, a chok, an incomprehensible divine law. In other words, no one understands the Red Cow.

The Nazis tried to ban Einstein’s theories and discoveries. They didn’t like quantum physics very much, and once branded it as a “Jewish science”.

Interestingly, there is a parallel phenomenon in the world of science. The past century and a half has seen the rise of a bewildering new field called quantum physics. Like the Red Cow ritual, many experiments in quantum physics yield results that are incomprehensible. They often contradict the foundational principles of classical physics, and are sometimes just plain bizarre. This may be why Albert Einstein once humorously described quantum physics as a “talmudical theory”. (And may be why Jews are so disproportionately represented in the field.) Niels Bohr, meanwhile, said something along the lines of “Those who are not profoundly shocked when they first come across quantum theory have not understood it.” And Richard Feynman concluded: “I think I can safely say that no one understands quantum mechanics.”

Quantum physics is to science what the Red Cow is to the Torah. In fact, a closer examination may reveal a very intimate connection between the two.


One of the central principles of quantum physics is entanglement. This refers to two particles that are intertwined, and appear to affect one another instantaneously even though they may be very far apart. For example, take the case of two entanglement particles, one with a clockwise spin, and the other with a counter-clockwise spin. If the clockwise particle is forced to spin the other way, the counter-clockwise particle immediately changes its spin as well. This is true even over vast distances, and the effect is immediate, suggesting faster-than-light communication. Einstein famously called this strange phenomenon “spooky action at a distance”.

Entanglement has the potential for many practical applications, and scientists are even working on an un-hackable “quantum internet”. Meanwhile, Stuart Hameroff and Roger Penrose have built an entire biological theory around entanglement, which provides a scientific explanation for the soul, the afterlife, and reincarnation.

Of course, from a Jewish mystical perspective, all souls are intertwined and “entangled”. Entanglement may even explain the strange nature of the Red Cow. Recall that when the pure person sprinkles the mixture upon the impure person, he instantly becomes impure himself while the impure person becomes pure. This is precisely like a counter-clockwise particle instantly switching its spin to clockwise when its fellow entangled particle is made to go from clockwise to counter-clockwise.

Uncertainty Principle

Another foundation of quantum physics is Heisenberg’s Uncertainty Principle. In short, this means that when measuring any given particle, we can either determine its position, or its speed, but not both. If we measure its position, then technically at that split instant the particle isn’t really in motion, so we cannot determine its speed. If we measure its speed, than it can’t be standing still in any one position, so we cannot determine exactly where it is. (The principle can be explained with a classic physics joke: a police officer pulls over a speeding particle and asks: “Do you have any idea how fast you were going?” The particle replies: “No sir, but I know where I am.”)

Rav Yitzchak Ginsburgh beautifully points out that the Torah actually speaks of the Uncertainty Principle. We read in Job 28 of the difference between man’s limited wisdom and God’s omniscience. We are then told that “God understands her path, and He knows her place.” (Job 28:23) Unlike man, who is incapable of grasping such things, God alone knows both the “path” (momentum) and “place” (location) of a particle! Rav Ginsburgh summarizes:

Now, what is the verse saying? Actually, it is saying exactly what Einstein said when he heard that the uncertainty principle was somehow inherent in nature: “God does not play dice with the universe.” It did not sit well with him that God cannot see beyond the uncertainty principle. Little did Einstein know that he had a verse in the Bible to support his intuition that God does know… (Lectures on Torah and Modern Physics, pg. 90)

Wave-Particle Duality

Perhaps the most well-known principle in quantum physics is that of wave-particle duality. This is the notion that every particle is also a wave. The discovery was a result of a much earlier debate (going back at least to the time of Newton) of whether light is a particle or wave. Over the decades, experiments would alternately show that light behaves as a particle, while others would show that light behaves as a wave. Eventually, it was found that photons (particles of light) behave in both ways, and the same is true for other particles, too.

Closely related to this is what is known as the “observer effect”, that the presence of a conscious “observer” actually affects whether a particle will behave as a particle or wave. In the famous double-slit experiment, whenever scientists “watch” a particle it always passes through one slit and leaves a single mark on the screen behind as expected. Yet, whenever they remove the measuring devices and shoot particles without any observation, the particle seemingly goes through both slits simultaneously, and produces a wave-like pattern on the screen!

Notions like this led Max Planck, often called the “father of quantum physics”, to conclude:

As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.

Rav Ginsburgh once more shows how wave-particle duality is secretly embedded in the language of the Torah. The Torah’s word for a “wave” is gal (גל), while the Torah’s word for a tiny drop, or “particle”, is egel (אגל). The two share one root, meaning there is a profound connection between them. Rav Ginsburgh cites ancient commentaries (ibid, pg. 128-129) which explain how a multitude of tiny drops of dew blanketing a field combine to form the appearance of a wave. The Sages are speaking of an observer who seems to be looking at a wave but, upon closer examination, is seeing individual particles of dew. This is little more than a poetic way of describing the scientific “observer effect”, where close observation and measurement shows particles while lack of measurement shows waves.

String Theory in Kabbalah

For decades, physicists have been looking for a “theory of everything” that can elegantly explain all of the various phenomena in the universe. Currently, one very popular such theory is string theory, which holds that the universe boils down to a set of tiny vibrating strings. Differing vibrations would result in particles of different masses and charges, giving rise to the variety of forces and particles in the universe, including a particle that carries gravity (called a graviton). String theory is therefore a good “theory of everything” that can neatly unify all of physics.

Edward Witten is also Jewish, and the son of Louis Witten, another well-known physicist.

In reality, string theory is not one theory, and has multiple versions. In the past, there were five major, accepted models. Then, in 1995 Edward Witten was able to unify these models into one wholesome theory, called M-theory, sparking a “superstring revolution”. Since then, a great deal of work has been done to strengthen and support M-theory, which continues to be one of the leading models in modern physics.

Interestingly, M-theory suggests that the universe has a total of 11 dimensions. Three of these are the familiar dimensions of space (length, width, height). The fourth is the dimension of time, which is really inseparable from the three of space, and part of one continuum. In addition to these, there are seven more dimensions unperceivable to human senses:


Etz Chaim, “Tree of Life”, showing the upper sefirot (Keter/Da’at, Chokhmah, and Binah, known as the Mochin), and the seven lower sefirot.

Anyone who has dabbled in Kabbalah will immediately recognize that this conception of 11 dimensions perfectly parallels the “dimensions” of Kabbalah, ie. the Sefirot. In the arrangement of the sefirot, too, we have the three sefirot of the mochin, which are tied to a fourth (usually hidden) sefirah of Da’at, just like the three spatial dimensions are intertwined with time. Below the three mochin are the seven middot. Like the 11 dimensions of M-theory, the Kabbalistic “Tree of Life”—as made popular by the Arizal—is typically shown depicting 11 sefirot. (Yet, the Sages insist that there are ten sefirot, never eleven! It should be noted that in non-M-theory versions of string theory, there are indeed only 10 dimensions.) One who studies both M-theory and the Arizal’s teachings of the sefirot will quickly find tremendous overlap between them.

And one who has delved into the Kabbalah of the Arizal will know just how easy it is to get lost in descriptions of dimensions within dimensions, and universes superimposed upon universes; in souls entangled across vast distances, and across eons of time; and in lengthy formulas of yichudim, kavvanot, and tikkunim (“unifications”, “meditations”, and “rectifications”). In fact, studying the Arizal sometimes feels like studying quantum physics. Truly, the two go hand-in-hand, and are poised to bridge the gap between the realm of science and the realm of the spirit.

A Mystical Look at Pregnancy and Abortion

Tazria begins by stating that a woman who gives birth to a son is spiritually impure for seven days, and requires another 33 days of purification afterwards. If she gives birth to a female, the impurity lasts fourteen days, followed by 66 days of purification.

The Zohar (III, 43b) comments on this section by first reminding us that each soul has male and female halves, and when the soul enters this world, it splits and enters two different bodies, male and female. If the two soulmates merit it, they will find each other and reunite. We are then told that the female part of the soul is larger and more powerful, which is why a woman who gives birth to a female needs double the purification time.

The Zohar explains why the Torah prescribes these specific time periods: 7 and 33 days for boys; 14 and 66 days for girls. It states that at birth, the soul first enters the body and is in complete disarray. For the first seven days, the unsettled soul “roams the body to find its place”. On the eighth day, the soul is finally getting comfortable in its new home. This is one reason why circumcision is done on the eighth day, once the soul is no longer distressed. The soul then needs an additional 33 days to acclimatize to its new environment until it has completely settled into the body. For the greater female souls, the time periods are doubled.

Note how these time periods are referring to the soul of the newborn, yet it is the mother that is described as being “impure”. This is because the mother carried the child, and its soul was housed within her temporarily. (Perhaps this extra soul is responsible for the well-known “pregnancy glow”.) Once the baby is born, its soul leaves the mother’s shelter and is now independent in the baby’s body. (And that pregnancy glow is gone!) The sudden loss of spiritual energy is difficult on the mother as well, and she requires forty (or eighty) days to get back to herself.

A major question arises here: if the soul only enters the newborn at birth, why is abortion forbidden? Religious groups of various faiths have argued for centuries on when exactly the soul enters the body, and many have taken the stance that a fetus already carries a soul, making abortion indistinguishable from murder. What do Jewish texts say?

Abortion and Gestation in the Talmud

In one passage, the Talmud includes abortion under the category of murder. However, it also famously states that if the mother’s life is at risk—at any point in the pregnancy—the fetus must be removed, “limb by limb” if necessary. In such cases, the fetus is seen as a rodef, a “pursuer”, referring to the Torah law that if one is “pursuing” another to kill them, it is permitted to kill the pursuer first. The Talmud concludes that a fetus can be aborted at any point until its head has emerged. Once the head has emerged, the newborn is considered completely alive, and in cases of life-risk, it is no longer clear who the “pursuer” is. The Sages suggest that the soul fully enters the newborn only at birth, and it is only then that the newborn is a complete person.

Three-month old fetus (Courtesy: BabyCentre)

Elsewhere in the Talmud (Niddah 8b), we are told that the fetus already resembles a person at the three-month mark. We now know that it is precisely around this point that the developing baby has the features of a human (and is no longer called an “embryo”, but a “fetus”). The Talmud adds (Berakhot 60a) that until this three-month mark, a person should pray every day that there shouldn’t be a miscarriage. After three months, a person should pray that the fetus will not be stillborn, and after six months, a person should pray that the mother has an easy delivery. We are told that one should pray for the baby’s desired gender only before the 40-day mark. This, too, shows incredible wisdom on the part of our Sages. Today we know scientifically that the sex organs begin their development around day 42. The ancient rabbis knew that after day 40, gender development is already in progress, and there is no point praying for something different.

In a related passage, we are told that until day 40, the fetus is insignificant and more lifeless than living (Yevamot 69b). Today we know that the neural tube which will make the brain forms around day 40, and this is when the first neurons start signalling. Scientifically speaking, there could be no talk of any kind of consciousness or brain activity before day 40.

Because of this, most rabbinic authorities are far more lenient when it comes to abortions before the 40th day of pregnancy. Rabbi Chaim Ozer Grodzinski (1863-1940), who was widely recognized as the greatest posek of his generation, even suggested that abortions before the 40th day are not Biblically prohibited (Achiezer, III, 65:14). Nevertheless, even before the 40th day there is a potential to produce a living human being, and life is valued above all else, which is why abortions are still forbidden except for cases of absolute necessity.

By the 20-week mark (midway through pregnancy), fetuses are seen rolling around, sucking their thumbs, and responding to the prodding of the ultrasound. There is no doubt that the fetus is alive and aware at this point, and any abortion other than a life risk is hardly distinguishable from murder.

Soul Infusion

The fact that the fetus is aware by the 20-week mark (if not sooner) suggests that it does indeed have some level of soul. Yet, earlier we saw sources seemingly propose that the soul does not enter until birth. How do we reconcile these apparent contradictions?

To answer this question it is important to keep in mind that the soul is not one uniform entity. Rather, the soul is composed of multiple layers, each made up of countless sparks. The lowest level of soul is called nefesh, the basic life essence. Above that is the ruach, “spirit”, an animating force that, among other things, gives a person their drives and inclinations. Then comes the neshamah, a higher level of consciousness and the part that gives one their unique traits and qualities. Further still is the chayah, the aura that emanates from the body, followed by the loftiest level, the yechidah, which may be described as a spiritual umbilical cord between each soul and its Creator.

The Arizal taught that ever-higher levels of soul are accessed gradually over the course of one’s life. At birth, a person has only a complete nefesh. As they grow, they are infused with ruach, which becomes fully accessible at bar or bat mitzvah age. At this point one starts to tap into their neshamah, which is wholly available only at age 20. (For this reason, the Torah considers an adult one who is over 20 years of age. Only those over 20 were counted in the census and allowed to join the military. Our Sages state that although one may be judged for their crimes before age 20 here on Earth, only those sins accrued after age 20 are judged in Heaven. Meanwhile, the Midrash notes that Adam and Eve were created as 20 year olds.) The Arizal taught that most people never end up accessing their entire neshamah, and only the most refined individuals ever unlock their chayah and yechidah.

Based on this model, we see that right from conception the developing embryo is steadily infused with nefesh, the basic life force. By day 40, there is enough nefesh for the embryo to be considered alive. In fact, it is said that this is why the gematria of אם, “mother”, is 41, since a woman becomes a mother on the 41st day of pregnancy.

Once its entire nefesh has been infused, the baby is ready to be born. At birth, it begins to receive its next soul level, the ruach. A careful look at the Zohar passage with which we started reveals that this is precisely what the Zohar meant, as it explicitly mentions the ruach entering at birth, requiring forty days to fully settle in. Therefore, a developing fetus does indeed have a soul, which is why abortion is so highly discouraged—reserved only for true medical cases—and why it has been compared to murder.

Solving a Scientific Mystery

The above also answers a mystery that has been perplexing biologists for decades: what is it that drives an embryo to grow? Why do the cells multiply, and how do they know to differentiate? Each cell is exactly the same, with the exact same set of DNA, yet one clump of cells knows to form the eyes while another knows to form the liver, and so on. Scientists have still not been able to figure out how the embryo “knows” what to do. (For that matter, we can’t figure out how any cell really “knows” what to do.)

The Kabbalists have an answer: it is the steady infusion of soul that drives a mass of undifferentiated cells to do what it needs to. It is the soul that gives the instructions for how the DNA is to be transcribed and translated in each cell, and how the cells are to interact with one another. As the soul grows, so too does the body. It is therefore not surprising that around the age when most people’s bodies stop growing, their souls tend to stop “growing” as well.

This should remind us that our education does not end with formal schooling, nor does maturing stop with the end of puberty. The process of growth and refinement, both physical and spiritual, must continue throughout life. This is the key to true self-fulfillment and happiness.

The Spiritual Significance of Sefirat haOmer

The Torah commands that each day between the holidays of Pesach and Shavuot be verbally counted (Leviticus 23:15). Along with this counting, a bundle of barley was brought as an offering in the Holy Temple. The barley was measured in units of omer, with one omer being equal to approximately 3 litres. Today, we no longer have a Temple or barley offerings, but the mitzvah of counting the days between Pesach and Shavuot remains, and is referred to as Sefirat HaOmer, “the Counting of the Omer”. Since there are exactly seven weeks between the two holidays, there are 49 days which need to be counted. What is the deeper meaning behind this seemingly mundane practice?

The Fifty Levels

There are a number of spiritual explanations for Sefirat haOmer. Perhaps the most popular is the idea that in Egypt, the Jews were so deeply mired in the immoral and idolatrous Egyptian society that they had descended all the way down to the 49th level of impurity.

It is said that there are 50 levels of impurity, rooted in (or at least suggested by) the numerical value of the Hebrew word for “impure” (tam’e, טמא) which has a gematria of 50. The Jews had stooped down to the 49th level, and had they reached the 50th, there would have been no hope of salvation for them. Thus, God cut short the 400 year period of slavery that was decreed upon them, and immediately took the Jews out of Egypt before they could fall any further.

Corresponding to these, the Jewish mystics teach that there are 50 levels of constriction in the world. Egypt represented these 50 constrictions. Again, this can be illustrated through Hebrew and gematria: Egypt is Mitzrayim (מצרים), the root of which is tzar (צר, meaning “constrict” or “narrow”) and the suffix of which is ים, numerically equalling 50. Egypt is the land of 50 constrictions.

Following the Exodus, the task of the Jews was to cleanse themselves of the 49 levels of impurity which they had acquired, and to break free from all those constrictions that were imposed upon them. This is why they needed a 49-day period – one for each impurity and constriction – before they were ready for the Divine Revelation and reception of the Torah at Mt. Sinai on Shavuot.

The Tree of Life

The Passover Haggadah reminds us that each Jew must envision themselves as personally coming out of Egypt. Though we are thankfully no longer literally slaves, the truth is that each of us is still mired in some kind of constriction, be it a constriction to time or work, money or health, stress, fears, and all those others things that “narrow” our lives and confine us into various forms of spiritual slavery. The Torah commands each of us to break free, to remove all of those impurities and boundaries, and to elevate ourselves over this special period of 49 days. Each day is associated with a unique energy to help us in this path.

The 49 energies stem from the Kabbalistic “Tree of Life”. This Tree is composed of ten Sefirot (a term not coincidentally related to Sefirat HaOmer). These Ten Sefirot are regarded as the spiritual building blocks with which God created the universe (together with the twenty-two letters of the Hebrew alphabet). It is said that all things in existence are permeated with these ten energies, and all things that are “ten” in the Torah correspond to the ten sefirot: the Ten Divine Utterances of Creation, the Ten Trials of Abraham, the Ten Plagues, the Ten Commandments, etc.

The top three sefirot are called the Mochin – the mental or intellectual faculties. The bottom seven are referred to as the Middot – the emotional and practical elements. During the time of the Omer, we are meant to focus on the purification of the bottom seven sefirot. Meanwhile, on Shavuot – having received the Torah – we are then able to rise further to the upper three mental sefirot and focus on intellectual development.

Etz Chaim, “Tree of Life”, Showing the 10 Sefirot and the 22 Lines that Unite Them (Corresponding to the Hebrew Alphabet), as Depicted by the Arizal

Therefore, each of the seven weeks between Pesach and Shavuot is associated with one of the seven Middot. The first week of the Omer corresponds to the sefirah of Chessed – kindness. The second to the sefirah of Gevurah – restraint and self-control. The third to Tiferet – balance (also called Emet – truth). The fourth is Netzach – “victory”, or persistence (often associated with faith). The fifth, Hod – gratitude, and the sixth, Yesod – literally “foundation”, referring to sexual purity. Lastly there’s Malkhut, “kingdom”, which is associated with the faculty of speech.

Each of the seven days of the week is further associated with one of these seven sefirot. So, the first day of each week corresponds to Chessed, and the second day of each week to Gevurah, and so on. This gives each of the 49 days a totally unique quality which one should be meditating on, and more importantly, attempting to rectify.

For example, tonight we will count the third day, with the corresponding sefirah of Tiferet sh’b’Chessed, “Balance (or Truth) in Kindness”. This suggests developing a harmonious approach to kindness: being a more giving person; charitable, helpful, sympathetic, but also making sure not to be taken advantage of or tricked into false kindness. Unfortunately, misplaced kindness has become a staple of Western society. (How often do we see well-meaning liberals supporting the “poor and disadvantaged” terrorists?) Tonight’s sefirah might be summarized well by the old Midrashic teaching that “those who are kind to the cruel will ultimately be cruel to the kind.”

Similarly, each of the remaining 49 days has a powerful message to teach us, hence the tremendous importance of Sefirat HaOmer – counting and meditating upon each and every one of these very special days.