Tag Archives: Albert Einstein

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.

Torah on the Big Bang and the Age of the Universe

The Torah begins with Beresheet, the famous account of Creation.  In recent times, many have questioned the validity of this narrative in light of the findings of modern science. In reality, the Torah’s account is quite accurate in scientific terms, and the Jewish tradition described the origins of the universe and its age with stunning precision centuries before modern science caught up.

According to Science

The current scientific model holds that 13.7 billion years ago, the entire universe was compacted into a super tiny point with infinite density. For some unknown reason, this point suddenly burst in a massively vast and rapid expansion of energy and radiation. As the early universe cooled and expanded, particles began to form, and then whole atoms, starting with hydrogen. Hydrogen atoms fused into helium atoms, and later on heavy elements formed from further fusion in the cores of stars and their explosions. Everything that we see today—the entire universe and all matter within it—emerged from that initial expansion, “the Big Bang”.

The evidence for a Big Bang is extensive. In fact, you can see some of it when you look at the “snow” on an old television that is not tuned to any channel. The antenna is picking up some of the cosmic microwave background radiation, the “afterglow” of the Big Bang. The entire universe is still glowing from that initial expansion! Popular physicist Brian Greene writes in his bestselling The Hidden Reality (pg. 43):

…if you were to shut off the sun, remove the other stars from the Milky Way, and even sweep away the most distant galaxies, space would not be black. To the human eye it would appear black, but if you could see radiation in the microwave part of the spectrum, then every which way you turned, you’d see a uniform glow. It’s origin? The origin.

The universe is glowing, it’s just that most people cannot see it because human eyes perceive only a very narrow part of the electromagnetic spectrum, which we call “visible light”. Light of a higher energy and frequency includes dangerous x-rays and gamma rays, while light of lower energy and frequency includes microwaves and radio waves. The seeming blackness of the universe is actually radiating with light—we simply cannot see it. Incredibly, this is precisely what the Torah states.

The electromagnetic spectrum. Visible light makes up just a tiny sliver of the spectrum. Some living organisms can see in UV or infrared wavelengths.

Zohar haRakia

We read in the Tanakh (Daniel 12:3) that “they who are wise shall shine as bright as the rakia…” The Torah tells us that God established a rakia (wrongly translated as “firmament”) on the second day of Creation, and this is where all the stars and planets are suspended (Genesis 1:15). The Talmud (Chagigah 12a), composed over 1500 years ago, further elaborates that above the earth is the vilon, the atmosphere that stretches over the planet, and beyond the vilon is the rakia, a vast expanse within which are all the stars. Beyond the rakia is a region called shechakim, the interface between the physical and spiritual realms, and further still are the highest levels of the Heavens, inhabited by angels and transcendental beings. From this, and other ancient sources, it is clear that rakia refers to outer space.

Daniel tells us that the wise will shine like the rakia, and goes on to state that “they who turn the many to righteousness [shall shine] as the stars”. We can understand how people might shine bright like stars, but why would Daniel say the rakia is shining? Outer space is totally dark! Of course, as Brian Greene described, today we know that the universe is indeed glowing.

One of the most ancient Jewish mystical texts is Sefer HaBahir. According to tradition, it dates back some two thousand years, and was first published at least seven hundred years ago. This book gets its name from another verse in the Tanakh (Job 37:21), which states “And now, men do not see the light that is bright [bahir] in the skies.” Once again, Scripture tells us that the universe is glowing with a bright light that humans are unable to perceive. Science has found that this glow comes from the Big Bang, and this too is accurately described by the most famous of Jewish mystical texts, the Zohar.

Cosmic Microwave Background Radiation, the glow of the universe, discovered in the 1960s by Robert Wilson and Jewish physicist Arno Penzias.

The Secret of Beresheet and the Big Bang

Like Sefer HaBahir, the Zohar was first published around seven hundred years ago, with its teachings dating back two millennia. The Zohar is a parasha-by-parasha commentary on the Torah, and naturally begins with the first section in describing Creation. The book gets its name from the above verse in Daniel which speaks of Zohar haRakia, the glow of the universe. It elaborates (I, 2a, 15a):

בְּשַׁעְתָּא דִּסְתִימָא דְכָל סְתִימִין בָּעָא לְאִתְגַּלְּיָא, עֲבַד בְּרֵישָׁא נְקוּדָה חֲדָא, וְדָא סָלֵיק לְמֶהֱוֵי מַחֲשָׁבָה. צַיֵּיר בָּהּ כָּל צִיּוּרִין חָקַק בָּהּ כָּל גְּלִיפִין… וְרָזָא דָא, בְּרֵאשִׁית בָּרָא אֱלֹהִים. זֹהַר, דְּמִנֵּיהּ כָּלְהוֹ מַאֲמָרוֹת אִתְבְּרִיאוּ בְּרָזָא דְאִתְפַּשְׁטוּתָא דִנְקוּדָה דְּזֹהַר סְתִים דָּא

When the Most Concealed One [God] began to create, He first made a singular point, with which he then brought forth all thought, drew all blueprints, and carved out all things… And the secret of “In the beginning, God created…” [Genesis 1:1] is radiance [zohar], from which all Utterances were created, in the secret of the expansion of that point of radiance.

Many centuries ago, the Zohar accurately and elegantly sums up the findings of modern science. God first created a tiny singular point which burst forth in light, and from which He “carved out” all things in existence. All of God’s Utterances (since the Torah says God created by speaking: “And God said ‘Let there be light.’”) came forth from the expansion of that initial primordial radiance.

Time is Relative

All that remains is the seeming contradiction in time. Science estimates 13.7 billion years, while the Torah speaks of six days. Of course, the nature of a “day” in the account of Creation is flexible, considering there was no Earth, sun, or moon until the third and fourth days (so how could there be a 24 hour day as we know it before this?) There were also no humans at this point, and the Torah describes Creation from the perspective of God, for whom “a thousand years is like one passing day” (Psalms 90:4). The fact that time runs differently for man and God actually highlights another scientific principle, as revealed by Albert Einstein.

Einstein’s theory of relativity holds that the passing of time varies depending on an entity’s speed. A person who could board a spaceship and fly near light-speed would experience very slow time. A few days for this person would be equivalent to many years on Earth. (This theme has been explored in countless science fiction books and films, including 2014’s Interstellar.) The Lubavitcher Rebbe often cited this fact to conclude that arguing about apparent space-time contradictions is therefore quite pointless. Meanwhile, physicist Gerald Schroeder has mathematically calculated that six days could be equivalent to 13.7 billion years when factoring in the universe’s expansion. After all, we are looking back in time at an ancient universe through human eyes, while God was looking forward in time from the universe’s first moments.

An infographic explaining the relativity of time. Note the conclusion: “there is no meaning to the concept of absolute time.” The whole debate of 6 days vs 13.7 billion years is therefore quite meaningless.

Physicist and Rabbi Aryeh Kaplan explored this issue extensively and cites multiple ancient Jewish texts that support the notion of a very ancient universe (see his book Kabbalah and the Age of the Universe). In multiple places, the Midrash states that before creating this world, God was creating and destroying many previous worlds (see, for example, Kohelet Rabbah 3:14), while the Talmud calculates that “there were 974 generations before Adam” (Chagigah 13b, Shabbat 88a).

On this last point, it has been shown that a generation according to the Torah is forty years (Numbers 32:13), and as we saw, a day for God is likened to 1000 human years (Psalms 90:4), therefore:

            974 generations × 40 years/generation × 365 days/year × 1000 human years/divine day =

14.2 billion years

Compared to the current best estimate of science at 13.7 billion years, it is amazing that one can come to a very similar number by simply putting together a few Torah verses.

What we see from all of the above is that ancient Jewish texts describe the universe’s origins in absolutely perfect detail. And it is only in recent decades that science has finally caught up. In many other ways, too, science has a lot of catching up to do.