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Half-Shekel – Metaphor for Entanglement

This they shall give, everyone who goes through the counting: half a shekel according to the holy shekel. Twenty gerahs equal one shekel; half of a shekel shall be an offering to the Lord Ex. 30:13 In this week’s Torah portion, Ki Tisa (Ex. 30), Jewish people are given the commandment of donating a coin as atonement, not just a coin – half a coin. But why half? If God thought, twenty gerahs would be too much, He could have commanded Moses to mint another coin worth ten gerahs. But no, the coin was to remain what it was—worth twenty gerahs—and Jews were to give half a coin. Don’t you find it peculiar? I don’t, because half-coins are my favorite metaphor when explaining entanglement to my physics students. What is entanglement? When obtaining [...]

Sacrifices and incenses – fields and entanglement

(Recent Purim celebrations distracted me from writing on the weekly Torah portion. But I didn’t want to miss the opportunity to share my thoughts on the last week’s Torah portion – Tetzaveh. So here it is.) At the end of the weekly portion, Tetzaveh, Torah speaks of the burnt offerings (Heb. qorbanot) and the incense offerings (Heb. qetoret). The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, contrasts these two types of offerings by highlighting their symbolism. The Hebrew word for a burnt offering or sacrifice, qorban, is etymologically related to the word  qarov “close,” qiruv “to bring close” and qerovim “relatives,” as they all share the same root QRB “to be close.” Sacrificial offering (qorban) meant to bring a person who brought it close (qarov) to God. The Hebrew word for incense offerings, qetoret, [...]

Entangled Cherubs

And thou shalt make two cherubim of gold; of beaten work shalt thou make them, at the two ends of the ark-cover. And make one cherub at the one end, and one cherub at the other end; of one piece with the ark-cover shall ye make the cherubim of the two ends thereof. And the cherubim shall spread out their wings on high, screening the ark-cover with their wings, with their faces one to another; toward the ark-cover shall the faces of the cherubim be. And thou shalt put the ark-cover above upon the ark; and in the ark thou shalt put the testimony that I shall give thee. And there I will meet with thee, and I will speak with thee from above the ark-cover, from between the two cherubim which are [...]

Covenant between the Parts as a Metaphor for Quantum Entanglement

And he took him all these, and divided them in the midst, and laid each half over against the other… And it came to pass, that, when the sun was going down, a deep sleep fell upon Abram; and, lo, a dread, even a great darkness, fell upon him…  And it came to pass, that, when the sun went down, and there was thick darkness, behold a smoking furnace, and a flaming torch that passed between these pieces. Gen. XV, 10-17 The above verses from this week’s parshah (Torah portion) Lech Lecha (Gen. XII,1–XVII,27) describe the Covenant between the Parts (ברית בין הבתרים), a.k.a. the Covenant of the Pieces, when God entered into eternal covenant with Abraham (at the time called Abram) – covenant symbolized by halved animals. The simple meaning of this ritual is apparent [...]

Sotah – Suspected Adulteress as a Schrödinger Cat

In quantum mechanics, the state of a physical system is described by the so-called wave function (or the "wavefunction").  What is the wavefunction?  The attempts by Schrödinger, who first introduced the wavefunction, and others to interpret it as a scalar potential of some physical field or as de Broglie wave (as in particle-wave dualism) were not successful.  In 1926, Max Born noticed that the square of the amplitude of the wavefunction of a particle in a given region gives the probability of finding the particle in this region of configuration space.  He suggested that the wavefunction represented not a physical reality but rather our knowledge of the quantum state of an object. The wavefunction represents our knowledge of all possible quantum-mechanical states of an object.  In other words, the quantum-mechanical state of a physical [...]

The Entangled Twins

Entanglement is often called the most baffling and the most quintessential aspect of quantum mechanics. What is entanglement, in a nutshell? Two particles born out of one reaction (or two particles that interacted through a collision) remain connected, no matter how distant from each other. A change in the status of one particle instantaneously causes a change in the status in the other particle. Einstein called it "spooky action at a distance." Entanglement is often associated with certain symmetry and corresponding laws of conservation. For example, the law of conservation of angular momentum requires that the spin (the quantum-mechanical analog of the angular momentum) of two entangled particles always point in the opposite directions. This means that, if two entangled particles have their spin in a state of superposition of Up (↑) and Down (↓) and we collapse [...]

By | November 3rd, 2013|Entanglement, Purim, Symmetry, Toledot, Uncategorized|0 Comments

Cosmological Rosh HaShanah

This Rosh HaShanah I had the strangest dream. I dreamed that I was giving a lecture in cosmology at a university when I suddenly realized that it was Rosh HaShanah. I panicked… What was I doing in university on such a day instead of being in shul, praying and listening to a shofar?! I decided to save the day by trying to weave the three main themes of Rosh HaShanah into my lecture on cosmology. And so I began… In the Rosh HaShanah liturgy, we refer to this day as yom harat olam – the birthday of the world (Machzor Rosh HaShanah). According to modern cosmology, the world was born in an unfathomable explosion called the Big Bang. Long before this concept was developed in cosmology during the 20th century, some 800 years [...]

By | September 9th, 2013|Uncategorized|2 Comments

Tale of Entangled Goats

In the last Torah portion, Metzorah, we learned about two entangled birds. This week, we learn about two entangled goats. I don’t know if these goats studied quantum mechanics but they can sure teach us a thing or two about quantum entanglement. Entanglement is one of the mysteries of quantum mechanics. On a macro level, entanglement is easy to understand. Imagine a coin sawn into two halves along the plane parallel to the face of the coin. One-half has only heads and the other only tails. Let’s send each of these halves to two people, Shimon and Reuven. If Shimon gets the half with the heads, he knows immediately that Reuven got the half with the tails even if Reuven didn’t yet open the envelope. In other words, the states (heads or tails) [...]