Wavefunction

/Wavefunction

Standing and Moving

According to the Saadia Gaon, these two Torah portions – Nitzavim and Vayelech – are really one portion, which sometimes is split into two.  In the language of Quantum Mechanics (QM), the two portions are entangled, in a manner of speech, and are described by the single "wavefunction."  Needless to say, this is not meant in a literal sense, as QM describes physical objects, whereas these biblical chapters are certainly not.  Nevertheless, taking poetic license, we can loosely say that these portions are entangled, i.e., they are really one.  Nitzavim and Vayelech, however, speak of the opposite themes – “nitzavim” connotes standing( lit., you stand), while “vayelech” connotes walking (lit., …and he walked). As much as it seems paradoxical at first, from the physicist’s point of view, it is not surprising at all.  Typically, [...]

When was the World Created?

There is a dispute in the Talmud as to when the world was created. According to Rabbi Eliezer, the world was created in the month of Tishrei, the seventh month of the Jewish calendar when we celebrate the Jewish New Year, Rosh HaShanah. According to Rabbi Yehoshua, the world was created in the first month of the year, the month of Nisan (Tr. Rosh HaShanah, 10b). The Chasidic thought attempts to reconcile these opposite opinions suggesting that both opinions are correct—the world was created in Nisan in thought, whereas in deed, it was created in Tishrei.  The problem with this approach is that for halakhic (Jewish ritual law) purposes of calculating the Jewish calendar, the planets are deemed to have commenced their heavenly orbits in Nisan, not in Tishrei!  How could planets that [...]

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. Genesis 15:10-17 The above verses from this week’s parshah (Torah portion) Lech Lecha (Gen. 12:1–17:27) describe the Covenant between the Parts (a.k.a. the Covenant of the Pieces), when God entered into eternal covenant with Abraham (at the time called Abram) – a covenant symbolized by halved animals. The simple meaning of this ritual is apparent: just as [...]

On Tzimtzum, Sefirot and Cardinal Numbers

Today is Yud Tes Kislev -- Rosh HaShanah of Chasidut. Today I received two gifts, which I'd like to share. Lately, while learning Samach Vov, I've been struggling to understand the meaning of Sefirot Ein Keitz. Today, during shacharis shemone esreh, it donned upon me that the literal meaning of Sefirot Ein Keitz is infinite numbers. I suddenly realized that while Sefirot after the Tzimtzum are ordinary numbers, Sefirot before Tzimtzum—Sefirot Ein Keitz—are cardinal numbers developed by the mathematician Georg Cantor at the end of the 19 c. Later during the day, I got the second epiphany that Tzimtzum is the collapse of the universal wavefunction describing the creation. Before Tzimtzum, all creations were in the state of "yecholot" -- potentialities. After the Tzimtzum, i.e., after the collapse of the wavefuction, these potentialities actualized in specific [...]

Schrödinger May Have Been Born Today

A man once came to a rabbi with said news – his cat just died. Rabbi politely expressed his sympathy to the owner of the deceased cat. He thanked the rabbi and asked if he could say kaddish (memorial prayer) for his cat. Rabbi was taken aback – a kaddish for a cat?! This is sacrilege! The man offered to donate to the synagogue a thousand dollars, if the rabbi would allow him to say kaddish for his cat, but to no avail. He offered two thousand, five thousand, but rabbi was unmoved. When the man finally offered ten thousand dollars, the rabbi exclaimed, “Why didn’t you tell me your cat was Jewish?!” Ervin Schrödinger I am not sure if the cat in this old Jewish joke was Jewish, but the [...]

Secrets of the Talking Ass

And God opened the mouth of the ass, and she said to Bilam: "What have I done to you, that you have struck me these three times?" And Bilam said to the ass: "Because you have mocked me; I would there were a sword in my hand, for now I would kill you." And the ass said to Bilam: "Am not I your ass, upon which you have ridden all your life to this day? Was I ever wont to do so to you?" And he said, "No." Num. 22:28-30 Despite the simple dialogue between Balaam (Bilam) and his ass in the Torah portion of Balak, this ass was no ordinary ass. This ass saw an angel where a prophet as great as her owner, Balaam, did not. It stands to reason that [...]

Prophesy by Entanglement

…And they prophesied in the camp. (Num. 11:27) In the Torah portion Behaalotecha, there is an interesting narrative: And the Lord said unto Moses: 'Gather unto Me seventy men of the elders of Israel, whom thou knowest to be the elders of the people, and officers over them; and bring them unto the tent of meeting, that they may stand there with thee. And I will come down and speak with thee there; and I will take of the spirit which is upon thee, and will put it upon them… And the LORD came down in the cloud, and spoke unto him, and took of the spirit that was upon him, and put it upon the seventy elders; and it came to pass, that, when the spirit rested upon them, they prophesied, but [...]

God Collapses Sotah’s Wave Function

The story of Sotah, a suspected adulteress, is very troubling on the first blush. Why would a woman be subjected to such humiliation?  The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, points out that, to the contrary, the story of Sotah is the story of the boundless love of the Creator for his people. Notwithstanding the strict Biblical prohibition of erasing God’s name, to vindicate the wrongly accused woman, God allows and, indeed, decrees to erase His holy Name by dissolving the scriptural verses written on a parchment in the water that the woman would drink to clear her name. For as long as a woman is being suspected of infidelity, she cannot be intimate with her husband.  It takes a Divine intervention, whereby God sacrifices His honor in allowing erasing His holy Name, [...]

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

Ye Shall be Disentangled

Ye shall be holy, for I, the Lord, your God, am holy. Leviticus 19:2 This Torah portion begins with an astonishing statement: Speak unto all the congregation of the children of Israel, and say unto them: Ye shall be holy; for I, the Lord, your God, am holy. Leviticus 19:2 The gist of this commandment is “Be kadosh (or pl., kedoshim) because I, the Lord, your God, am kadosh.” The question is, what does the word “kadosh” mean. It is usually translated as “holy.” The word “holy” means sacred, sanctified, blessed, divine. But this translation presents a problem. It would be a tautology to say that God is divine. It is also self-understood that God is holy. He is the definition and the source of all that is divine and holy, i.e., godly. [...]

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