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Collapse of the wavefunction

//Collapse of the wavefunction

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 [...]

Five Worlds

Today, Yud Shvat, is the yartzeit (anniversary of passing) of the sixth Lubavitcher Rebbe, Rabbi Yosef Yitzchak Schneersohn, a.k.a. the Rebbe Rayatz, or the Frierdiker Rebbe. On the day of his yartzeit, it is customary to study his last maamar (Chassidic discourse), Basi LeGani. One of the themes expounded in the first chapter of this discourse is the concepts of four worlds: Atzilut, Beriah, Yetzirah, and Assiyah (collectively referred to as ABYA). Actually, in Kabbala and Chassidic philosophy, we speak of five worlds and the “world,” which precedes Atzilut is call Adam Kadmon (Primordial Man, often referred to by its acronym as the A”K). In this post, I will draw a parallel between these spiritual worlds and stages of the creation of our physical world. Why do that? It is axiomatic in Jewish mysticism [...]

Chanukah Menorah, Burning Bush and Sotah

As I wrote in my previous post, Schrödinger  Menorah:  Burning  And  Not  Burning, the Lubavitcher Rebbe explains the miracle of Chanukah as a paradox of the menorah burning and not burning, thereby embodying the absolute nature of God, who is not limited by His infinity but combines all possibilities including infinitude (ko’ach bli gvul) and the finitude (ko’ach hagvul). The notion of the menorah burning and not burning easily lends itself to be cast in terms of the quantum superposition of states of burning and not burning. I couldn’t help myself to call it a Schrödinger Menorah. There a couple of problems, however, with this idea. Firstly, as the Rebbe wrote in 1971 in a letter to the editor of the Journal of the Association of Orthodox Jewish Scientists, “The idea of miracles implies [...]

Septuagint—Collapsing the Wave-function of the Torah

Today is the eighth day of the month of Tevet. On the 8th of Tevet of the Jewish year 3515 (246 BCE), the Torah was translated into Greek. In the ancient times, this day was commemorated by fast. Seventy sages translated the Torah into Greek for King Ptolemy. That day was as difficult for the people of Israel as the day on which the [Golden] Calf was made; for the Torah could not be fully translated. (Babylonian Talmud, Tr. Sefer Torah, 1:8) Why does the Talmud compare translation of Torah into Greek to the tragedy of Golden Calf that brought terrible retribution the consequence of which we still suffer today? According to Medrash Tanchuma, Moses translated Torah into seventy languages before Jews crossed Jordan river on the way to the Promised land. Moreover, [...]

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 Schrödinger cat [...]

Pinchas – the Slayer of Uncertainty

A strange episode at the end of the last Torah portion, Balak, where Pinchas (Phinehas) slain a Jewish prince caught in the act with a heathen woman, is rewarded in this week’s present eponymous Torah portion with the priesthood.  This begs the question, what is the connection between the act of zealotry by Pinchas and the reward of priesthood he receives for it? By way of background, as we read in the previous Torah portion, the evil king, Balak, fails to bring a curse on the Jewish people by Bilam (Balaam).  According to Midrash, Bilam advises Balak to send most beautiful Midian women to seduce Jewish men (see Flavius Josephus's Antiquities of the Jews, Book IV, Chapter VI, Paragraphs 6-12). Balak heads the advice and uses Moabite and Midianite women to seduce Jewish men [...]

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 [...]

God Collapses the Sotah’s Wavefunction

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 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, to restore [...]

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 [...]