Schrödinger cat

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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 Tišrei, the seventh month of the Jewish calendar when we celebrate the Jewish New Year, Rosh HaShanah (or Roš HaŠanah). According to Rabbi Yehoshua, the world was created in the first month of the year, the month of Nisan (Talmud, tr. Roš HaŠanah, 10b). The Hassidic 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 Tišrei.  The problem with this approach is that for halaḵic (Jewish ritual law) purposes of calculating the Jewish calendar, the planets are deemed to have commenced their heavenly orbits in Nisan, not in Tišrei!  [...]

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 [...]

G‑d 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 G‑d’s name, to vindicate the wrongly accused woman, G‑d 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 G‑d 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 [...]

Witnesses – See and be Seen

By the mouth of two witnesses, or three witnesses, shall the one liable to death be put to death; he shall not be put to death by the mouth of one witness. (Devarim-Deuteronomy 17:6) I wrote about witnesses in my earlier post imaginatively called Witnesses. As Deuteronomy, restates many mitzvoth (commandments) introduced earlier, which is why it is also called Mishneh Torah – the repetition of Torah – the portion Shoftim-Judges restates the law of witnesses first introduced in in the book of Bamidbar-Numbers, portion Massei. So we shall revisit this fascinating subject. The Judgment of the Sanhedrin: "He is Guilty!" (1892 painting by Nikolai Ge) I.     An accused criminal and a Schrödinger cat Most criminals are convicted in the US bases on circumstantial evidence. Rare is the case when a jury gets to hear [...]

Two Beginnings

B’reshit bara Elokim et hashamaim v’et haaretz… In the beginning, G‑d created heaven and earth… Alternative translation: With two beginnings G‑d created heaven and earth… Genesis 1:1   *This is an abridged and updated version of my paper “Towards Reconciliation of Biblical and Cosmological Ages of the Universe” Presented at the Third Miami International Conference on Torah & Science in Dec. of 1999 and published in B’Or HaTorah, 13 (2002) p. 19. Contemporary science places the age of the universe in the thirteen to fourteen billion years range, or 13.787 ± 0.02, [1] to be precise.  This age is derived from both theoretical models as well as experimental data.  (For an overview of theoretical and experimental approaches to dating the universe and our planet Earth see my original paper TOWARDS RECONCILIATION OF BIBLICAL AND [...]

Leprous Cats and Angry Birds

In the Torah portion Tazriah (Leviticus 13), the Schrödinger cat[1] gets leprosy. Well, it’s not really leprosy, it’s a mysterious supernatural disease called tzara’as, nowadays translated as psoriasis. And it’s not a cat, but a Jew who gets afflicted by tzara’as. In fact, cats, other animals, and even gentiles (i.e., non-Jewish humans) are immune to this spiritual malady. So why do I call a poor Jew afflicted with tzara’as a “Schrödinger cat”? Because he sure acts like one. Indeed, had I not studied quantum mechanics and had I not learned about the collapse of the wave function[2] back at the university, I would have surely discovered it by reading this Torah portion (parshah)! A Jewish person with a skin lesion or boldness (present company excluded) is brought to a priest (kohen), who examines it [...]

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