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The Entangled Twins

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 of the other particle. Einstein called it "spooky action at a distance." Entanglement is often associated with a certain symmetry and corresponding conservation laws. 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 Alexander Poltorak|2018-11-07T21:37:36-05:00November 3rd, 2013|Bereshit, Entanglement, Genesis, Parshah, Pentateuch (Chumash), Physics, Purim, Quantum Theory, Symmetry, Toledot, Uncategorized|3 Comments

Maarat HaMachpelah – Double Cave

Maarat HaMachpelah – Double Cave

Give me the Machpelah (double) Cave Genesis 23:9 The first legal acquisition of land in Israel takes place in this Torah portion, Chayei Sarah, when Abraham purchases a double cave, Maarat HaMachpelah, in the city of Chevron (Hebron) as an ancestral burial plot. Today, the immense rectangular structure built over the cave more than 2000 years ago during Herodian era is the oldest house of worship in the world in continuous use. Biblical commentator Rashi explains that the cave was called Machpelah (lit., double) because it had two structures—an upper chamber and a lower chamber. (Another explanation given in the Talmud relates the name of this cave to thee couples buried there—Abraham and Sarah, Isaac and Rebecca, and Jacob and Leah. According to Kabbalah, Adam and Eve are buried there as well (Zohar, Ruth 96). Cave of the Patriarchs [...]

By Alexander Poltorak|2018-11-22T15:13:27-05:00October 27th, 2013|Chayei Sarah, Genesis, Kabbalah, Parshah, Pentateuch (Chumash), Physics, Soul, Space, Spirituality, Superposition, Uncategorized, Uncertainty Principle, Zohar|3 Comments

Saved by Randomness

Saved by Randomness

Some people may be fooled by randomness but, when we realize that randomness opens the door to the Divine, we are saved by randomness. It is for this reason that two days a year—on Purim and on Yom HaKippurim (which is a Day like Purim)—we read about two lots and we celebrate randomness.

By Alexander Poltorak|2024-03-20T20:32:22-04:00September 16th, 2013|G‑d, Holidays (Yomim Tovim), Purim, Quantum Theory, Randomness, Uncategorized, Yom Kippur, Zohar|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 at the university on such a day instead of being in my synagogue, praying and listening to sounds of 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… NASA/WMAP Science Team - Original version: NASA; modified by Cherkash 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 [...]

By Alexander Poltorak|2019-10-03T22:58:56-04:00September 9th, 2013|Cosmology, Holidays (Yomim Tovim), Kabbalah, Rosh HaShanah, Space, Uncategorized|2 Comments

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. 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 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 based on circumstantial evidence. Rare is the case when a jury gets to hear an [...]

By Alexander Poltorak|2024-09-06T10:02:17-04:00August 11th, 2013|Collapse of the wavefunction, Entanglement, Massei, Quantum Theory, Shoftim, Superposition, Uncategorized, Uncertainty Principle, Wavefunction, Witnesses|1 Comment

Witnesses

Massei -- Bamidbar-Numbers 35 Whoever kills a person, based on the testimony of witnesses, he shall slay the murderer. A single witness may not testify against a person so that he should die. Bamidbar-Numbers 35:30 In this verse, the Torah states that a murderer can only be convicted based on testimony of live witnesses. Contrary to common law jurisprudence in the US and the UK, and civil law jurisprudence of most other western countries, circumstantial evidence cannot be used alone to convict according to the Torah law. (It may, however, be used to interrogate witnesses in order to ascertain their truthfulness or to acquit the accused.) The only basis for a Torah conviction is eye-witness testimony. This seems strange, though. Why, for example, may fingerprints or DNA evidence, which is, surely, incontrovertible, not be used to [...]

By Alexander Poltorak|2013-08-11T13:55:16-04:00July 7th, 2013|Collapse of the wavefunction, Massei, Parshah, Superposition, Uncategorized, Wavefunction, Witnesses|2 Comments

A curious Case of Retrocausality—Dead Inherit the Living

Pinchas You shall apportion the Land among these as an inheritance, in accordance with the number of names. To the large [tribe] you shall give a larger inheritance and to a smaller tribe you shall give a smaller inheritance, each person shall be given an inheritance according to his number. Only through a lot shall the Land be apportioned; they shall inherit it according to the names of their fathers' tribes. Bamidbar-Numbers 26:53-55 Albert Einstein and Kurt Gödel in Princeton Einstein once said that he only went to his office at the Institute for Advanced Studies in Princeton to have an opportunity to chat on the way home with his friend, Viennese mathematician, Kurt Gödel. Once, the story goes, Gödel came to Einstein's birthday party with a present – a new cosmological solution [...]

By Alexander Poltorak|2013-08-11T13:57:24-04:00July 5th, 2013|Entanglement, Parshah, Pinchas, Retrocausality, Time, Uncategorized, Wavefunction|2 Comments

Paradox of the Red Heifer

Paradox of the Red Heifer

Speak to the children of Israel and have them take for you a perfectly red unblemished cow, upon which no yoke was laid… The cow shall then be burned in his presence… The one who burns it shall wash his clothes in water and cleanse his body in water, and he shall be unclean until evening… Anyone touching the corpse of a human soul shall become unclean for seven days. On the third and seventh days, he shall cleanse himself with it, so that he can become clean. But if he does not sprinkle himself with it on the third and seventh days, he shall not become clean… They shall take for that unclean person from the ashes of the burnt purification offering, and it shall be placed in a vessel [filled] with [...]

By Alexander Poltorak|2023-06-29T21:43:11-04:00June 24th, 2013|Chukat, Entanglement, Holidays (Yomim Tovim), Numbers, Parshah, Passover (Pesach), Pentateuch (Chumash), Space, Spirituality, Time, Uncategorized, Wavefunction|1 Comment

Tumah and Taharah

Tumah and Taharah

The Hebrew words taharah and tumah, which are the subjects of the Torah portion of Chukat (Numbers 19:1–22:1), are usually translated as ritual purity and ritual impurity respectively. This, of course, has nothing to do with physical purity or impurity, as these are strictly spiritual concepts. But what is a “spiritual concept” in the first place? The word “spiritual” is thrown around a lot by religious pundits and new age gurus. This word is anathema to scientists as anything spiritual is deemed to be antithetical to science. However, this word can be given a simple, precise and strictly scientific definition. (As Descartes famously said, most arguments would disappear if people bothered giving definitions to the concepts they argue about.) Well, one thing everyone would agree with, that spiritual is not physical. Since all [...]

By Alexander Poltorak|2017-06-29T21:27:41-04:00June 19th, 2013|Chukat, Parshah, Spirituality, Time, Uncategorized|0 Comments

Koraḥ Disentangled

Koraḥ Disentangled

Koraḥ the son of Yitzhar, the son of Kehos, the son of Levi took [himself to one side] along with Dasan and Aviram, the sons of Eliav, and On the son of Peles, descendants of Reuven. Num. 16:1 There is a curious aspect to the story of Koraḥ’s rebellion. We can understand why Koraḥ (or Korach), being of the tribe of Levi, may have had a claim to the priesthood thus causing a rebellion against Mosheh and Aaron HaKohen, the High Priest. The Torah tells us, however, that some Reubenites, that is, members of the tribe of Reuven, got entangled with the followers of Koraḥ in this rebellion as well. But what did they have to do with it? Not being descendants of Levi, they surely had no claim on the priesthood. Why [...]

By Alexander Poltorak|2023-06-22T22:05:44-04:00June 6th, 2013|Bamitbar, Entanglement, Korach, Numbers, Parshah, Pentateuch (Chumash), Uncategorized|1 Comment

Freedom in Space, Time and Spirituality

And the entire Mount Sinai smoked because the Lord had descended upon it in fire, and its smoke ascended like the smoke of the kiln… Exodus 19:18 The Holiday of Shavuot is thought to be a culmination of the Passover. Just as Shmini Atzeret is a culmination of the Holiday of Sukkot and comes after seven days of Sukkot, Shavuot is also called Atzeret and comes after the Holiday of Pesach, albeit separated from it by forty-nine days of Omer. On Shavuot, we read a Torah portion from Chapter 19 of the Book of Shemot (Exodus). We already discussed verse 18, "Mount Sinai smoked," in the previous post. Mount Sinai smoked because the Lord had descended upon it. Here, I'd like to focus on the word "smoked" from a different perspective. It hints at [...]

By Alexander Poltorak|2024-06-09T10:47:09-04:00May 18th, 2013|Freedom, Holidays (Yomim Tovim), Omer, Passover (Pesach), Shavuot, Time, Uncategorized|0 Comments

Holy Smoke

And the entire Mount Sinai smoked because the Lord had descended upon it in fire, and its smoke ascended like the smoke of the kiln… Exodus 19:18 In the last post, Thou Shall Not Collapse G‑d's Wavefunction, we discussed the notion that G‑d only appears to man in a cloud of smoke, for which reason, the Kohen Gadol – High Priest – had to fill Kodesh Hakadoshim – the Holy of Holies – with the smoke of ketoret (incense), before entering it. On Shavuot, we read the Torah portion from Shemot (Exodus), Ch. XIX, in which this concept is made very explicit – "The entire Mount Sinai smoked because the Lord had descended upon it…" There is great symbolism in this smoke, which preceded the Revelation, when G‑d gave Jewish People Ten Commandments. As we discussed [...]

By Alexander Poltorak|2013-08-11T14:00:21-04:00May 17th, 2013|Uncategorized, Uncertainty Principle, Wavefunction, Wavefunction of G‑d|0 Comments

Thou Shall Not Collapse G‑d’s Wavefunction

Acharei Mot 1. And the Lord spoke to Moses after the death of Aaron's two sons, when they drew near before the Lord, and they died. 2. And the Lord said to Moses: Speak to your brother Aaron, that he should not come at all times into the Holy within the dividing curtain, in front of the cover that is upon the ark, so that he should not die, for I appear over the ark cover in a cloud. (Leviticus 16:1-2) This parshah describes the service of the Kohen Gadol – the High Priest – performed on Yom Kippur. Why does it start by referencing the death of the two sons of Aaron (the first Kohen Gadol), Nadav and Avihu? What relevance does this have to the topic at hand? As we read earlier, [...]

By Alexander Poltorak|2013-08-11T14:21:46-04:00April 22nd, 2013|Collapse of the wavefunction, Uncategorized, Uncertainty Principle, Wavefunction|1 Comment

Schrödinger Pots

Vaikra-Leviticus 14:35-36 (Metzora) 35. and the one to whom the house belongs comes and tells the kohen, saying, "Something like a plague has appeared to me in the house," 36. the kohen shall order that they clear out the house, before the kohen comes to look at the lesion, so that everything in the house should not become unclean. After this, the kohen shall come to look at the house. Let us analyze these two verses from the point of view of quantum mechanics. An owner of the house sees a suspicious lesion on the house that looks like tzara’as and calls a cohen (priest) to inspect the house. There are two possible states of the house: Pure (no tzara’as) or Impure (contaminated by tzara’as). At this moment, before the cohen inspects the [...]

By Alexander Poltorak|2013-04-14T00:54:09-04:00April 14th, 2013|Collapse of the wavefunction, Entanglement, Uncategorized|0 Comments

Four Camps at Sea – Four Fundamental Interactions

On the penultimate day of the Passover Holidays (which is called Shvii shel Pesach – the Sevenths Day of Passover), we read in the Torah about Kriat Yam Suf – splitting of the sea. The Talmud (Yerushalmi Pesachim) and Midrash (Pirka deRabeinu Hakadosh) tells us that at that dramatic moment, when the Jews, who just escaped Egypt, were trapped between the sea and the Egyptian army pursuing them, the Jews were divided into four camps (so many Jews and only four opinions?!), each advocating a different course of action: one group proposed to wage a war with Egyptians; the other group wanted to jump into the sea; the third group advocated prayer and the fourth insisted on returning to Egypt. "The Crossing of the Red Sea", Nicholas Poussin Classical commentators [...]

By Alexander Poltorak|2020-10-15T23:11:13-04:00April 7th, 2013|Atomic Theory, Uncategorized|0 Comments

Passover, Shabbat and the Principle of Least Action

Passover, Shabbat and the Principle of Least Action

There is hardly a Jewish holiday more widely celebrated than Passover (Pesach). Jews of all denominations, affiliations, and levels of religious observance, if any at all, gather at the Passover Seder to tell the story of the Exodus from Egypt. What is often lost amid all of the beautiful rituals, not least among them the singing of Had Gadia and other Seder songs, is the deep meaning of this holiday, which is far more profound than a mere recollection of historical events, no matter how important they may be. What is, then, the deeper meaning of the Passover that transcends its historical significance? On the morrow of Shabbat One obscure and little-known (outside of the observant Jewish community) commandment ("mitzvah") may lead us to a deeper understanding of the meaning of the Passover—this [...]

By Alexander Poltorak|2021-03-14T20:50:19-04:00March 31st, 2013|Creation, Holidays (Yomim Tovim), Omer, Passover (Pesach), Physics, Science, Shabbat, Shavuot, Uncategorized|3 Comments

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 [...]

By Alexander Poltorak|2019-10-25T00:22:55-04:00October 12th, 2012|Age of the Universe, Bereishit, Bereshit, Collapse of the wavefunction, Cosmology, Creation, Entanglement, Genesis, G‑d, Kabbalah, Parshah, Pentateuch (Chumash), Quantum Theory, Superposition, Uncategorized, Wavefunction|4 Comments

On the Age of the Universe in the Many-Worlds Interpretation of Quantum Mechanics

On the Age of the Universe in the Many-Worlds Interpretation of Quantum Mechanics[*] Alexander Poltorak Abstract The present paper addresses the apparent discrepancy between the cosmological age of the universe, estimated at twelve to fourteen billion years, and the “biblical” age, believed in the Jewish tradition to be less than six thousand years. This paper is a sequel to my previous paper, "On the Age of the Universe," presented at the Third Miami International Conference on Torah and Science, which aimed to resolve this contradiction from the point of view of the collapse of the wave function in the Copenhagen interpretation of Quantum Mechanics (QM). Continuing this discussion, I shall now approach the problem from the slightly different point of view of the many-worlds interpretation of QM. This paper [...]

By Alexander Poltorak|2018-09-21T11:05:55-04:00September 15th, 2012|Age of the Universe, Collapse of the wavefunction, Superposition, Uncategorized, Wavefunction|5 Comments

On the Nature of Time and the Age of the Universe

Presented at the International Torah and Science Conference in Miami International University on December 18, 2005 Alexander Poltorak Introduction. This is the third in a series of articles, in which I attempt to sketch various approaches to reconciling a cosmological age of the universe currently estimated at 13.75 billion years with the Jewish tradition setting this age at less than six thousand years (5770 as of the day of this writing, to be exact). The first article [1] tackled this problem from the point of view of Copenhagen interpretation of quantum mechanics suggesting that there were two distinct forms of existence—physical and proto-physical—and that the first conscious observers, Adam and Eve, collapsed the universal wavefunction, bringing the world from amorphous proto-physical existence into tangible physical existence. This approach leads to two distinct [...]

By Alexander Poltorak|2020-10-15T23:00:27-04:00August 15th, 2012|Age of the Universe, Cosmology, Spirituality, Time, Uncategorized, Wavefunction, Witnesses|8 Comments

Towards Reconciliation of Biblical and Cosmological Ages of the Universe

Towards Reconciliation of Biblical and Cosmological Ages of the Universe[1] Alexander Poltorak Abstract Two opposite views of the age of the universe are considered. According to the traditional Jewish calendar based on the Talmud the age of the universe is less then six thousand years. The cosmological models of the universe supported by the abundant empirical data place the age of the universe in the twelve billion years range. Critical examination of both views is presented in the first part of the paper. In the second part, we consider quantum-mechanical state of matter before and after the introduction of a conscious observer. Role of the observer’s free will is examined. The definitions of physical and proto-physical states of matter are proposed. It is suggested that creation of the first conscious being with [...]

By Alexander Poltorak|2013-08-11T14:23:15-04:00August 15th, 2012|Age of the Universe, Collapse of the wavefunction, Uncategorized, Wavefunction|10 Comments

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