Science

The Second Derivative — The Secrets of The Double Cave

The Second Derivative — The Secrets of The Double Cave

And he [Avraham] spoke with them, saying, “…Listen to me and entreat for me to Ephron the son of Zohar. That he may give me the Machpelah (Double) Cave, which belongs to him, which is at the end of his field…" (Genesis 23:8-9) double: A house with an upper story over it. Another interpretation: because it was doubled with couples (Er. 53a) (Rashi on Genesis 23:9) In the Torah portion Chayei Sarah, Avraham purchases a Double Cave, Machpelah, as the ancestral burial plot. Almost all classical Biblical commentators interpret Machpelah (that is, "double") to mean a cave with two chambers. Rashi takes an entirely different approach and states that the cave was known for a two-story house built on top of it. So, the word Machpelah refers not to the cave itself, but to [...]

By Alexander Poltorak|2020-11-11T00:04:58-05:00November 7th, 2018|Bereshit, Chayei Sarah, Genesis, Mathematics, Parshah, Pentateuch (Chumash), Randomness, Uncategorized|0 Comments

Biblical Relativity

Biblical Relativity

And the life of Sarah was one hundred years and twenty years and seven years... (Gen. 23:1) Why did Esther merit to rule over 127 countries? Said G‑d: “Let Esther, the descendant of Sarah who lived 127 years, come and rule over 127 lands. (Esther Rabbah 1:8) The Midrash Ester Rabbah compares 127 years of Sarah’s life with 127 provinces that Esther ruled. How can one compare time with space? When the Midrash says that Adam gifted 70 years of his life to his descendant, King David, it’s understandable – a year for a year. But a year for a province? What’s the connection? Hermann Minkowski When, in 1905, Albert Einstein published his Special Theory of Relativity, it was nothing short of a scientific revolution. For the first time, Einstein showed [...]

By Alexander Poltorak|2024-10-13T21:44:20-04:00November 4th, 2018|Bereshit, Chayei Sarah, Genesis, Pentateuch (Chumash), Physics, Relativity, Science, Space, Time, Uncategorized|1 Comment

Wellsprings from Above and Wellsprings from Below

Wellsprings from Above and Wellsprings from Below

In the six hundredth year of Noah's life, in the second month, on the seventeenth day of the month… all the fountains of the great deep were broken up, and the windows of heaven were opened. (Gen. 7:11) In calculating the time of the dawn of Messianic revelation, the Zohar writes, And after six hundred years of the sixth thousand there will be opened the gates of wisdom above and the fountains of wisdom below, and the world will make preparations to enter on the seventh thousand as man makes preparation on the sixth day of the week, when the sun is about to set. (Zohar I, 117a) The Zohar calculates this based on the letters of the Tetragrammaton, but brings the verse from this parashah as the mnemonic: “In the six hundredth [...]

By Alexander Poltorak|2022-05-30T22:03:48-04:00October 14th, 2018|Bereshit, Genesis, Kabbalah, Mashiach (Messiah), Names of G‑d, Noach, Parshah, Pentateuch (Chumash), Physics, Quantum Field Theory, Science, Uncategorized, Zohar|2 Comments

The Beard of the Long Face is Found

The previous Lubavitcher Rebbe, the Rebbe Rayatz (a.k.a. the Fridriker Rebbe) told the story about his father, the Rebbe Rashab. Once the brother of Rebbe Rashab, Rabbi Menachem Mendel (a.k.a. the RM”M) told him that he read in a magazine an article that stated that scientists found a nerve in the brain regulating the cognitive function so that when a person needed to remember something he would tilt his head looking up, whereas when the person needed to concentrate, he’d tilt his head down. The Rebbe Rashab took his brother to his study, took from the shelf a book by the Second Lubavitcher Rebbe, the Mittler Rebbe, in which it stated the same thing. The Rebbe Rashab said to his brother, “You’d think he was a doctor, but he wasn’t. He saw Adam [...]

By Alexander Poltorak|2018-11-10T23:01:55-05:00August 31st, 2018|Bereshit, Biology, Genesis, Kabbalah, Neuroscience, Parshah, Pentateuch (Chumash), Science, Sefirot, Sefirot, Toledot, Uncategorized, Zohar|4 Comments

Sanctuary in Five Dimensions

Sanctuary in Five Dimensions

In my last post, Tisha B’Av on Shabbat – A Relativistic Perspective, I wrote that G‑d created His sanctuary in four dimensions — Bet HaMikdash (preceded by the Mishkan in the desert) in the three spatial dimensions, and Shabbat in the fourth dimension, time. I emphasized four dimensions because that was all we needed to explain the connection between the Temple and Shabbat and why we do not fast when Tish B’Av falls on Shabbat (but, instead, fast on the following day—Sunday). In truth, however, G‑d created His sanctuary in five dimensions. As we discussed in several posts on this blog (On the Nature of Time and the Age of the Universe, The Fifth Force, The Fifth Force – Epilog, Tumah and Taharah), Sefer Yetzirah, the oldest surviving book of Kabbalah, describes our [...]

By Alexander Poltorak|2024-10-13T21:51:42-04:00July 27th, 2018|G‑d, Mathematics, Shabbat, Soul, Space, Spirituality, Uncategorized|3 Comments

Tisha B’Av on Shabbat – A Relativistic Perspective

Tisha B’Av on Shabbat – A Relativistic Perspective

Yesterday was the 9th day of the month of Av or, in Hebrew, Tisha B’Av. Usually, Tisha B’Av is marked by mourning and fasting. Yesterday, however, we ate festive meals, drank wine and were prohibited from fasting or displaying any signs of mourning. Because yesterday was Shabbat. Shabbat pushes off the observances of Tisha B’Av by a day. Indeed, today, Sunday, we fast and mourn the destruction of the First and the Second Holy Temple – Bet Hamikdash – in Jerusalem, we remember the Holocaust and many other tragedies that befell the Jewish people. Why couldn’t we observe Tisha B’Av on Shabbat? After all, that was the day when on the 9th of Av, both Temples were destroyed! The simple explanation, of course, is that on Shabbat there is no mourning. On Shabbat, [...]

By Alexander Poltorak|2018-07-24T14:20:03-04:00July 22nd, 2018|Holidays (Yomim Tovim), Kabbalah, Mathematics, Mathematics, Physics, Science, Space, Time, Tisha B'Av, Uncategorized|0 Comments

Purim—the Day when We Celebrate Spontaneous Symmetry Breaking

Purim—the Day when We Celebrate Spontaneous Symmetry Breaking

This is what Haman did not understand. Even at the highest level, where there is a complete symmetry between Jacob and Esau, G‑d chooses Jacob—a spiritual example of the spontaneous symmetry breaking: "I loved you, said the Lord, and you said, “How have You loved us?” Was not Esau a brother to Jacob? says the Lord. And I loved Jacob. And I hated Esau…" (Malachi I, 2-3). Haman failed the test on quantum field theory and ended up hanging on a gallows.

By Alexander Poltorak|2024-03-20T23:07:19-04:00March 2nd, 2018|Holidays (Yomim Tovim), Physics, Purim, Quantum Field Theory, Quantum Theory, Randomness, Symmetry, Uncategorized, Yom Kippur|0 Comments

Grand Unification

Grand Unification

In physics, we seek Grand Unification, also known as the Theory of Everything. The Standard Model describes three out of the four fundamental forces: the strong (nuclear) force, the weak force (beta decay), and the electromagnetic force. The gravitational force, described by the General Theory of Relativity, does not fit into the Standard Model. Developing a quantum theory of gravity, and unifying gravity with the other three forces is the holy grail of theoretical physics. Jewish people are also in need of Grand Unification. There is a schism that runs through the history: it is the schism between Joseph (Yosef) and Judah (Yehuda). Judah represents a “shtetl yid,” a Jew who lives in a ghetto, who sits in a yeshivah, who learns Torah, and who sees the world outside as hostile, as a [...]

By Alexander Poltorak|2018-12-10T23:07:02-05:00December 23rd, 2017|Bereshit, Chanukah, Deuteronomy, Ezekiel, Holidays (Yomim Tovim), Kabbalah, Mashiach (Messiah), Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Resurrection, Science, Uncategorized, Vayigash|0 Comments

Dreams of Pharaoh—A Lesson in Symmetry

Dreams of Pharaoh—A Lesson in Symmetry

In the Torah portion Miketz, Pharaoh has two dreams. He wakes up agitated and calls on all the wise men of Egypt to interpret his dreams. Nobody is able to come up with an acceptable interpretation, so they fetch Joseph from prison and he successfully interprets the dreams of Pharaoh—that there will be seven years of plenty followed by seven years of famine. Joseph proceeds to instruct Pharaoh on how to prepare for the seven years of famine. In the previous posts, "Interpreting Dreams" and "Joseph—the Master of Time," we already explained how Joseph was able to interpret dreams in terms of units of time and why Pharaoh appointed Joseph as the viceroy of Egypt. This story, however, still has mysteries to unlock. Perhaps it can teach us more lessons. In Talmudic and [...]

By Alexander Poltorak|2020-12-20T14:57:57-05:00December 16th, 2017|Bereshit, Dreams, Genesis, Mathematics, Miketz, Parshah, Pentateuch (Chumash), Physics, Quantum Field Theory, Symmetry, Uncategorized|2 Comments

Symmetry and Love — Jewish Chromodynamics

Symmetry and Love — Jewish Chromodynamics

Ye are standing this day all of you before the Lord your G‑d: your heads, your tribes, your elders, and your officers, even all the men of Israel, your little ones, your wives, and thy stranger that is in the midst of thy camp, from the hewer of thy wood unto the drawer of thy water; that thou shouldest enter into the covenant of the Lord thy G‑d—and into His oath—which the Lord thy G‑d maketh with thee this day. (Deut. 29:9-11) The above verses at the beginning of the Torah portion Nitzavim that is always read in the week preceding the Jewish New Year, Rosh HaShanah, are usually interpreted in terms of the unity of Jewish people: You are standing this day all of you [read: standing together in perfect unity]. This is not [...]

By Alexander Poltorak|2020-04-01T23:41:15-04:00September 13th, 2017|Collapse of the wavefunction, Deuteronomy, Devarim, Holidays (Yomim Tovim), Mathematics, Mathematics, Nitzavim, Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Rosh HaShanah, Science, Superposition, Symmetry, Uncategorized|2 Comments

First Fruits and the Wave-Particle Duality of Nature

First Fruits and the Wave-Particle Duality of Nature

…Thou shalt take of the first of all the fruit of the ground, which thou shalt bring in from thy land that the Lord thy G‑d giveth thee; and thou shalt put it in a basket and shalt go unto the place which the Lord thy G‑d shall choose to cause His name to dwell there. And thou shalt come unto the priest that shall be in those days, and say unto him: 'I profess this day unto the Lord thy G‑d, that I am come unto the land which the Lord swore unto our fathers to give us.' And the priest shall take the basket out of thy hand, and set it down before the altar of the Lord thy G‑d. Deuteronomy 26:2-4 The debate about the nature of matter goes back [...]

By Alexander Poltorak|2023-08-31T19:51:45-04:00September 10th, 2017|Atomic Theory, De Broglie–Bohm theory, Deuteronomy, Devarim, Ki Tavo, Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Science, Uncategorized|1 Comment

The Pilot Wave

The Pilot Wave

And on the day that the tabernacle was reared up, the cloud covered the tabernacle, even the tent of the testimony; and at even there was upon the tabernacle as it were the appearance of fire, until morning. So it was always: the cloud covered it, and the appearance of fire by night. And whenever the cloud was taken up from over the Tent, then after that the children of Israel journeyed; and in the place where the cloud abode, there the children of Israel encamped. At the commandment of the Lord the children of Israel journeyed, and at the commandment of the Lord they encamped: as long as the cloud abode upon the tabernacle they remained encamped. And when the cloud tarried upon the tabernacle many days, then the children of Israel [...]

By Alexander Poltorak|2024-06-21T11:38:52-04:00June 11th, 2017|Bamitbar, Behaalotecha, De Broglie–Bohm theory, Numbers, Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Uncategorized, Wavefunction|3 Comments

Shavuot — Three States of Consciousness

Shavuot — Three States of Consciousness

Shavuot (a.k.a. the Feast of Weeks, or “Pentecost”) is the only Jewish holiday with no fixed day on the calendar—it is always the fiftieth day from the beginning of the counting of the Omer (which itself starts on the second day of Passover). What is so special about the number 50, and what is its connection to Shavuot? Shavuot is not only the culmination of the counting of the Omer—Sefirat HaOmer—but also the culmination of the process of the maturation of our consciousness. On Shavuot, it is customary to read the Book of Ruth (Megilat Rut). The story begins with Lot and his daughters running away from Sodom and hiding in a mountain cave. Seeing the destruction of Sodom, the daughters of Lot suspected that God, in his fury, destroyed the whole of [...]

By Alexander Poltorak|2024-06-09T16:48:17-04:00May 30th, 2017|Holidays (Yomim Tovim), Mashiach (Messiah), Omer, Physics, Shavuot, Uncategorized|3 Comments

Mishkan – a Metaphor for Quantum Reality, II

Mishkan – a Metaphor for Quantum Reality, II

Continuing the theme of my last post, Mishkan – a Metaphor for Quantum Reality, the analogy between the Tabernacle (“Mishkan”) and quantum reality goes even deeper. The quantum world is best described today by the Quantum Field Theory. According to this theory, there are no particles, only fields. When we interact with a field, it manifests itself as a quantum of the field, which, to some extent, looks and behaves like a particle. For example, when we interact with an electromagnetic field, it manifests itself as a photon – a quantum of the electromagnetic field. An electron, according to the Quantum Field Theory, is not really a particle but a quantum of the electron field, which is a quantum field that is spread across the entire universe. This quantum is an excitation of [...]

By Alexander Poltorak|2019-06-03T09:46:40-04:00May 29th, 2017|Bamidbar, Bamitbar, G‑d, Isaiah, Mashiach (Messiah), Names of G‑d, Numbers, Parshah, Physics, Quantum Theory, Science, Space, Uncategorized|2 Comments

Mishkan – a Metaphor for Quantum Reality

Mishkan – a Metaphor for Quantum Reality

And when the Tabernacle setteth forward, the Levites shall take it down; and when the Tabernacle is to be pitched, the Levites shall set it up… (Num. 1:51) During the wonders of Israelites in the desert, the Tabernacle (Heb. “Mishkan”), existed as a sanctuary only during their encampments. Whenever they traveled, the Mishkan was taken down and disassembled to be carried by Levites during the journey. When G‑d commanded Moses to set the camp, the Mishkan was reassembled and set up again. Let us fast forward some three-and-a-half thousand years to the beginning of the 20 c. It was a time of great intellectual turmoil. The discovery of the atom’s structure by Rutherford, according to which an atom resembled the solar system with a nucleus at the center and electrons orbiting the nucleus, [...]

By Alexander Poltorak|2019-06-03T09:26:48-04:00May 26th, 2017|Atomic Theory, Bamidbar, Bamitbar, Numbers, Parshah, Physics, Quantum Theory, Uncategorized|4 Comments

Half-Shekel – Metaphor for Entanglement

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 G‑d 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 the favorite metaphor for explaining quantum entanglement. What is entanglement? When obtaining information about one [...]

By Alexander Poltorak|2019-02-20T15:23:07-05:00March 16th, 2017|Collapse of the wavefunction, Entanglement, Exodus (Shemot), Ki Tisa, Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Shemot, Superposition, Uncategorized|2 Comments

Sacrifices and incenses – fields and entanglement

Sacrifices and incenses – fields and entanglement

At the end of the weekly portion, Tetzaveh, the 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 G‑d. The Hebrew word for incense offerings, qetoret, literally means “smoke," "the odor of sacrifice," or "incense.” However, Rabbi David Kimchi ("Radak") points out that the word qeturot means “connected” as it is etymologically related to the Aramaic word qeter “to bind” and [...]

By Alexander Poltorak|2024-02-21T20:59:41-05:00March 15th, 2017|Entanglement, Parshah, Physics, Quantum Theory, Shemot, Tetzaveh, Uncategorized|1 Comment

Purim: Celebrating Randomness

Purim: Celebrating Randomness

Ultimately, I suppose Einstein was right—G‑d does not play dice. So when Haman reached that spiritual level through casting the lots, he discovered the true will of G‑d, who chose the Jewish People. Jews are called “ the chosen people” not because we are better or smarter than others but because it was a simple choice of G‑d. Call this choice “capricious,” call it “irrational,” but ultimately, as Niels Bohr quipped, “Quit telling G‑d what to do!” This is the ultimate lesson of the story of Purim.

By Alexander Poltorak|2024-03-20T22:40:32-04:00March 12th, 2017|G‑d, Holidays (Yomim Tovim), Kabbalah, Names of G‑d, Purim, Quantum Theory, Randomness, Science, Uncategorized|0 Comments

Five Worlds

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 [...]

By Alexander Poltorak|2017-05-23T19:06:38-04:00February 6th, 2017|Collapse of the wavefunction, Creation, Kabbalah, Physics, Quantum Theory, Science, Sefirot, Sefirot, Space, Spirituality, Time, Uncategorized, Wavefunction|0 Comments

Schrödinger Menorah: Burning and not Burning

Schrödinger Menorah: Burning and not Burning

The miracle of Chanukah revolves around a single-day-supply of olive oil burning for eight days during the rededication of the Holy Temple in Jerusalem (Bet HaMikdash), after Maccabees liberated Israel from the occupation by the Greco-Syrian Seleucid empire. Rabbi Menachem Mendel Schneerson There are countless explanations of the miracle of the oil lasting eight days. The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, offers a unique explanation. The Rebbe dismisses any explanation of the miracle that relies on the miraculous nature of the oil itself. The Rebbe maintains that to be kosher for the Menorah, the oil had to be natural olive oil, not some miraculous oil. According to the Rebbe, the miracle was that natural oil was burning and not burning at the same time. The Rebbe draws an analogy with [...]

By Alexander Poltorak|2020-12-13T22:43:25-05:00December 25th, 2016|Chanukah, G‑d, Holidays (Yomim Tovim), Physics, Quantum Theory, Science, Superposition, Uncategorized|1 Comment

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