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Purim—the Day when We Celebrate Spontaneous Symmetry Breaking

The Zohar compares Yom Kippur to Purim stating that Yom HaKipurim may be interpreted as “a day like Purim” (k-purim in Hebrew means “like purim”).  On Purim we feast; on Yom Kippur we fast—what the two can have in common? Indeed, Purim and Yom Kippur have something very important in common.  Both days share a common root—pur—meaning  a “lot” (or pl. purim—“lots”). On Yom Kippur, two lots were placed in a wooden  box—one say “to God”, and the other “to Azazel.”  (See my post, “Tale of Entangled Goats”). The High Priest relied on a lottery to choose which goat would be used for a sacrifice to God and which to atone for the sins of Jewish People. On Purim, Haman threw two lots to determine the month and the day of a pogrom, [...]

Dreams of Pharaoh—a Lesson in Symmetry

In the Torah portion Miketz, Pharaoh sees two dreams. He wakes up agitated and calls on all wise men of Egypt to interpret his dreams. Nobody is able to come up with an acceptable interpretation, so they fetch Joseph from a prison and he successfully interprets dreams of Pharaoh—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, is still puzzling. Perhaps it can teach us more lessons… In Talmudic and Kabbalah literature, Joseph is called [...]

Joseph and His Brothers

I grew up In Russia and was raised on the metric system based on the decimal arithmetic. When we immigrated to the U.S., I had to learn a new to me (but, actually, very old) Imperial system of measurements having 12 inches in a foot. I still struggle with it (decimal system, apparently, was hardwired in my brain). There are many number systems or positional notation systems. Ancient Babylonians used base-60, Hindu-Arabic system uses familiar decimal base-10 system, Mayans used base-20 system. There are base-2 binary, base-12 duodecimal, and base-16 hexadecimal systems, to name a few. Aside from the binary system used by computers, we humans mostly use decimal and, sometimes, duodecimal systems. The all-familiar decimal system is used in the metric system of measurements. In base-10 positional notation there are 10 decimal [...]

Entangled Sisters

Vayeitzei The story of entangled twins is continuing in the Torah portion Vayeitzei (Genesis 28:10–32:3.)  Structurally, it is very similar to the story of the previous Torah portion, Toldot (see Entangled Twins).  In this portion, we again read about two entangled siblings—albeit, this time, sisters—about deception and spontaneous symmetry breaking. Two sisters were Rachel and Leah. Moreover, according to Midrash, Rachel and Leah were twins (Seder Olam Rabbah). As twins, who emerge from the same womb, they were entangled.  They were somewhat opposite—one is introvert, the other is extrovert; one is beautiful, the other has weak eyes. Rachel and Leah are earthly embodiments of spiritual partzufim (configurations of sephirot—Divine emanations).  Kabbalah teaches that in spiritual realms, there is Partzuf Rachel and Partzuf Leah, which are two aspects of the Nukva—the feminine aspect of Godliness.  Partzuf Rachel represents [...]

By | November 8th, 2013|Entanglement, Parshah, Symmetry, Vayetze|0 Comments

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 [...]