spontaneous symmetry breaking

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Breaking Symmetry

And Moses turned, and went down from the mount, with the two tablets of the testimony in his hand; tablets that were written on both their sides; on the one side and on the other were they written. And the tables were the work of God, and the writing was the writing of God, graven upon the tables… And it came to pass, as soon as he came nigh unto the camp, that he saw the calf and the dancing; and Moses' anger waxed hot, and he cast the tablets out of his hands, and broke them beneath the mount. (Ex. 32:15-19) The Torah portion Ki Tisa (Ex. 30:11-34:35) is, perhaps, has one of the most enigmatic episodes in the Torah—the breaking of the Tablets of the Covenant. The sin of the Golden [...]

By |2018-03-04T18:54:42-05:00March 4th, 2018|Uncategorized|2 Comments

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 [...]

Entangled Sisters

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 in 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 also twins (Seder Olam Rabbah).[1] As inseparable twins, they were “entangled,” as it were. They were somewhat opposite—one introvert, the other extrovert; one beautiful, the other, perhaps not so much (she had “weak eyes”): Now Laban had two daughters: the name of the elder was Leah, and the name of the younger was Rachel. And Leah’s eyes were weak; but Rachel was of beautiful form and fair to look upon (Genesis 29:17). Rachel and [...]

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 [...]

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