Higgs-Boson

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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.

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 [...]

Jacob’s Sheep—Particles, Fields and Strings

And it came to pass at the time that the flock conceived, that I lifted up mine eyes, and saw in a dream, and, behold, the he-goats which leaped upon the flock were streaked, speckled, and spotted. (Gen. 31:10)   This week’s Torah reading, Vayeitzei (Gen. 28:10-32:3) talks about three kinds of sheep: streaked, speckled, and spotted.   Streaked Sheep   Streaked sheep (“akudim”) were ankle-ringed. They looked as if their ankles were bound together with a black rope. Hence the name—"akidim" (Hebrew world for streaked, “akud” means bound as in “Akeda”—binding of Isaac). Speckled Sheep Speckled sheep (Heb. “nekudim” from sing. “nakod”.) were sheep with black dots.   Spotted Sheep   Spotted or flecked sheep (Heb. "berudim") were blotched. What is the significance of these streaks, speckles and blotches that the Torah devotes [...]

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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