I'm figuring out some stuff about nuclear physics! I was really puzzled by the Interacting Boson Model of atomic nuclei, which treats a nucleus as a collection of 6 different kinds of particles: one kind with spin 0 and five with spin 2. What the hell is that about?
Now I understand. We can sometimes treat a nucleus as an oscillating ellipsoid. As the nucleus oscillates, you can imagine its surface as a world-wide ocean with waves on it. It takes 6 numbers to say what these waves are like at any moment.
That's because it takes 6 numbers to describe an ellipsoid centered at the origin:
• one number to specify its volume
• three numbers to specify its longest axis (since that's a vector v if we pick which way it points)
• two numbers to specify its second longest axis (since that's another vector w but we know it's at right angles to w).
So far this is classical physics. But in reality a nucleus is quantum-mechanical, so these waves also act like particles: 6 kinds of particles!
The volume of the ellipsoid doesn't change when you rotate it, so the first kind of particle is unchanged by rotation. That's the definition of a spin-0 particle.
The other 5 aspects of an ellipsoid do change when you rotate it. They're described by 5 numbers in exactly the way you'd describe a spin-2 particle.
So this is what the Interacting Boson Model is really about: a quantum ellipsoid! I made all this much more precise here:
https://johncarlosbaez.wordpress.com/2025/04/07/quantum-ellipsoids/
But I could use help from a real algebraic geometer, in both senses of the word 'real'. What's the best way to think about the space of all ellipsoids centered at the origin of ℝ³?
John Carlos Baez /
npub17u…8pd6m
2025-04-09 19:29:22
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npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6mPublished at
2025-04-09 19:29:22Event JSON
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"content": "I'm figuring out some stuff about nuclear physics! I was really puzzled by the Interacting Boson Model of atomic nuclei, which treats a nucleus as a collection of 6 different kinds of particles: one kind with spin 0 and five with spin 2. What the hell is that about?\n\nNow I understand. We can sometimes treat a nucleus as an oscillating ellipsoid. As the nucleus oscillates, you can imagine its surface as a world-wide ocean with waves on it. It takes 6 numbers to say what these waves are like at any moment. \n\nThat's because it takes 6 numbers to describe an ellipsoid centered at the origin:\n\n• one number to specify its volume\n• three numbers to specify its longest axis (since that's a vector v if we pick which way it points)\n• two numbers to specify its second longest axis (since that's another vector w but we know it's at right angles to w).\n\nSo far this is classical physics. But in reality a nucleus is quantum-mechanical, so these waves also act like particles: 6 kinds of particles! \n\nThe volume of the ellipsoid doesn't change when you rotate it, so the first kind of particle is unchanged by rotation. That's the definition of a spin-0 particle. \n\nThe other 5 aspects of an ellipsoid do change when you rotate it. They're described by 5 numbers in exactly the way you'd describe a spin-2 particle. \n\nSo this is what the Interacting Boson Model is really about: a quantum ellipsoid! I made all this much more precise here:\n\nhttps://johncarlosbaez.wordpress.com/2025/04/07/quantum-ellipsoids/\n\nBut I could use help from a real algebraic geometer, in both senses of the word 'real'. What's the best way to think about the space of all ellipsoids centered at the origin of ℝ³?",
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