{"product_id":"noethers-ledger-plate-004-physics-poster","title":"Noether's Ledger – Plate 004 Physics Poster","description":"\u003cp\u003ePlate 4 speaks for itself: \u003cem\u003e“Every symmetry keeps a promise.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eNoether's theorem ties each continuous symmetry of the action to a conserved quantity. For a central potential the Lagrangian does not depend on the angle φ, so the angular momentum m r²φ̇ is conserved; Kepler's equal areas in equal times is that promise kept.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ed\/dt (m r² φ̇) = ∂L\/∂φ = 0\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003em: mass, kg\u003c\/li\u003e\n\u003cli\u003er: radial distance, m\u003c\/li\u003e\n\u003cli\u003eφ: polar angle, rad\u003c\/li\u003e\n\u003cli\u003eφ̇: angular velocity, rad s⁻¹\u003c\/li\u003e\n\u003cli\u003eL: Lagrangian (1\/2)m(ṙ² + r²φ̇²) − V(r), J\u003c\/li\u003e\n\u003cli\u003eV(r): central potential energy, J\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eL lacks φ. Equal areas in equal times.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\u003cli\u003eE. Noether, Nachr. Ges. Wiss. Göttingen, 235 (1918).\u003c\/li\u003e\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 004, “Noether's Ledger”: the pixel-art plate with its slogan “Every symmetry keeps a promise.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50961474650215,"sku":"19333845559597297716","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50961474682983,"sku":"19653087710564748623","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50961474715751,"sku":"33276739653934694770","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50961474748519,"sku":"14521266937737252363","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50961474781287,"sku":"56706160230220911571","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50961474814055,"sku":"24522318129016070804","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50961474846823,"sku":"11060484506745516478","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50961474879591,"sku":"25153478201987472382","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50961474912359,"sku":"16537481923250082994","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/12128234472902622747_2048.jpg?v=1793631882","url":"https:\/\/pixelatedphysics.com\/zh-hans\/products\/noethers-ledger-plate-004-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}