{"product_id":"nocturna-olbers-paradox-physics-t-shirt","title":"Nocturna – Olbers' Paradox Physics T-Shirt","description":"\u003cp\u003eNocturna wraps herself in the night sky and asks the oldest question in astronomy: why is it dark?\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIf the universe were infinite, eternal and evenly filled with stars, every line of sight would end on a star and the night sky would blaze. A thin shell of radius r holds a number of stars growing as r², while each star's light falls as 1\/r², so every shell adds the same brightness. The way out: the universe has a finite age, t₀ ≈ 13.8 billion years, so light from beyond a certain distance has not reached us, and redshift dims what does arrive.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003estars in shell ∝ r² dr,   light per star ∝ 1\/r²   ⇒   each shell adds equal flux\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003er: distance to the shell (m)\u003c\/li\u003e\n\u003cli\u003edr: shell thickness (m)\u003c\/li\u003e\n\u003cli\u003et₀: age of the universe, ≈ 13.8 billion years (≈ 4.35 × 10¹⁷ s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eHeinrich Olbers stated it in 1823 and proposed interstellar dust as the answer, which fails; Edgar Allan Poe guessed the real answer in Eureka (1848). Halley and de Chéseaux had raised the puzzle earlier.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Dust does not work: over time it would heat up and glow.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Nocturna, the pixel-art character, with the title. Back: the shell argument, why dust fails, the finite-age answer and the Poe, Halley and de Chéseaux history. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936547803239,"sku":"16956457560214721066","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936547836007,"sku":"21361657106149074250","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936547868775,"sku":"14400661825737357060","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936547901543,"sku":"23986576011332807166","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936547934311,"sku":"26721348093600243777","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936547967079,"sku":"49709516690511564302","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936547999847,"sku":"31869702179199528230","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936548032615,"sku":"29559821007535331065","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936548065383,"sku":"10935876148990402737","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936548098151,"sku":"12146667036978355646","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936548130919,"sku":"23897508962784593711","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936548163687,"sku":"61849434464058569123","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936548196455,"sku":"19192116770454788291","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936548229223,"sku":"17646670951565209903","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936548261991,"sku":"41772137720338813149","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936548294759,"sku":"37767991190799666022","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/olbers-paradox_front_16_white.png?v=1793595471","url":"https:\/\/pixelatedphysics.com\/products\/nocturna-olbers-paradox-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}