{"product_id":"twinne-twynne-the-twin-paradox-physics-t-shirt","title":"Twinne \u0026 Twynne – The Twin Paradox Physics T-Shirt","description":"\u003cp\u003eTwinne stays home. Twynne flies out at 0.8c and back. They meet again 20 years later for one of them and 12 for the other.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eEach clock records the proper time along its own path through spacetime. The traveller's path is shorter in proper time, so at 0.8c a 20-year round trip on Earth lasts 12 years for the traveller. The gap comes from the geometry of the two paths, not from acceleration itself.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eτ = ∫ √(1 − v²\/c²) dt\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eτ: proper time on the clock (s)\u003c\/li\u003e\n\u003cli\u003ev: clock speed (m\/s)\u003c\/li\u003e\n\u003cli\u003ec: speed of light (m\/s)\u003c\/li\u003e\n\u003cli\u003et: Earth-frame time (s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eEinstein predicted the clock effect in 1905, and Paul Langevin recast it as a human traveller in 1911.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Twinne \u0026amp; Twynne, the pixel-art character, with the title. Back: the proper-time integral, the 0.8c worked example, the geometry note and the 1905 and 1911 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936450089063,"sku":"12049429195297266262","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936450121831,"sku":"22508556025200180239","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936450154599,"sku":"23010577820714975618","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936450187367,"sku":"13077713451821439077","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936450220135,"sku":"32718273146642267030","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936450252903,"sku":"22652741322964829331","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936450285671,"sku":"20013412527330675835","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936450318439,"sku":"13788424077865772251","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936450351207,"sku":"60716632633686902528","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936450383975,"sku":"23268972601941667967","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936450416743,"sku":"32364692383906308132","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936450449511,"sku":"27967635298713154749","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936450482279,"sku":"18273298242788225842","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936450515047,"sku":"17559007317402298445","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936450547815,"sku":"37297535258945046871","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936450580583,"sku":"15533427900947116897","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/twin-paradox_front_01_white.png?v=1793595231","url":"https:\/\/pixelatedphysics.com\/pt\/products\/twinne-twynne-the-twin-paradox-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}