{"product_id":"tethra-bells-spaceship-paradox-physics-t-shirt","title":"Tethra – Bell's Spaceship Paradox Physics T-Shirt","description":"\u003cp\u003eSame burn. Same speed. Tethra's twin rockets fly in perfect step, and the thread between them still snaps.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eTwo ships start at rest a distance L apart and accelerate identically. In the launch frame their gap stays L the whole time, but a thread moving with them is Lorentz-contracted: to span a gap of L at speed v it would need a proper length of γL. Its proper length is only L, so it is stretched and breaks. Equivalently, once both coast at speed v, in the ships' momentary rest frame their separation has grown to γL while the thread's rest length is still L.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eships'-frame gap = γL,   γ = 1\/√(1 − v²\/c²)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eL: initial (and launch-frame) separation (m)\u003c\/li\u003e\n\u003cli\u003ev: final common speed (m\/s)\u003c\/li\u003e\n\u003cli\u003ec: speed of light, 299 792 458 m\/s (exact)\u003c\/li\u003e\n\u003cli\u003eγ: Lorentz factor (dimensionless)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eE. Dewan and M. Beran published the puzzle in 1959; J. S. Bell made it famous in \"How to teach special relativity\" (1976).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The γL gap applies after both ships reach the same final speed; during acceleration they share no single rest frame.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Tethra, the pixel-art character, with the title. Back: the launch-frame and ships'-frame gaps, the Lorentz factor, the broken-thread line and both sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936476303463,"sku":"22432678534987512185","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936476336231,"sku":"28711729129764044286","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936476368999,"sku":"22142656146234274901","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936476401767,"sku":"24817559030383117524","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936476434535,"sku":"66835403588251029624","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936476467303,"sku":"13901987116546493631","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936476500071,"sku":"27568475392179762829","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936476532839,"sku":"19874359280744626510","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936476565607,"sku":"12903788037484701128","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936476598375,"sku":"14451382568814143916","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936476631143,"sku":"18895333195120449015","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936476663911,"sku":"29498727025405262871","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936476696679,"sku":"19783683004979210937","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936476729447,"sku":"25811672172979990656","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936476762215,"sku":"82165651579844326272","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936476794983,"sku":"18778354415194606549","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/bell-spaceship_front_01_white.png?v=1793595287","url":"https:\/\/pixelatedphysics.com\/id\/products\/tethra-bells-spaceship-paradox-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}