{"product_id":"kochenspek-the-kochen-specker-theorem-physics-t-shirt","title":"Kochenspek – The Kochen–Specker Theorem Physics T-Shirt","description":"\u003cp\u003eKochenspek wears a crown of vectors and tries to paint each one 0 or 1. Every time, one basis is left without a consistent answer.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eCan every quantum measurement have a pre-set answer, waiting to be read, no matter which other compatible measurements are made alongside it? Kochen and Specker proved in 1967 that it cannot. In a Hilbert space of dimension 3 or more, you cannot assign 0 or 1 to every direction so that each orthogonal basis gets exactly one 1. Their original proof used 117 directions in three dimensions.\u003c\/p\u003e\u003cp\u003eCabello, Estebaranz and García-Alcaine gave a short proof in four dimensions: 18 vectors arranged in 9 orthogonal bases, with each vector in exactly 2 bases. A parity count finishes it.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e9 bases × 1 one each = 9 (odd)   but   each vector counted twice ⇒ even\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eBasis: a set of 4 mutually orthogonal vectors in 4 dimensions\u003c\/li\u003e\n\u003cli\u003e9 bases × 4 vectors = 36 = 18 vectors × 2\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eKochen \u0026amp; Specker, J. Math. Mech. 17, 59 (1967); Cabello, Estebaranz \u0026amp; García-Alcaine, Phys. Lett. A 212, 183 (1996).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The theorem rules out non-contextual hidden variables, not all hidden variables: contextual theories such as Bohmian mechanics survive. It is not Bell's theorem and makes no locality assumption. The mathematics is settled; what it means for interpretations is still debated.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Kochenspek, the pixel-art character, with “NO HIDDEN LABELS”. Back: a schematic diagram of 9 bases and 18 vectors (an illustration of the counting, not Cabello's actual vectors), the parity argument and the 1967 and 1996 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960502390887,"sku":"28599388792280442648","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960502423655,"sku":"26850930769423330933","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960502456423,"sku":"12676048975538639996","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960502489191,"sku":"29687853798388377356","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960502521959,"sku":"52742224510475310553","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960502554727,"sku":"15898590222352873063","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960502587495,"sku":"86194256534381241524","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960502620263,"sku":"18699266505186918853","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960502653031,"sku":"22711228890460125766","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960502685799,"sku":"12010899166645927797","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960502718567,"sku":"68539821361477799654","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960502751335,"sku":"24449737089331041596","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960502784103,"sku":"26474356288658128422","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960502816871,"sku":"14492293800670752163","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960502849639,"sku":"25745427815234857824","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960502882407,"sku":"21953646433471840882","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/kochen-specker_front_16_white.png?v=1793622459","url":"https:\/\/pixelatedphysics.com\/id\/products\/kochenspek-the-kochen-specker-theorem-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}