{"product_id":"marina-dirac-the-dirac-sea-physics-t-shirt","title":"Marina Dirac – The Dirac Sea Physics T-Shirt","description":"\u003cp\u003eMarina Dirac rises from a sea of filled states, and the hole she leaves behind shines like a positive electron.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eDirac's equation for a free electron allows negative as well as positive energies, separated by a gap of 2mc². Dirac proposed that every negative-energy state is already filled, so electrons cannot fall into them. An empty state, a hole, would move like a positively charged electron.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e(iħ γ^μ ∂_μ − m c) ψ = 0,   E = ± √(p²c² + m²c⁴)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eħ: reduced Planck constant (J·s)\u003c\/li\u003e\n\u003cli\u003eγ^μ: Dirac matrices (dimensionless)\u003c\/li\u003e\n\u003cli\u003e∂_μ: spacetime derivative (1\/m)\u003c\/li\u003e\n\u003cli\u003em: electron mass (kg)\u003c\/li\u003e\n\u003cli\u003ec: speed of light (m\/s)\u003c\/li\u003e\n\u003cli\u003eψ: electron wavefunction\u003c\/li\u003e\n\u003cli\u003eE: energy (J)\u003c\/li\u003e\n\u003cli\u003ep: momentum (kg·m\/s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eDirac proposed the sea in 1930 (he first suggested the holes were protons); C. D. Anderson reported the positron in cosmic rays in 1933. The gap is 2m_ec² ≈ 1.022 MeV.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The sea is a historical picture. Quantum field theory keeps the positron and drops the sea.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Marina Dirac, the pixel-art character, with the title. Back: the Dirac equation, the two energy branches, the 1.022 MeV gap, Anderson's positron and the historical-picture note. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936503697511,"sku":"21820107102456971650","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936503730279,"sku":"28573081023427470650","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936503763047,"sku":"26402928676735692584","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936503795815,"sku":"25932338423253601820","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936503828583,"sku":"24192390721485098309","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936503861351,"sku":"16254755701097716829","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936503894119,"sku":"26317523152597789924","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936503926887,"sku":"22492769467097231341","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936503959655,"sku":"17663274428171255190","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936503992423,"sku":"20252425782005852001","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936504025191,"sku":"92919204188851816058","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936504057959,"sku":"12444988291915509996","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936504090727,"sku":"13074038621829815570","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936504123495,"sku":"25392315526683278922","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936504156263,"sku":"77338055576525263384","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936504189031,"sku":"20105805124871764349","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/dirac-sea_front_16_white.png?v=1793595379","url":"https:\/\/pixelatedphysics.com\/de\/products\/marina-dirac-the-dirac-sea-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}