{"product_id":"splitra-the-schwinger-effect-physics-t-shirt","title":"Splitra – The Schwinger Effect Physics T-Shirt","description":"\u003cp\u003eSplitra opens her hands in a storm of electric field and tears a gleaming electron and positron out of empty space.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eA strong enough electric field should pull electron–positron pairs out of the vacuum. In Dirac's picture an electron in the negative-energy sea must tunnel across a gap of 2mc², and the field tilts that gap. The rate is exponentially suppressed unless the field approaches a critical value, where the field does work mc² over one reduced Compton wavelength.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eE_c = m²c³ \/ (eħ) ≈ 1.32 × 10¹⁸ V\/m   and   rate ∝ exp(−πE_c \/ E)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eE_c: critical field (V\/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\u003ee: elementary charge (C)\u003c\/li\u003e\n\u003cli\u003eħ: reduced Planck constant (J s)\u003c\/li\u003e\n\u003cli\u003eE: applied electric field (V\/m)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eSauter found the tunnelling factor in 1931, Heisenberg and Euler built the effective theory in 1936, and Julian Schwinger gave the full QED result in Phys. Rev. 82, 664 (1951).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The exponential is the leading factor only. The effect has not yet been seen directly in the vacuum with a static field, because no lab field comes close to E_c. A “Schwinger-like” production of electron–hole plasma reported in graphene superlattices (Berdyugin et al., Science 2022) is an analogue in a material, not the vacuum effect. The pair's energy comes from the field, not from nothing.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Splitra, the pixel-art character, with “TEARING THE VACUUM”. Back: the critical field, the leading pair-rate factor, the not-yet-seen note and the 1931, 1936 and 1951 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960503144551,"sku":"11009576892225595039","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960503177319,"sku":"29898645808949702619","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960503210087,"sku":"12601532353641324987","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960503242855,"sku":"74301562659167417152","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960503275623,"sku":"20625563189360355248","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960503308391,"sku":"19489715244534738394","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960503341159,"sku":"17486142417987679446","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960503373927,"sku":"10630102108480980526","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960503406695,"sku":"13200657008953807546","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960503439463,"sku":"12199168581720400159","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960503472231,"sku":"15663573761964746572","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960503504999,"sku":"23899067513610050241","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960503537767,"sku":"71967329590640077275","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960503570535,"sku":"19542706043016605311","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960503603303,"sku":"12575120638685544449","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960503636071,"sku":"13120103085136439928","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/schwinger-effect_front_16_white.png?v=1793622486","url":"https:\/\/pixelatedphysics.com\/ja\/products\/splitra-the-schwinger-effect-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}