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A spin-½ particle must turn 720°, not 360°, to come back to itself: one full turn flips the sign of its wavefunction. This is a 3\" × 3\" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50655021269095,"sku":"56357372242490519763","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50409235218535,"sku":"13196069967734126009","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50655021301863,"sku":"58347697891299679606","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50655021334631,"sku":"20729087780467186063","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/14158163780091174421_1200.jpg?v=1793667561"},{"product_id":"stairohm-quantum-hall-effect-pixel-sticker","title":"Stairohm – Quantum Hall Effect \/ Resistance Plateaus Physics Sticker","description":"\u003cp\u003eStairohm is a Pixelated Physics law character, one of our quantum designs. Integer quantum Hall effect: Hall resistance locks onto exact plateaus at h\/ne², and some disorder helps make the steps flat. This is a 3\" × 3\" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50655005180007,"sku":"10157764930266772313","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50409249144935,"sku":"67363099801434461719","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50655005212775,"sku":"23445541233189885886","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50655005245543,"sku":"14749014747772901524","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/17764159847932947941_1200.jpg?v=1793666426"},{"product_id":"sortex-maxwells-demon-pixel-sticker","title":"Sortex – Maxwell’s Demon \/ Landauer Erasure Physics Sticker","description":"\u003cp\u003eSortex is a Pixelated Physics law character, one of our thermodynamics designs. In the standard, still-debated answer to Maxwell’s demon, sorting can be free but erasing a bit costs at least kT ln 2 of heat. This is a 3\" × 3\" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50655003082855,"sku":"21162152326476518281","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50409251995751,"sku":"15259867609443798688","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50655003115623,"sku":"25350771008503702129","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50655003148391,"sku":"20924121030700621617","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/559620385846478775_1200.jpg?v=1793666740"},{"product_id":"invertia-negative-absolute-temperature-pixel-sticker","title":"Invertia – Negative Absolute Temperature \/ Population Inversion Physics Sticker","description":"\u003cp\u003eInvertia is a Pixelated Physics law character, one of our thermodynamics designs. More particles on the top level than the bottom: negative absolute temperature by the Boltzmann definition, still debated. This is a 3\" × 3\" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50655002689639,"sku":"17642299807748091622","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50409252716647,"sku":"14509998878219109146","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50655002722407,"sku":"40899530172099460953","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50655002755175,"sku":"14149433335647681039","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/11634243443185081838_1200.jpg?v=1793666783"},{"product_id":"condensa-bose-einstein-condensate-pixel-sticker","title":"Condensa – Bose–Einstein Condensate Physics Sticker","description":"\u003cp\u003eCan atoms share one state? 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A 3\" pixel-art sticker; equation, symbols and sources in the physics panel below.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50654992433255,"sku":"15718577286160713428","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50432036012135,"sku":"61090527422127908458","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50654992466023,"sku":"31034564289387813208","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50654992498791,"sku":"45261686716696564024","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/4865425427847823842_1200.jpg?v=1793667147"},{"product_id":"enrico-fermi-sticker-within-an-order-physics-sticker","title":"Enrico Fermi Sticker – Within An Order | Physics Sticker","description":"\u003cp\u003eHow many piano tuners work in Chicago? Enrico Fermi loved questions like that, answered to within a power of ten. He also worked out, in 1926 alongside Dirac, how identical fermions such as electrons fill energy levels. In the Fermi–Dirac distribution, a state at the chemical potential μ is exactly half occupied at any temperature. A 3\" pixel-art physicist sticker; equation, symbols and sources in the physics panel below.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50654991646823,"sku":"32668363440278647528","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50443422335079,"sku":"10450578915400850268","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50654991679591,"sku":"31298237354183100130","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50654991712359,"sku":"33333395382256299719","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/5114179727933881714_1200.jpg?v=1793660000"},{"product_id":"casimira-casimir-effect-pixel-sticker","title":"Casimira – The Casimir Effect Pixel Sticker","description":"\u003cp\u003eCasimira, an armoured knight-mage, presses two upright plates together with a sliver of gap between them while violet vacuum light crackles all around.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003ePut two uncharged, perfectly conducting parallel plates a small distance a apart in vacuum and they attract. Between the plates only electromagnetic modes that fit the boundary conditions are allowed; outside, every mode is. Summing the zero-point energies ½ħω of the modes, and subtracting the free-space value, leaves a finite energy that falls as the plates approach. Hendrik Casimir derived it in 1948.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eP = π²ħc \/ (240 a⁴)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eP: attractive pressure, force per unit plate area (Pa)\u003c\/li\u003e\n\u003cli\u003eħ: reduced Planck constant, h\/2π = 1.054 571 817 × 10⁻³⁴ J s\u003c\/li\u003e\n\u003cli\u003ec: speed of light, 299 792 458 m s⁻¹\u003c\/li\u003e\n\u003cli\u003ea: gap between the plates (m)\u003c\/li\u003e\n\u003cli\u003eπ²\/240: numerical factor from summing the allowed modes\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eAt a = 1 µm, P ≈ 1.3 × 10⁻³ Pa (1.3 mPa); halve the gap and the pressure rises sixteen-fold. S. K. Lamoreaux first measured the force accurately in 1997, using a sphere and a flat plate (\u003cem\u003ePhys. Rev. Lett.\u003c\/em\u003e 78, 5); Bressi and colleagues measured it between true parallel plates in 2002 (\u003cem\u003ePhys. Rev. Lett.\u003c\/em\u003e 88, 041804). Source for the theory: H. B. G. Casimir, \u003cem\u003eProc. K. Ned. Akad. Wet.\u003c\/em\u003e 51, 793 (1948).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The formula is for ideal mirrors at zero temperature; real metals, roughness and temperature change it. Whether the force “proves” vacuum energy is debated: R. L. Jaffe (\u003cem\u003ePhys. Rev. D\u003c\/em\u003e 72, 021301, 2005) showed it can be derived as a relativistic van der Waals force between the plates’ charges, without reference to zero-point energy.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eLeave me nothing but a gap and I will still push. The emptiness outside is fuller than the emptiness within, and that difference is my strength.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003ePrinted text: \u003cstrong\u003eCASIMIRA\u003c\/strong\u003e with the line \u003cstrong\u003eP = π²ħc\/(240a⁴)\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker in 2″, 3″, 4″ and 6″ sizes. See more \u003ca href=\"\/hi\/collections\/stickers\"\u003ephysicist stickers\u003c\/a\u003e or \u003ca href=\"\/hi\/collections\/quantum-physics-t-shirts\"\u003equantum designs\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50654988730471,"sku":"86020910698195047825","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50586289930343,"sku":"25944383438766048735","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50654988763239,"sku":"19092551843076278650","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50654988796007,"sku":"11409284345474330245","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/17135163981716564855_1200.jpg?v=1793668866"}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/collections\/gifts-for-the-grad-student.png?v=1793678011","url":"https:\/\/pixelatedphysics.com\/hi\/collections\/gifts-for-the-grad-student.oembed","provider":"Pixelated Physics","version":"1.0","type":"link"}