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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. 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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. 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Quantum electrodynamics adds a small correction; Schwinger's first-order term is α\/2π.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ea = (g − 2)\/2 ≈ α\/2π\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ea: anomalous magnetic moment, dimensionless\u003c\/li\u003e\n\u003cli\u003eg: g-factor, dimensionless\u003c\/li\u003e\n\u003cli\u003eα: fine-structure constant ≈ 1\/137.036, dimensionless\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eDirac g = 2; measured: slightly more. Schwinger 1948: a = α\/2π ≈ 0.0011614.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e α\/2π is the leading term; the measured a_e = 0.00115965218… agrees once higher-order QED terms are included.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eJ. Schwinger, Phys. Rev. 73, 416 (1948).\u003c\/li\u003e\n\u003cli\u003eX. Fan et al., Phys. Rev. Lett. 130, 071801 (2023).\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 055, “Schwinger's α\/2π”: the pixel-art plate with its slogan “Small extra spin.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50962507726951,"sku":"92241412525896142765","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50962507759719,"sku":"63518425060646649234","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50962507792487,"sku":"21600108749273696203","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50962507825255,"sku":"11951162748753356879","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50962507858023,"sku":"13119446597991360847","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50962507890791,"sku":"25206226362616299227","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50962507923559,"sku":"18682361815486996095","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50962507956327,"sku":"24720926234327618122","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50962507989095,"sku":"19574519662427778629","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/17096781165678940246_2048.jpg?v=1793634841"}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/collections\/quantum-physics-t-shirts.png?v=1793678023","url":"https:\/\/pixelatedphysics.com\/pt\/collections\/quantum-physics-t-shirts.oembed?page=5","provider":"Pixelated Physics","version":"1.0","type":"link"}