{"title":"Sweats à capuche","description":"\u003cp\u003eTous les sweats à capuche Pixelated Physics réunis. Noirs, imprimés à la commande, en tailles S–5XL. Chaque sweat illustre une loi ou un phénomène avec son équation, des lignes nodales de Chladni et de l’attracteur étrange à la double fente, aux orbites de Kepler et aux points de Lagrange.\u003c\/p\u003e","products":[{"product_id":"nebulia-pixel-hoodie","title":"Nebulia – The Forbidden [O III] 500.7 nm Line Pixel Hoodie","description":"\u003cp\u003eNebulia, a veiled oracle in deep-navy robes, holds a ring of doubly ionised oxygen whose green light fills a planetary-nebula halo.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eThe bright green nebular lines at 5006.84 Å and 4958.91 Å (air wavelengths) were long blamed on a hypothetical element, “nebulium”. In 1927 I. S. Bowen identified them as forbidden transitions of doubly ionised oxygen, O²⁺ (spectroscopic notation O III), from the metastable ¹D₂ level of the 2p² ground configuration down to the ³P₂ and ³P₁ levels. Because both levels share the same configuration and parity, an electric-dipole (E1) transition is forbidden; the lines go mainly by the much slower magnetic-dipole (M1) channel. In a lab gas, collisions empty ¹D₂ long before it can radiate. In a nebula they do not, because the density sits far below the level’s critical density.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003en\u003csub\u003ecrit\u003c\/sub\u003e = A\u003csub\u003eul\u003c\/sub\u003e \/ q\u003csub\u003eul\u003c\/sub\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eλ = hc \/ ΔE\u003csub\u003eul\u003c\/sub\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003en\u003csub\u003ecrit\u003c\/sub\u003e: critical electron density, where collisional de-excitation equals radiative decay (m⁻³)\u003c\/li\u003e\n\u003cli\u003eA\u003csub\u003eul\u003c\/sub\u003e: Einstein spontaneous-emission coefficient from upper level u to lower level l (s⁻¹)\u003c\/li\u003e\n\u003cli\u003eq\u003csub\u003eul\u003c\/sub\u003e: collisional de-excitation rate coefficient (m³ s⁻¹)\u003c\/li\u003e\n\u003cli\u003eλ: emitted wavelength (m)\u003c\/li\u003e\n\u003cli\u003eh: Planck constant, 6.626 070 15 × 10⁻³⁴ J s (exact)\u003c\/li\u003e\n\u003cli\u003ec: speed of light in vacuum, 299 792 458 m s⁻¹ (exact)\u003c\/li\u003e\n\u003cli\u003eΔE\u003csub\u003eul\u003c\/sub\u003e: energy gap between the two levels (J)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eBelow n\u003csub\u003ecrit\u003c\/sub\u003e nearly every excitation ends in a photon, so a weak transition can still be one of the brightest lines in the spectrum. William Huggins first saw these lines in 1864 in NGC 6543. Sources: I. S. Bowen, \u003cem\u003eNature\u003c\/em\u003e 120, 473 (1927), doi:10.1038\/120473a0; A. Fowler, \u003cem\u003eNature\u003c\/em\u003e 120, 582 (1927); NIST Atomic Spectra Database (O III).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e “Forbidden” means strongly suppressed, not impossible. Quoted wavelengths are in air (500.68 nm); the vacuum value is slightly longer.\u003c\/p\u003e\u003cp\u003eThe glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eI was called a new element for sixty years. I was oxygen all along, speaking only where the dark is quiet enough to hear me.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a three-level ladder emblem with a dashed green ¹D→³P arrow. Back: Nebulia in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “NEBULIUM WAS OXYGEN.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/coronix-pixel-hoodie\"\u003eCoronix\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/flipwarden-pixel-hoodie\"\u003eFlipwarden\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/viridael-pixel-hoodie\"\u003eViridael\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sanguora-pixel-hoodie\"\u003eSanguora\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sulphra-pixel-hoodie\"\u003eSulphra\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964464762983,"sku":"23364393242333113942","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964464795751,"sku":"86037443440874778334","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964464828519,"sku":"18292876638205299572","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964464861287,"sku":"24641802712931612922","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964464894055,"sku":"48639394253285931488","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964464926823,"sku":"67718269315531573106","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964464959591,"sku":"12022848020915244183","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964464992359,"sku":"24807988142212132362","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H02.png?v=1793678357"},{"product_id":"coronix-pixel-hoodie","title":"Coronix – The Forbidden Fe XIV Coronal Line Pixel Hoodie","description":"\u003cp\u003eCoronix, a knight in blackened iron, wears a crown of 13 broken spikes against an eclipsed Sun, each tip burning coronal green.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eThe green coronal line at 530.3 nm (5302.86 Å in air), seen at total eclipses, was blamed on an unknown element, “coronium”. Walter Grotrian (1939) matched the red 637.4 nm line to Fe X, and Bengt Edlén (announced 1941, full paper in \u003cem\u003eZ. Astrophys.\u003c\/em\u003e 22, 30, 1942) identified the green line as Fe XIV: iron with 13 of its 26 electrons stripped away, Fe¹³⁺. The transition is the magnetic-dipole decay ²P°\u003csub\u003e3\/2\u003c\/sub\u003e → ²P°\u003csub\u003e1\/2\u003c\/sub\u003e inside the 3s²3p ground term, a fine-structure flip that an electric dipole cannot drive.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFe + 13 ionisations → Fe¹³⁺ (Fe XIV)\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eχ(Fe¹²⁺ → Fe¹³⁺) ≈ 361 eV ≫ k\u003csub\u003eB\u003c\/sub\u003eT\u003csub\u003ephotosphere\u003c\/sub\u003e ≈ 0.5 eV\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eFe XIV: spectroscopic notation for the ion with 13 electrons removed (Roman numeral = charge + 1)\u003c\/li\u003e\n\u003cli\u003eχ: ionisation energy needed to remove the 13th electron (eV)\u003c\/li\u003e\n\u003cli\u003ek\u003csub\u003eB\u003c\/sub\u003e: Boltzmann constant, 1.380 649 × 10⁻²³ J K⁻¹ (exact)\u003c\/li\u003e\n\u003cli\u003eT\u003csub\u003ephotosphere\u003c\/sub\u003e: temperature of the visible solar surface, about 5800 K\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eMaking Fe¹³⁺ in collisional equilibrium needs electron temperatures of about a million kelvin or more, so the identification proved the corona is far hotter than the surface below it. Sources: B. Edlén, \u003cem\u003eMNRAS\u003c\/em\u003e 105, 323 (1945), doi:10.1093\/mnras\/105.6.323; W. Grotrian, \u003cem\u003eNaturwiss.\u003c\/em\u003e 27, 214 (1939); P. Swings, \u003cem\u003eApJ\u003c\/em\u003e 98, 116 (1943); NIST Atomic Spectra Database (Fe XIV).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Why the corona is so hot (the coronal heating problem) is still unsolved; wave heating and many small reconnection events (“nanoflares”) are both studied. The ionisation-energy figure is from the NIST database and rounded.\u003c\/p\u003e\u003cp\u003eThe glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eThirteen spikes, thirteen electrons surrendered to a million-kelvin crown. They named me coronium. I am iron that refused to stay cool.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: an eclipsed disc emblem with a green ring and pixel “XIV”. Back: Coronix in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “CORONIUM WAS IRON.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/nebulia-pixel-hoodie\"\u003eNebulia\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/flipwarden-pixel-hoodie\"\u003eFlipwarden\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/viridael-pixel-hoodie\"\u003eViridael\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sanguora-pixel-hoodie\"\u003eSanguora\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sulphra-pixel-hoodie\"\u003eSulphra\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964465156199,"sku":"11321626474428457629","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964465188967,"sku":"16887944514829888669","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964465221735,"sku":"30752224223844355610","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964465254503,"sku":"13968668967395919465","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964465287271,"sku":"27594334369793468256","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964465320039,"sku":"28271541142016493123","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964465352807,"sku":"15837063366898941815","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964465385575,"sku":"28835126505246358574","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H13.png?v=1793678366"},{"product_id":"flipwarden-pixel-hoodie","title":"Flipwarden – The 21 cm Hydrogen Spin-Flip Line Pixel Hoodie","description":"\u003cp\u003eFlipwarden, a cowled monk-warden, waits beside an almost-full hourglass while one hydrogen atom above his palm flips its spin.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn ground-state hydrogen the electron and proton spins couple through their magnetic moments. The level with total spin F = 1 (spins parallel) lies just above F = 0 (antiparallel), and the magnetic-dipole spin flip between them emits a photon at 1420.405751768 MHz, a wavelength of 21.106 cm. The spontaneous rate is tiny, so each atom waits about 11 million years on average.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΔE = hν = 5.874 µeV,   λ = c\/ν = 21.106 cm\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eA\u003csub\u003e10\u003c\/sub\u003e ≈ 2.9 × 10⁻¹⁵ s⁻¹  ⇒  τ = 1\/A\u003csub\u003e10\u003c\/sub\u003e ≈ 3.5 × 10¹⁴ s ≈ 11 Myr\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eΔE: hyperfine splitting of the hydrogen 1s level (eV)\u003c\/li\u003e\n\u003cli\u003eh: Planck constant, 6.626 070 15 × 10⁻³⁴ J s\u003c\/li\u003e\n\u003cli\u003eν: transition frequency, 1420.405751768 MHz\u003c\/li\u003e\n\u003cli\u003eλ: wavelength (m)\u003c\/li\u003e\n\u003cli\u003ec: speed of light, 299 792 458 m s⁻¹\u003c\/li\u003e\n\u003cli\u003eA\u003csub\u003e10\u003c\/sub\u003e: Einstein coefficient for spontaneous F = 1 → F = 0 decay (s⁻¹)\u003c\/li\u003e\n\u003cli\u003eτ: mean radiative lifetime of the upper level, per atom (s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eRare per atom, the line is still radio astronomy’s principal tracer of neutral hydrogen, because the Galaxy holds so much of it. The frequency is known to 13 significant figures thanks to hydrogen masers, which run on this very transition by stimulated emission. Sources: Kulkarni, ASTR501 lecture notes (A = 2.8843 × 10⁻¹⁵ s⁻¹); Zaroubi, \u003cem\u003eThe Epoch of Reionization\u003c\/em\u003e (A₁₀ = 2.85 × 10⁻¹⁵ s⁻¹).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The 11 Myr is a per-atom average lifetime, not a waiting time anyone has watched. The violet glow is symbolic: 21 cm is a radio wave and has no visible colour.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eOne grain falls. One spin turns. I have kept this watch eleven million years, and the sky still hears every flip I make.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: two violet spin-arrow pairs, ↑↑ to ↑↓. Back: Flipwarden in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “ONE FLIP PER 11 MILLION YEARS.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/nebulia-pixel-hoodie\"\u003eNebulia\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/coronix-pixel-hoodie\"\u003eCoronix\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/viridael-pixel-hoodie\"\u003eViridael\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sanguora-pixel-hoodie\"\u003eSanguora\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sulphra-pixel-hoodie\"\u003eSulphra\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964465713255,"sku":"13078080911991187289","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964465746023,"sku":"15526425071000076403","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964465778791,"sku":"52243355899520614626","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964465811559,"sku":"10625248146536432879","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964465844327,"sku":"14351088639385296846","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964465877095,"sku":"15495369749119146940","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964465909863,"sku":"21869795945365652919","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964465942631,"sku":"18837958601923582490","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H05.png?v=1793678376"},{"product_id":"viridael-pixel-hoodie","title":"Viridael – The Forbidden [O I] 557.7 nm Green Aurora Line Pixel Hoodie","description":"\u003cp\u003eViridael, a hooded keeper with closed eyes, holds a single droplet of green light beneath auroral curtains that stop at a haze line.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eThe aurora’s dominant green line at 557.7 nm, first examined spectroscopically by Anders Ångström in 1867, was identified in 1925 by J. C. McLennan and G. M. Shrum as the forbidden ¹S₀ → ¹D₂ transition of atomic oxygen, both levels inside the 2p⁴ ground configuration (an electric-quadrupole transition). The ¹S₀ level is metastable, lifetime about 0.74 s. Below roughly 100 to 120 km, collisions de-excite it before it can radiate, so the green curtain has a lower edge.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eτ(¹S₀) ≈ 0.74 s\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eLine emitted when  A ≳ k\u003csub\u003eq\u003c\/sub\u003e[M]   (quenching rate per atom below radiative rate)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eτ: radiative lifetime of the upper level (s)\u003c\/li\u003e\n\u003cli\u003eA: Einstein spontaneous-emission coefficient, = 1\/τ for a single decay channel (s⁻¹)\u003c\/li\u003e\n\u003cli\u003ek\u003csub\u003eq\u003c\/sub\u003e: collisional quenching rate coefficient (m³ s⁻¹)\u003c\/li\u003e\n\u003cli\u003e[M]: number density of colliding air molecules (m⁻³), which rises steeply with falling altitude\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eStatistically the green emission peaks near 114 km. Sources: McLennan \u0026amp; Shrum, \u003cem\u003eProc. R. Soc. A\u003c\/em\u003e 108, 501 (1925), doi:10.1098\/rspa.1925.0088; \u003cem\u003eAstron. \u0026amp; Geophys.\u003c\/em\u003e 47, 1.11 (2006); Whiter et al., \u003cem\u003eAnn. Geophys.\u003c\/em\u003e 41, 1 (2023).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Published lifetimes for ¹S₀ range from about 0.7 to 0.8 s; we use 0.74 s. The quench altitude is a range, not a sharp line.\u003c\/p\u003e\u003cp\u003eThe glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eHold still. I can keep this light for less than a second, and only above the noise of the crowded air. That is enough to paint the sky.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a green droplet in a ¹S→¹D ladder glyph. Back: Viridael in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “HOLD IT 0.74 SECONDS.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/nebulia-pixel-hoodie\"\u003eNebulia\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/coronix-pixel-hoodie\"\u003eCoronix\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/flipwarden-pixel-hoodie\"\u003eFlipwarden\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sanguora-pixel-hoodie\"\u003eSanguora\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sulphra-pixel-hoodie\"\u003eSulphra\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964466106471,"sku":"19414848035613386043","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964466139239,"sku":"17016648611276429798","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964466172007,"sku":"87744045058325625784","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964466204775,"sku":"11275585377535559326","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964466237543,"sku":"21643665374794089763","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964466270311,"sku":"29664513403508579823","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964466303079,"sku":"20794520443654310472","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964466335847,"sku":"30785834400081188521","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H14.png?v=1793678386"},{"product_id":"sanguora-pixel-hoodie","title":"Sanguora – The Forbidden [O I] 630.0 nm Red Aurora Line Pixel Hoodie","description":"\u003cp\u003eSanguora, a tall oracle on a high spire, trails a slow red veil of light far above a thin band of green aurora.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eAtomic oxygen’s red auroral doublet at 630.0 nm and 636.4 nm is the forbidden ¹D₂ → ³P transition (to ³P₂ for 630.0 nm and ³P₁ for 636.4 nm), mainly magnetic dipole. The ¹D₂ level lives about 110 s, around 150 times longer than the green line’s upper level. Collisions therefore quench it everywhere below roughly 200 km, and the red aurora shines only from the thinnest high air. ¹D₂ is also the lower level of the 557.7 nm green line, so each green photon leaves an atom ready to emit red.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eτ(¹D₂) ≈ 110 s\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eI\u003csub\u003e630\u003c\/sub\u003e ∝ P(¹D₂) · A\u003csub\u003e630\u003c\/sub\u003e \/ (A\u003csub\u003etot\u003c\/sub\u003e + k\u003csub\u003eq\u003c\/sub\u003e[M])\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eτ: radiative lifetime of ¹D₂ (s)\u003c\/li\u003e\n\u003cli\u003eI\u003csub\u003e630\u003c\/sub\u003e: 630.0 nm emission rate per unit volume (photons m⁻³ s⁻¹)\u003c\/li\u003e\n\u003cli\u003eP(¹D₂): production rate of ¹D₂ atoms (m⁻³ s⁻¹)\u003c\/li\u003e\n\u003cli\u003eA\u003csub\u003e630\u003c\/sub\u003e: Einstein coefficient of the 630.0 nm branch (s⁻¹)\u003c\/li\u003e\n\u003cli\u003eA\u003csub\u003etot\u003c\/sub\u003e: total radiative decay rate of ¹D₂, = 1\/τ (s⁻¹)\u003c\/li\u003e\n\u003cli\u003ek\u003csub\u003eq\u003c\/sub\u003e[M]: collisional quenching rate per atom (s⁻¹)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eSources: \u003cem\u003eAstron. \u0026amp; Geophys.\u003c\/em\u003e 47, 1.11 (2006), doi:10.1111\/j.1468-4004.2006.47111.x; Stoffregen \u0026amp; Derblom, “Life-time of the atomic oxygen 6300 Å line”, \u003cem\u003eNature\u003c\/em\u003e 185, 28 (1960), doi:10.1038\/185028a0.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The green cascade is not the only source of ¹D₂: slow electrons and chemical reactions populate it directly. “Above about 200 km” is approximate and varies with solar activity.\u003c\/p\u003e\u003cp\u003eThe glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eDown there the air is loud. Up here I have a hundred and ten seconds of silence, and I spend every one of them on red.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a red veil curl over a ¹D→³P ladder. Back: Sanguora in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “110 SECONDS, OR NOTHING.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/nebulia-pixel-hoodie\"\u003eNebulia\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/coronix-pixel-hoodie\"\u003eCoronix\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/flipwarden-pixel-hoodie\"\u003eFlipwarden\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/viridael-pixel-hoodie\"\u003eViridael\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sulphra-pixel-hoodie\"\u003eSulphra\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964466434151,"sku":"31589461466487302190","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964466466919,"sku":"13976056328637914017","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964466499687,"sku":"26675432088594547446","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964466532455,"sku":"11314529587195495811","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964466565223,"sku":"29213941198584587947","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964466597991,"sku":"33598749605627957709","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964466630759,"sku":"13981346293377287018","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964466663527,"sku":"94709181752167870614","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H15.png?v=1793678396"},{"product_id":"sulphra-pixel-hoodie","title":"Sulphra – The [S II] 671.6\/673.1 nm Density Doublet Pixel Hoodie","description":"\u003cp\u003eSulphra, a two-faced porcelain oracle, breathes two unequal ribbons of red light into a balance that tips toward the brighter one.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eSingly ionised sulphur, S⁺ (S II), emits a forbidden red doublet at 671.6 nm and 673.1 nm (air 6716.44 \/ 6730.82 Å) from the ²D°\u003csub\u003e5\/2\u003c\/sub\u003e and ²D°\u003csub\u003e3\/2\u003c\/sub\u003e levels down to the ⁴S°\u003csub\u003e3\/2\u003c\/sub\u003e ground level. The two upper levels lie at almost the same energy, so temperature hardly matters, but they have different radiative rates. That makes the line ratio a gauge of electron density.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eR = I(671.6) \/ I(673.1)\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003en\u003csub\u003ee\u003c\/sub\u003e → 0:  R → g(²D\u003csub\u003e5\/2\u003c\/sub\u003e)\/g(²D\u003csub\u003e3\/2\u003c\/sub\u003e) = 6\/4 ≈ 1.5      n\u003csub\u003ee\u003c\/sub\u003e → ∞:  R → (g A)\u003csub\u003e5\/2\u003c\/sub\u003e\/(g A)\u003csub\u003e3\/2\u003c\/sub\u003e ≈ 0.44\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eR: intensity ratio of the doublet (dimensionless)\u003c\/li\u003e\n\u003cli\u003eI: line intensity (W m⁻² sr⁻¹)\u003c\/li\u003e\n\u003cli\u003en\u003csub\u003ee\u003c\/sub\u003e: electron number density (cm⁻³)\u003c\/li\u003e\n\u003cli\u003eg: statistical weight 2J + 1 of the upper level\u003c\/li\u003e\n\u003cli\u003eA: Einstein spontaneous-emission coefficient of each line (s⁻¹)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eAt low density every collisional excitation radiates, so R follows the collision strengths (proportional to g). At high density the levels reach Boltzmann populations and R follows gA. In between, roughly 50 to 2000 cm⁻³, R measures n\u003csub\u003ee\u003c\/sub\u003e: gas more than ten million billion (10¹⁶) times thinner than air. Sources: Osterbrock \u0026amp; Ferland, \u003cem\u003eAstrophysics of Gaseous Nebulae and Active Galactic Nuclei\u003c\/em\u003e (2006); Sanders et al., \u003cem\u003eApJ\u003c\/em\u003e 816, 23 (2016); Kakkad et al., \u003cem\u003eA\u0026amp;A\u003c\/em\u003e 618, A6 (2018).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The limiting ratios (about 1.45 to 1.5 and 0.44) depend on the atomic data adopted and weakly on temperature, so density values carry real systematic uncertainty.\u003c\/p\u003e\u003cp\u003eThe glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eAsk one tongue and you hear a colour. Ask both and compare, and I will tell you how crowded the dark is.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: two red bars of unequal height under a tiny scale. Back: Sulphra in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “TWO LINES. ONE DENSITY.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/nebulia-pixel-hoodie\"\u003eNebulia\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/coronix-pixel-hoodie\"\u003eCoronix\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/flipwarden-pixel-hoodie\"\u003eFlipwarden\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/viridael-pixel-hoodie\"\u003eViridael\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/sanguora-pixel-hoodie\"\u003eSanguora\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964466827367,"sku":"32611904393364746608","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964466860135,"sku":"35020292875147891017","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964466892903,"sku":"13135463546790499486","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964466925671,"sku":"13373872655449288521","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964466958439,"sku":"64132118080329792959","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964466991207,"sku":"88439314632111916075","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964467023975,"sku":"77328200518484374728","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964467056743,"sku":"76089834310947899755","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H02_aabed8d2-2644-45a7-be4a-1bbbfceeb38e.png?v=1793678406"},{"product_id":"sir-aetheron-pixel-hoodie","title":"Sir Aetheron – The Luminiferous Aether and Michelson–Morley Pixel Hoodie","description":"\u003cp\u003eSir Aetheron, a fallen knight in cracked aether-glass armour, kneels on a cross-shaped stone interferometer floating on mercury, its fringes perfectly still.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eThe aether was the proposed medium for light waves, reaching back to Huygens’s \u003cem\u003eTraité de la Lumière\u003c\/em\u003e (1690). If Earth moves through it at its orbital speed, light should take slightly different times along two perpendicular arms of an interferometer. In 1887 A. A. Michelson and E. W. Morley floated their interferometer on mercury, rotated it, and looked for the fringe shift. They expected about 0.4 fringe. They saw less than one-twentieth of that, “probably less than one-fortieth”.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΔN ≈ 2 L v² \/ (λ c²)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eΔN: expected fringe shift on rotating the apparatus by 90° (fringes)\u003c\/li\u003e\n\u003cli\u003eL: effective optical arm length, about 11 m with repeated reflections (m)\u003c\/li\u003e\n\u003cli\u003ev: Earth’s orbital speed, about 3 × 10⁴ m s⁻¹\u003c\/li\u003e\n\u003cli\u003eλ: wavelength of the light used, about 5.9 × 10⁻⁷ m\u003c\/li\u003e\n\u003cli\u003ec: speed of light, 299 792 458 m s⁻¹\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eWith these numbers ΔN ≈ 0.37, the expected 0.4. Lorentz–FitzGerald contraction could save a stationary aether, but Einstein’s 1905 special relativity made the medium unnecessary. Sources: Michelson \u0026amp; Morley, \u003cem\u003eAm. J. Sci.\u003c\/em\u003e 34, 333 (1887), doi:10.2475\/ajs.s3-34.203.333; APS News, “This Month in Physics History”, Nov 2007.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The 1887 null result did not kill every aether theory overnight; Lorentz’s version survived until relativity replaced it. The dates on the back mark the claim and the decisive test, not a single death certificate.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eI waited for the wind of the Earth’s passage. It never came. My armour cracked, but the light ran straight through me, unmoved.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a cracked cross-shaped interferometer with a flat fringe bar. Front label: “AETHER DRIFT · NULL RESULT 1887”. Back: Sir Aetheron in full pixel art with “BORN 1690 - DIED 1887” and “THE STILL WIND.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eGhost Particles That Were Wrong\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/enrayne-pixel-hoodie\"\u003eEnrayne\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/calorus-pixel-hoodie\"\u003eCalorus\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/diphantom-pixel-hoodie\"\u003eDiphantom\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/prematura-pixel-hoodie\"\u003ePrematura\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/thetarch-pixel-hoodie\"\u003eThetarch\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/relativity-cosmos-t-shirts\"\u003erelativity \u0026amp; cosmos designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964467155047,"sku":"27950117142796064536","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964467187815,"sku":"20160912485558213266","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964467220583,"sku":"26332867976694335576","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964467253351,"sku":"23263471025259455711","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964467286119,"sku":"20076881190543740589","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964467318887,"sku":"26919207936067971170","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964467351655,"sku":"31906747619846215901","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964467384423,"sku":"12937325822508555935","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H13_ab204fc8-d859-4762-9a69-db24a60aaa79.png?v=1793678417"},{"product_id":"enrayne-pixel-hoodie","title":"Enrayne – The N-Ray Delusion Pixel Hoodie","description":"\u003cp\u003eEnrayne, a knight in violet-grey armour whose visor shows only two faint eyes, leans toward an empty prism cradle and still sees rays.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn 1903 René Blondlot at Nancy announced “N-rays”, a new radiation he said made a faint spark brighter and could be dispersed by an aluminium prism into a spectrum. Dozens of papers followed. In 1904 the American physicist R. W. Wood visited and, in the darkened lab, secretly removed the prism. The observers went on reading the same spectrum. His letter in \u003cem\u003eNature\u003c\/em\u003e 70, 530 (29 September 1904) ended the field. N-rays do not exist; what was measured was the observers’ expectation.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eReal signal test:  S \/ σ\u003csub\u003eobs\u003c\/sub\u003e  with the observer blind to the condition\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eS: change in the measured quantity when the claimed cause is present versus absent\u003c\/li\u003e\n\u003cli\u003eσ\u003csub\u003eobs\u003c\/sub\u003e: spread of readings from observer judgement alone, including bias, when the observer does not know which condition is set\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eJudging the brightness of a faint spark by eye sits near the threshold of vision, where expectation dominates. Wood’s prism swap was in effect a blind control: with the cause removed, S should vanish, and it did not. Sources: R. W. Wood, “The n-Rays”, \u003cem\u003eNature\u003c\/em\u003e 70, 530 (1904), doi:10.1038\/070530a0; APS News, “This Month in Physics History”, Aug 2007.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Wood made other tests too; this design keeps to the prism story. Blondlot was a respected physicist, and the episode is a warning about method, not a joke about him.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eI saw them. I swear I saw them, even after the cradle went empty. That is the lesson I carry: the eye finds what the heart expects.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: an empty prism cradle with a dotted spectrum. Back: Enrayne in full pixel art with “BORN 1903 - DIED 29 SEP 1904” and “HE STILL SAW THEM.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eGhost Particles That Were Wrong\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sir-aetheron-pixel-hoodie\"\u003eSir Aetheron\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/calorus-pixel-hoodie\"\u003eCalorus\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/diphantom-pixel-hoodie\"\u003eDiphantom\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/prematura-pixel-hoodie\"\u003ePrematura\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/thetarch-pixel-hoodie\"\u003eThetarch\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/electromagnetism\"\u003eelectromagnetism designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964467581031,"sku":"46222158712318947529","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964467613799,"sku":"97765360616890677820","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964467646567,"sku":"89969539674633512609","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964467679335,"sku":"25766894198004153497","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964467712103,"sku":"12980833173745820419","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964467744871,"sku":"26942251648958401363","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964467777639,"sku":"71792467814026907098","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964467810407,"sku":"33344964816125237008","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H05_0d098cb9-e2c2-45fb-86ea-67451bbb4d2a.png?v=1793678428"},{"product_id":"calorus-pixel-hoodie","title":"Calorus – The Caloric Theory of Heat Pixel Hoodie","description":"\u003cp\u003eCalorus, a bronze-armoured knight with a sealed glass chest-plate of glowing fluid, is pierced by a blunt borer; from the wound pours heat-shimmer, not fluid, and the vessel stays full.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eAntoine Lavoisier’s \u003cem\u003eTraité élémentaire de chimie\u003c\/em\u003e (1789) listed caloric, a conserved, weightless heat fluid, among the elements. In 1798 Count Rumford reported that boring a cannon with a blunt borer kept producing heat seemingly without limit, enough to boil water in about two and a half hours, and argued that heat is a form of motion. The fluid picture faded around 1850, when J. P. Joule’s “On the mechanical equivalent of heat” and Rudolf Clausius’s founding paper of thermodynamics made heat a transfer of energy, not a substance.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΔU = Q − W\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eJoule 1850: 772 ft·lbf per Btu  ≈ 4.15 J per calorie   (modern: 1 cal\u003csub\u003eth\u003c\/sub\u003e = 4.184 J exactly)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eΔU: change in a system’s internal energy (J)\u003c\/li\u003e\n\u003cli\u003eQ: heat added to the system (J)\u003c\/li\u003e\n\u003cli\u003eW: work done by the system (J)\u003c\/li\u003e\n\u003cli\u003eft·lbf: foot-pound-force, ≈ 1.356 J\u003c\/li\u003e\n\u003cli\u003eBtu: heat to warm one pound of water by 1 °F, ≈ 1055 J\u003c\/li\u003e\n\u003cli\u003ecal\u003csub\u003eth\u003c\/sub\u003e: thermochemical calorie (J)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe first law says heat and work are two ways of moving the same energy, so there is no stock of caloric to run out of, and none to conserve. Rumford’s borer converted mechanical work W into internal energy indefinitely. Sources: Rumford, \u003cem\u003ePhil. Trans. R. Soc.\u003c\/em\u003e 88, 80 (1798), doi:10.1098\/rstl.1798.0006; Joule, \u003cem\u003ePhil. Trans. R. Soc.\u003c\/em\u003e 140, 61 (1850), doi:10.1098\/rstl.1850.0004; Clausius, \u003cem\u003eAnn. Phys.\u003c\/em\u003e 155, 368 (1850), doi:10.1002\/andp.18501550306.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Heat-fluid ideas are older than 1789; Lavoisier named and listed caloric. Rumford’s result was not accepted as decisive at the time, and 1850 is a conventional end date, marked by Joule’s and Clausius’s 1850 papers; caloric theory faded gradually.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eThey pierced me and waited for me to drain. I never did. Whatever pours out of me is motion, and the more they bore, the more I give.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a cracked glass flask holding a flame, with a borer across it. Back: Calorus in full pixel art with the character name and printed dates for the theory (RUMFORD 1798 - JOULE 1850). Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eGhost Particles That Were Wrong\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sir-aetheron-pixel-hoodie\"\u003eSir Aetheron\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/enrayne-pixel-hoodie\"\u003eEnrayne\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/diphantom-pixel-hoodie\"\u003eDiphantom\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/prematura-pixel-hoodie\"\u003ePrematura\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/thetarch-pixel-hoodie\"\u003eThetarch\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/thermodynamics-t-shirts\"\u003ethermodynamics designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964467875943,"sku":"30415561719805009476","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964467908711,"sku":"15448148543604733055","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964467941479,"sku":"65091056722388620558","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964467974247,"sku":"76945071081196408436","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964468007015,"sku":"25708564579182111490","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964468039783,"sku":"29606816254305219352","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964468072551,"sku":"31385764956232233152","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964468105319,"sku":"13291385646835404039","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H14_d3e5dd7f-b9ca-4288-847d-5206062addb0.png?v=1793678437"},{"product_id":"diphantom-pixel-hoodie","title":"Diphantom – The 750 GeV Diphoton Excess Pixel Hoodie","description":"\u003cp\u003eDiphantom, a spectral knight made of two crossing beams of light, carries a small flickering bump at his heart while a skyline of histogram bars falls away behind him.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eOn 15 December 2015 the ATLAS and CMS collaborations each showed a small excess of photon pairs with invariant mass near 750 GeV in the first 13 TeV LHC data. A new heavy boson decaying to two photons would show up as exactly such a bump above the smoothly falling background. Hundreds of theory papers followed. With roughly four to five times more data (ATLAS 15.4 fb⁻¹ in 2016 against 3.2 fb⁻¹ in 2015; CMS 12.9 fb⁻¹ against 3.3 fb⁻¹), both experiments reported at ICHEP on 5 August 2016 that the excess had gone. It was a statistical fluctuation.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003em\u003csub\u003eγγ\u003c\/sub\u003e² c⁴ = 2 E₁ E₂ (1 − cos θ)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003em\u003csub\u003eγγ\u003c\/sub\u003e: invariant mass of the photon pair (GeV\/c²)\u003c\/li\u003e\n\u003cli\u003eE₁, E₂: measured photon energies (GeV)\u003c\/li\u003e\n\u003cli\u003eθ: opening angle between the two photons in the lab frame\u003c\/li\u003e\n\u003cli\u003ec: speed of light\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eWhen many mass bins are searched, an excess somewhere is likely by chance (the look-elsewhere effect), so its local significance overstates the global one. Sources: ATLAS briefing, “High-mass di-photon resonances: the first 2016 ATLAS results” (Aug 2016); CMS ICHEP 2016 public results; Physics World, Aug 2016.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Nothing was wrong with the detectors or analyses; small samples fluctuate. The data rule out this particular bump, not every heavy diphoton resonance.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eFor eight months I wore a crown of a thousand papers. Then the data grew, and I was what I always was: noise, standing a little too tall.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: two crossing photon lines with a hollow dot at the crossing. Front label: “750 GeV DIPHOTON · FADED 2016”. Back: Diphantom in full pixel art with “BORN 15 DEC 2015 - DIED 5 AUG 2016” and “A FLUCTUATION WEARING A CROWN.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eGhost Particles That Were Wrong\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sir-aetheron-pixel-hoodie\"\u003eSir Aetheron\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/enrayne-pixel-hoodie\"\u003eEnrayne\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/calorus-pixel-hoodie\"\u003eCalorus\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/prematura-pixel-hoodie\"\u003ePrematura\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/thetarch-pixel-hoodie\"\u003eThetarch\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/particle-physics\"\u003eparticle \u0026amp; nuclear physics designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964468367463,"sku":"10237940436925301286","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964468400231,"sku":"20341608686246934641","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964468432999,"sku":"25462335692149801443","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964468465767,"sku":"19100754457203331811","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964468498535,"sku":"33619771665418655161","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964468531303,"sku":"16636946075454964806","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964468564071,"sku":"30942987810949317717","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964468596839,"sku":"18847333557252584756","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H15_d3152f2e-bdfd-4579-a005-7d7d6d4fad72.png?v=1793678447"},{"product_id":"prematura-pixel-hoodie","title":"Prematura – The OPERA Faster-Than-Light Neutrino Anomaly Pixel Hoodie","description":"\u003cp\u003ePrematura, a lean herald-knight, strides one step ahead of his own glowing shadow, a loose cable dangling from his gauntlet.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eOn 23 September 2011 the OPERA experiment reported muon neutrinos from CERN arriving at Gran Sasso, about 730 km away, (60.7 ± 6.9 ± 7.4) ns earlier than light would, an apparent faster-than-light result implying (v − c)\/c = (2.48 ± 0.28 ± 0.30) × 10⁻⁵. In February 2012 the collaboration found two equipment faults: a badly connected optical-fibre connector on the GPS timing link, which added about 73 ns of delay and made the flight time look shorter, and a master-clock oscillator running slightly fast, which pushed the other way. ICARUS measured light-speed-consistent arrival times in March 2012, and on 8 June 2012 OPERA and the other Gran Sasso experiments reported results consistent with c.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eδt = L\/c − t\u003csub\u003eν\u003c\/sub\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e(v − c)\/c ≈ c δt \/ L\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eδt: early arrival of the neutrinos relative to light (s)\u003c\/li\u003e\n\u003cli\u003eL: CERN-to-Gran Sasso baseline, about 730 km (m)\u003c\/li\u003e\n\u003cli\u003ec: speed of light, 299 792 458 m s⁻¹\u003c\/li\u003e\n\u003cli\u003et\u003csub\u003eν\u003c\/sub\u003e: measured neutrino time of flight (s)\u003c\/li\u003e\n\u003cli\u003ev: inferred neutrino speed (m s⁻¹)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eWith L ≈ 730 km the light travel time is about 2.4 ms, so 60 ns is a 2.5 × 10⁻⁵ effect. Supernova 1987A neutrinos had already bounded (v − c)\/c far more tightly at lower energy. Sources: OPERA, arXiv:1109.4897; ICARUS, \u003cem\u003ePhys. Lett. B\u003c\/em\u003e 713, 17 (2012); OPERA, \u003cem\u003eJHEP\u003c\/em\u003e 10 (2012) 093; CERN press release, 23 Sep 2011 (update 8 Jun 2012).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The neutrinos were never wrong; the measurement was. “It was the cable” is a simplification: two faults pulled in opposite directions, and the fibre was the bigger one.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eI arrived sixty nanoseconds early and the world held its breath. Then someone checked the plug. I was never ahead of the light, only ahead of the clock.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a fibre plug with a light gap and a dashed arrow. Front label: “OPERA FTL CLAIM · REFUTED 2012”. Back: Prematura in full pixel art with “BORN 23 SEP 2011 - DIED 8 JUN 2012” and “IT WAS THE CABLE.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eGhost Particles That Were Wrong\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sir-aetheron-pixel-hoodie\"\u003eSir Aetheron\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/enrayne-pixel-hoodie\"\u003eEnrayne\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/calorus-pixel-hoodie\"\u003eCalorus\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/diphantom-pixel-hoodie\"\u003eDiphantom\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/thetarch-pixel-hoodie\"\u003eThetarch\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/particle-physics\"\u003eparticle \u0026amp; nuclear physics designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964468662375,"sku":"41884972481716868349","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964468695143,"sku":"22357627898620936775","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964468727911,"sku":"19450815920967072780","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964468760679,"sku":"10247419536980902274","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964468793447,"sku":"10026433366790311234","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964468826215,"sku":"24911543395893396281","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964468858983,"sku":"18293210009403699799","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964468891751,"sku":"20474148342641469237","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H02_0b8fe972-67b1-4f6b-8e67-303b4c92e6a0.png?v=1793678457"},{"product_id":"thetarch-pixel-hoodie","title":"Thetarch – The Θ⁺(1540) Pentaquark Pixel Hoodie","description":"\u003cp\u003eThetarch, a pretender-king in tarnished violet plate, wears a crown of five jewels, four warm and one cold, whose linking thread is snapping.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn 2003 the LEPS collaboration at SPring-8 reported a narrow peak near 1540 MeV in the K⁺n system, read as an exotic five-quark baryon, the Θ⁺, with minimal content uudd s̄. Its positive strangeness could not be made from three quarks, which is what made it exotic. Several other groups quickly reported sightings, but higher-statistics searches found nothing, and the Particle Data Group’s 2008 review judged the case that the Θ⁺ does not exist to be compelling, describing the whole story as a curious episode in the history of science.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΘ⁺ = u u d d s̄:   Q = +1,  B = +1,  S = +1\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eu, d: up and down quarks, charges +2\/3 e and −1\/3 e\u003c\/li\u003e\n\u003cli\u003es̄: strange antiquark, charge +1\/3 e, strangeness +1\u003c\/li\u003e\n\u003cli\u003eQ: electric charge in units of e\u003c\/li\u003e\n\u003cli\u003eB: baryon number (each quark +1\/3, antiquark −1\/3)\u003c\/li\u003e\n\u003cli\u003eS: strangeness\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eOrdinary baryons qqq cannot have S = +1, so a narrow K⁺n resonance would have been unambiguous. The early peaks came from small samples and background modelling. Sources: T. Nakano et al. (LEPS), \u003cem\u003ePhys. Rev. Lett.\u003c\/em\u003e 91, 012002 (2003); C. Amsler et al. (PDG), “Pentaquark update”, \u003cem\u003ePhys. Lett. B\u003c\/em\u003e 667, 1 (2008).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Only this pentaquark is a ghost. Hidden-charm pentaquarks of a different kind were observed by LHCb in 2015. The 1540 MeV mass is approximate (about 1.53 to 1.54 GeV in early reports).\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eFive jewels, they said, and a throne of my own. But the thread would not hold under more light, and the crown was only ever borrowed.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a five-jewel ring with one jewel hollow. Back: Thetarch in full pixel art with “BORN 2003 - DIED 2008” and “FIVE QUARKS, ZERO PARTICLE.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eGhost Particles That Were Wrong\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sir-aetheron-pixel-hoodie\"\u003eSir Aetheron\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/enrayne-pixel-hoodie\"\u003eEnrayne\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/calorus-pixel-hoodie\"\u003eCalorus\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/diphantom-pixel-hoodie\"\u003eDiphantom\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/prematura-pixel-hoodie\"\u003ePrematura\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/particle-physics\"\u003eparticle \u0026amp; nuclear physics designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964469055591,"sku":"15472995321786188732","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964469088359,"sku":"24802921168101708604","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964469121127,"sku":"13900074891296054172","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964469153895,"sku":"31893557861827652449","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964469186663,"sku":"20591729413732960410","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964469219431,"sku":"25440209351725703863","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964469252199,"sku":"15793698387747725447","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964469284967,"sku":"24907106921285903727","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H13_31727e01-b77b-45fe-8abb-bc407d8ef051.png?v=1793678467"},{"product_id":"sponara-pixel-hoodie","title":"Sponara – Hertha Sponer and the Birge–Sponer Method Pixel Hoodie","description":"\u003cp\u003eSponara is a respectful pixel portrait of Hertha Sponer, after a 1913 public-domain photograph, beside a glowing ladder whose rungs close up toward a bright limit line.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHertha Sponer (1895–1968) took her doctorate at Göttingen in 1920 under Peter Debye and worked with James Franck on molecular spectroscopy. On a fellowship at Berkeley she and Raymond T. Birge showed in 1926 how to estimate a molecule’s dissociation energy from its band spectrum. The vibrational levels of a real bond crowd together as they climb. Adding up the gaps until they shrink to zero gives the energy at which the molecule falls apart. Dismissed from Göttingen under Nazi law in 1934, she went to Oslo and in 1936 joined Duke University, the first woman on its physics faculty.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eG(v) = ω\u003csub\u003ee\u003c\/sub\u003e(v + ½) − ω\u003csub\u003ee\u003c\/sub\u003ex\u003csub\u003ee\u003c\/sub\u003e(v + ½)²\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eD₀ ≈ Σ\u003csub\u003ev\u003c\/sub\u003e ΔG\u003csub\u003ev+½\u003c\/sub\u003e   (for this two-term form, D\u003csub\u003ee\u003c\/sub\u003e ≈ ω\u003csub\u003ee\u003c\/sub\u003e² \/ 4ω\u003csub\u003ee\u003c\/sub\u003ex\u003csub\u003ee\u003c\/sub\u003e)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eG(v): vibrational term value of level v (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003ev: vibrational quantum number, 0, 1, 2, …\u003c\/li\u003e\n\u003cli\u003eω\u003csub\u003ee\u003c\/sub\u003e: harmonic vibrational constant (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003eω\u003csub\u003ee\u003c\/sub\u003ex\u003csub\u003ee\u003c\/sub\u003e: anharmonicity constant (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003eΔG\u003csub\u003ev+½\u003c\/sub\u003e: spacing G(v+1) − G(v) between neighbouring levels (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003eD₀: dissociation energy from the lowest level v = 0 (cm⁻¹ or eV)\u003c\/li\u003e\n\u003cli\u003eD\u003csub\u003ee\u003c\/sub\u003e: dissociation energy measured from the bottom of the potential well\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003ePlot ΔG against v + ½ and extrapolate to ΔG = 0; the area under the line is D₀. Source: R. T. Birge \u0026amp; H. Sponer, “The heat of dissociation of non-polar molecules”, \u003cem\u003ePhys. Rev.\u003c\/em\u003e 28, 259 (1926), doi:10.1103\/PhysRev.28.259; Duke Physics, “Hertha Sponer”.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Birge–Sponer is an extrapolation and only an estimate: real level spacings near the dissociation limit bend away from a straight line, so the method can overestimate or underestimate D₀.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eCount the steps, watch them shrink, and follow them to where there are no more. That is where the bond lets go, and that is the number.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a tiny ladder with shrinking gaps under a pixel crown. Back: a pixel portrait of Hertha Sponer with “CROWNED IN HER OWN LIGHT” and “HERTHA SPONER - 1926”. Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eUnsung Hands\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/recoilwyn-pixel-hoodie\"\u003eRecoilwyn\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/ayrtha-pixel-hoodie\"\u003eAyrtha\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/quantum-physics-t-shirts\"\u003equantum designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964469383271,"sku":"21994265210478376952","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964469416039,"sku":"32205395793648449551","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964469448807,"sku":"59886375318620799164","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964469481575,"sku":"32306011724677858891","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964469514343,"sku":"19658560549868276941","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964469547111,"sku":"24150544771332124072","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964469579879,"sku":"22576485165543150713","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964469612647,"sku":"26212679212273883683","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H05_72846dbf-4aef-4ee6-b837-e32ca67a9537.png?v=1793678478"},{"product_id":"recoilwyn-pixel-hoodie","title":"Harriet Brooks: First Glimpse of Radioactive Recoil (1904)","description":"\u003cp\u003eRecoilwyn is a respectful pixel portrait of Harriet Brooks, after William Notman \u0026amp; Son’s 1898 photograph, with two motes of light flying apart before her: a light fast one and a heavy slow one.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHarriet Brooks (1876–1933) was Ernest Rutherford’s first graduate student at McGill. She helped show that radium’s “emanation” was a new radioactive gas (radon), early evidence that one element can turn into another. Her 1904 \u003cem\u003eNature\u003c\/em\u003e letter, “A Volatile Product from Radium”, reported active deposit turning up on the walls of the vessel, an early observation of what was later explained as alpha recoil: when a nucleus emits an alpha particle, the daughter nucleus is kicked the other way.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ep\u003csub\u003eα\u003c\/sub\u003e = −p\u003csub\u003eR\u003c\/sub\u003e   ⇒   E\u003csub\u003eR\u003c\/sub\u003e = (m\u003csub\u003eα\u003c\/sub\u003e \/ m\u003csub\u003eR\u003c\/sub\u003e) E\u003csub\u003eα\u003c\/sub\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ep\u003csub\u003eα\u003c\/sub\u003e, p\u003csub\u003eR\u003c\/sub\u003e: momenta of the alpha particle and the recoiling daughter nucleus (kg m s⁻¹)\u003c\/li\u003e\n\u003cli\u003eE\u003csub\u003eα\u003c\/sub\u003e, E\u003csub\u003eR\u003c\/sub\u003e: their kinetic energies (non-relativistic) (J or MeV)\u003c\/li\u003e\n\u003cli\u003em\u003csub\u003eα\u003c\/sub\u003e, m\u003csub\u003eR\u003c\/sub\u003e: their masses (kg or u)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eFor radium-226 (E\u003csub\u003eα\u003c\/sub\u003e ≈ 4.78 MeV) the radon-222 daughter recoils with about 4.78 × 4.0\/222 ≈ 86 keV, enough to fly free of a surface and lodge in the walls. Sources: H. Brooks, \u003cem\u003eNature\u003c\/em\u003e 70, 270 (1904), doi:10.1038\/070270b0; Dictionary of Canadian Biography, “Brooks, Harriet”; Russ \u0026amp; Makower, \u003cem\u003eProc. R. Soc. A\u003c\/em\u003e 82, 205 (1909), doi:10.1098\/rspa.1909.0028.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Brooks observed the effect; the recoil explanation came later (Hahn, and Russ \u0026amp; Makower, 1909). The discovery of radon is shared with Rutherford, Owens and Dorn.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eSomething leapt from the radium and landed where it should not have been. I wrote down exactly what I saw. The explanation could catch up later.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: two arrows from one dot, a long thin one and a short thick one. Front label: “HARRIET BROOKS · FIRST OBSERVED 1904”. Back: a pixel portrait of Harriet Brooks with “CROWNED IN HER OWN LIGHT” and “HARRIET BROOKS - 1904”. Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eUnsung Hands\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sponara-pixel-hoodie\"\u003eSponara\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/ayrtha-pixel-hoodie\"\u003eAyrtha\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/particle-physics\"\u003eparticle \u0026amp; nuclear physics designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964469678183,"sku":"19100564941867237194","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964469710951,"sku":"11023687066335426289","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964469743719,"sku":"18878982911652344048","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964469776487,"sku":"20926109071667663055","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964469809255,"sku":"66217581007825812341","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964469842023,"sku":"99630455220650024172","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964469874791,"sku":"13135308702553509835","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964469907559,"sku":"22030571145965897991","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H14_9bbbba37-6e77-4f00-8ebe-63e945d3389c.png?v=1793678488"},{"product_id":"ayrtha-pixel-hoodie","title":"Ayrtha – Hertha Ayrton, the Electric Arc and Sand Ripples Pixel Hoodie","description":"\u003cp\u003eAyrtha is a respectful pixel portrait of Hertha Ayrton, after a Bain News Service photograph of about 1900, holding a white-violet carbon arc above a basin of sand ripples.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHertha Ayrton (1854–1923) showed that the hissing and instability of carbon arc lamps came from oxygen reaching the hot crater of the positive carbon, and summed up her arc work in \u003cem\u003eThe Electric Arc\u003c\/em\u003e (1902). There she gave an empirical law for the voltage across an arc, now called the Ayrton equation. Her ripple paper on how vortices build sand ripple marks, “The origin and growth of ripple-mark”, was read before the Royal Society on 16 June 1904. In 1906 she became the first woman to receive the Society’s Hughes Medal.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eV = a + b l + (c + d l) \/ I\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eV: voltage across the arc (V)\u003c\/li\u003e\n\u003cli\u003eI: arc current (A)\u003c\/li\u003e\n\u003cli\u003el: arc length, the gap between the carbons (m)\u003c\/li\u003e\n\u003cli\u003ea, b, c, d: empirical constants fitted for given electrodes (units V, V m⁻¹, W, W m⁻¹)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe (c + d l)\/I term makes V fall as I rises, a negative differential resistance, which is why an arc needs a series resistor to stay stable. Sources: H. Ayrton, \u003cem\u003eThe Electric Arc\u003c\/em\u003e (1902); \u003cem\u003eProc. R. Soc. Lond.\u003c\/em\u003e 74, 565 (1904), doi:10.1098\/rspl.1904.0159, and full paper \u003cem\u003eProc. R. Soc. A\u003c\/em\u003e 84, 285 (1910), doi:10.1098\/rspa.1910.0076; MacTutor, “Hertha Marks Ayrton”; English Heritage blue plaque.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The Ayrton equation is empirical, fitted to carbon arcs; it is not derived from plasma physics and does not hold for every arc. How sand ripples grow and choose their spacing is still studied.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eThey said the arc hissed because it was fickle. It hissed because it was breathing oxygen. I listened until it told me why.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a tiny arc between two rods over three ripples. Back: a pixel portrait of Hertha Ayrton with “CROWNED IN HER OWN LIGHT” and “HERTHA AYRTON - 1906”. Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eUnsung Hands\u003c\/strong\u003e set with \u003ca href=\"\/fr\/products\/sponara-pixel-hoodie\"\u003eSponara\u003c\/a\u003e, \u003ca href=\"\/fr\/products\/recoilwyn-pixel-hoodie\"\u003eRecoilwyn\u003c\/a\u003e. Browse all \u003ca href=\"\/fr\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/fr\/collections\/electromagnetism\"\u003eelectromagnetism designs\u003c\/a\u003e, or the \u003ca href=\"\/fr\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964470005863,"sku":"10012611444486418513","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964470038631,"sku":"17536997199752288188","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964470071399,"sku":"35361978633547981427","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964470104167,"sku":"30667800467075846342","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964470136935,"sku":"15658650901028805190","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964470169703,"sku":"20426556088540888526","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964470202471,"sku":"19461674590263711571","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964470235239,"sku":"10402213787029082724","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H15_4f43f7cb-cfac-4d6e-af1a-f76a730e0d82.png?v=1793678497"}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/collections\/hoodies.png?v=1793678014","url":"https:\/\/pixelatedphysics.com\/fr\/collections\/hoodies.oembed","provider":"Pixelated Physics","version":"1.0","type":"link"}