{"product_id":"boltzbrain-boltzmann-brain","title":"Boltzbrain – The Boltzmann Brain \/ A Mind from a Fluctuation Physics Sticker","description":"\u003cp\u003eBoltzbrain, a villain of the Paradox Parlour, is a lone brain that has flickered into being out of random thermal noise in the heat death of the Universe.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn the 1890s Ludwig Boltzmann suggested that our ordered world might be a rare fluctuation in a universe otherwise in thermal equilibrium. The difficulty is that a small fluctuation is far more likely than a big one. A single brain, complete with false memories, needs a much smaller drop in entropy than a whole ordered universe, so in such a picture most observers would be lone “Boltzmann brains”. Andreas Albrecht and Lorenzo Sorbo (Phys. Rev. D 70, 063528, 2004) discussed it as the so-called “Boltzmann's brain” paradox.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eP ∝ exp(ΔS\/k\u003csub\u003eB\u003c\/sub\u003e)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eP: relative probability of a fluctuation\u003c\/li\u003e\n\u003cli\u003eΔS: entropy change of the fluctuation, negative for a fluctuation into order (J\/K)\u003c\/li\u003e\n\u003cli\u003ek\u003csub\u003eB\u003c\/sub\u003e: Boltzmann constant, 1.380 649 × 10⁻²³ J\/K exactly in the 2019 SI\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThis is Einstein's fluctuation formula. Since ΔS is negative and huge compared with k\u003csub\u003eB\u003c\/sub\u003e, the probability is fantastically small, yet in an eternal universe it is never zero.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Nobody claims such brains exist. The argument is a reductio: a cosmological model in which typical observers are Boltzmann brains is judged to be wrong, because it would make our own observations unreliable. Whether our Universe faces the problem is open. It depends on whether a de Sitter (dark-energy) vacuum truly has thermal fluctuations of this kind, how long it lasts, and how to count observers in an infinite universe (the measure problem). Physicists disagree on all three.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eBoltzbrain, a glowing violet brain on a skeletal body, holds a single bright orb in a grey sea of noise. Printed text: \u003cstrong\u003eBOLTZBRAIN\u003c\/strong\u003e with the line \u003cstrong\u003eP ∝ exp(ΔS\/k)\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50963719880807,"sku":"12654172320610824482","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50963719913575,"sku":"92676703071852852056","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50963719946343,"sku":"13401165743896587327","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50963719979111,"sku":"42859695402764926477","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/13060995151985079622_1200.jpg?v=1793666661","url":"https:\/\/pixelatedphysics.com\/products\/boltzbrain-boltzmann-brain","provider":"Pixelated Physics","version":"1.0","type":"link"}