{"id":138,"date":"2024-10-17T16:04:30","date_gmt":"2024-10-17T13:04:30","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/caglart\/?p=138"},"modified":"2024-10-17T17:17:14","modified_gmt":"2024-10-17T14:17:14","slug":"zenodan-einsteina-kuvantum-b","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/caglart\/2024\/10\/17\/zenodan-einsteina-kuvantum-b\/","title":{"rendered":"ZENO\u2019dan E\u0130NSTE\u0130N\u2019a KUVANTUM\u2013b \u2013"},"content":{"rendered":"

F\u0130Z\u0130K -4 \/ b-<\/p>\n

\u0130\u00e7erik: Zeno, Maxwell, Boltzmann, Einstein, f\u0131r\u0131n, karacisim ve az\u0131c\u0131k matematik, bolca d\u00fc\u015f\u00fcnce<\/p>\n

S\u0131cakl\u0131\u011f\u0131 T olan bir karacisim, \u00f6rne\u011fin bir f\u0131r\u0131n, mikrodalga veya lazer gibi tek frekansl\u0131 \u0131\u015f\u0131nlarla \u0131s\u0131t\u0131lsa bile, yayd\u0131klar\u0131 \u0131\u015f\u0131n dizgesi (\u2018spectrum\u2019) her frekansta dalga i\u00e7erir. Her frekans i\u00e7in sahip olunan enerji de\u011feri de ayn\u0131 olmay\u0131p gayet b\u00fcy\u00fck bir farkl\u0131l\u0131k g\u00f6sterir. K\u00fc\u00e7\u00fck frekanslar i\u00e7in, bu enerji frekans\u0131n karesi ile artarken (parabolik) sonralar\u0131 bu art\u0131\u015f\u0131n paraboliklikten ayr\u0131ld\u0131\u011f\u0131, artan frekansla daha az artt\u0131\u011f\u0131 g\u00f6zlenir. Derken, (Wien Yasas\u0131 ile saptanan (*)) bir kritik de\u011ferde zirve yap\u0131p daha da b\u00fcy\u00fcyen frekansla azalmaya ba\u015flar.
\nBu g\u00f6rg\u00fcl (\u2018empirical\u2019) davran\u0131\u015f\u0131n, benzetim (\u2018fitting\u2019) yoluyla form\u00fcl\u00fcn\u00fcn elde edilmesinden sonra bkz., https:\/\/blog.metu.edu.tr\/caglart\/2024\/10\/13\/zenodan-einsteina-kuvantum\/ yaz\u0131s\u0131ndaki E\u015fitlik 2 sorun, bu form\u00fcl\u00fc verecek fiziksel alt yap\u0131n\u0131n a\u00e7\u0131\u011fa \u00e7\u0131kart\u0131lmas\u0131na indirgenmi\u015fti.
\n\u0130lkin, bir \u00fcstteki kaynakta (**) verilen E\u015fitlik 1\u2019deki matematiksel ifade \u2013aradaki baz\u0131 minik a\u015famalar\u0131 atlayarak\u2013 \u015f\u00f6yle revize edilmi\u015fti.
\nBir \u2018canonical ensemble\u2019 yani sabit s\u0131cakl\u0131ktaki bir \u0131s\u0131 banyosu ile \u0131s\u0131sal dengede duran ve enerji de\u011ferleri klasik fizik form\u00fclleriyle tan\u0131mlanabilen ayr\u0131k par\u00e7ac\u0131klar toplulu\u011fu i\u00e7in kanonik payla\u015f\u0131m fonksiyonu \u015fu \u015fekilde tan\u0131ml\u0131d\u0131r:<\/p>\n

mavi 1<\/a><\/p>\n

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A_aaa! Bu da ne b\u00f6yle? F\u0130Z\u0130K -2- B\u00d6L B\u00d6L, NEREYE DEK? Ba\u015fl\u0131kl\u0131 ve https:\/\/blog.metu.edu.tr\/caglart\/2024\/09\/ adresteki Sonu\u00e7 1 e\u015fitli\u011fimiz ile t\u0131pa t\u0131p ayn\u0131 de\u011fil midir? L\u00fctfen \u015fu PDF dosyas\u0131n\u0131 indirin Bl bl<\/a><\/p>\n

mavi 2<\/a><\/p>\n

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Gelgelelim, bu yaz\u0131n\u0131n ba\u015fl\u0131\u011f\u0131nda Einstein\u2019\u0131n ad\u0131 var ama Einstein\u2019dan hen\u00fcz s\u00f6z etmedik.
\nHadi edelim!
\nIs\u0131 s\u0131\u011fas\u0131, herhangi bir cismin s\u0131cakl\u0131\u011f\u0131n\u0131 bir birim de\u011fi\u015ftirmek i\u00e7in eklenmesi veya d\u0131\u015far\u0131 al\u0131nmas\u0131 gereken \u0131s\u0131 yani enerji miktar\u0131d\u0131r ve g\u00f6rg\u00fcl olarak bilindi\u011fi gibi pek \u00e7ok malzemenin \u0131s\u0131 s\u0131\u011fas\u0131 s\u0131cakl\u0131k artarken deyim yerindeyse doygunlu\u011fa ula\u015f\u0131yor, art\u0131\u015f h\u0131z\u0131 giderek yava\u015fl\u0131yor. Bu olgular\u0131n alt\u0131nda yatan fizik mekanizmas\u0131n\u0131 (\u2018underlying dynamics\u2019) a\u00e7\u0131\u011fa \u00e7\u0131karmak da tabii ki ba\u015fl\u0131 ba\u015f\u0131na b\u00fcy\u00fck bir ba\u015far\u0131 say\u0131l\u0131yordu, 20. yy. ba\u015flar\u0131nda bile.
\n\u0130\u015fte \u015fen ve sevgili Einstein\u2019\u0131m\u0131z, \u0131s\u0131 s\u0131\u011fas\u0131 olgusunun alt\u0131nda yatan\u0131n da kuvantum etkisi olabilece\u011fini adeta hissetti ve yukar\u0131daki E\u015fitlik 6 ile E\u015fitlik 14\u2019\u00fc ve \u0131s\u0131 s\u0131\u011fas\u0131 tan\u0131m\u0131n\u0131 kullanarak bir ba\u011f\u0131nt\u0131 elde etti. (***) Bu ba\u011f\u0131nt\u0131 pek \u00e7ok malzemenin deneysel \u00f6l\u00e7\u00fcmleri ile uyumlu oldu\u011fu gibi, \u0131s\u0131 s\u0131\u011falar\u0131n\u0131n y\u00fcksek s\u0131cakl\u0131klarda yatayla\u015fmas\u0131n\u0131 da sergilemekteydi.
\nYine de, anlamas\u0131, anla\u015f\u0131lmas\u0131 zorluk i\u00e7eren baz\u0131 hususlar var burada. Paket\u00e7iklenmi\u015f enerji d\u00fczeylerine sahip sistemlerin toplam enerjisini veren form\u00fcl\u00fc (yukar\u0131daki E\u015fitlik 6 ile E\u015fitlik 14) Planck da Boltzmann da biliyordu. Ni\u00e7in s\u0131cakl\u0131\u011fa yani T\u2019ye g\u00f6re t\u00fcrev al\u0131p Is\u0131 S\u0131\u011fas\u0131 ba\u011f\u0131nt\u0131s\u0131n\u0131 Planck ya da Boltzmann elde etmedi de o zafer Einstein\u2019a kald\u0131?
\nDaha da tuhaf\u0131. Hemen alttaki Karacisim I\u015f\u0131mas\u0131 \u0130zgesi\u2019nde de g\u00f6r\u00fclece\u011fi \u00fczre,
\n\"\"<\/a>
\nherhangibir makul s\u0131cakl\u0131ktaki (T), \u00f6rne\u011fin insan ya\u015fam s\u0131cakl\u0131klar\u0131, \u0131\u015f\u0131ma ye\u011finli\u011fi y\u00fcksek frekanslarda s\u0131f\u0131ra e\u015fit olmuyor ama s\u0131f\u0131r de\u011ferine frekans b\u00fcy\u00fcd\u00fck\u00e7e daha yak\u0131ns\u0131yor. Oysa, yukar\u0131daki E\u015fitlik 4\u2019de yaz\u0131l\u0131 oldu\u011fu gibi, frekans b\u00fcy\u00fcd\u00fck\u00e7e enerji de b\u00fcy\u00fcyor ve sonsuz b\u00fcy\u00fck frekans i\u00e7in enerji de sonsuz oluyor. Buna kar\u015f\u0131l\u0131k biliyoruz ki, evrende sonsuz b\u00fcy\u00fck enerji yok, olamaz. Ayn\u0131 \u015fekilde, sonsuz b\u00fcy\u00fck frekansl\u0131 sal\u0131n\u0131m da olamaz. Durum b\u00f6yle ise, \u015fu sorular sa\u00e7ma m\u0131 say\u0131lmal\u0131? Evrendeki en b\u00fcy\u00fck frekansl\u0131 sal\u0131n\u0131m ve en b\u00fcy\u00fck enerji ne kadard\u0131r ki, bu de\u011ferleri \u015fu anki sat\u0131ra dek yap\u0131lm\u0131\u015f bilimum analizlerde \u00fcst limit olarak de\u011ferlendirelim. Aksi takdirde, evrende var olmayan enerji ve frekans de\u011ferleri kullanm\u0131\u015f durumuna d\u00fc\u015fm\u00fcyor mu Planck da, Boltzmann da, Einstein da\u2026
\nMavi 3<\/a><\/p>\n

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(*) https:\/\/www.google.com\/search?q=Wien+Yasas%C4%B1
\n(**) https:\/\/blog.metu.edu.tr\/caglart\/2024\/10\/13\/zenodan-einsteina-kuvantum\/
\n(***) https:\/\/www.google.com\/search?q=einstein+solid
\nAyr\u0131ca; https:\/\/www.google.com\/search?q=einstein+collected+works
\n(****) https:\/\/blog.metu.edu.tr\/caglart\/2024\/10\/16\/paradoks-mu-absurd-mu-b\/<\/p>\n","protected":false},"excerpt":{"rendered":"

F\u0130Z\u0130K -4 \/ b- \u0130\u00e7erik: Zeno, Maxwell, Boltzmann, Einstein, f\u0131r\u0131n, karacisim ve az\u0131c\u0131k matematik, bolca d\u00fc\u015f\u00fcnce S\u0131cakl\u0131\u011f\u0131 T olan bir karacisim, \u00f6rne\u011fin bir f\u0131r\u0131n, mikrodalga veya lazer gibi tek frekansl\u0131 \u0131\u015f\u0131nlarla \u0131s\u0131t\u0131lsa bile, yayd\u0131klar\u0131 \u0131\u015f\u0131n dizgesi (\u2018spectrum\u2019) her frekansta dalga i\u00e7erir. Her frekans i\u00e7in sahip olunan enerji de\u011feri de ayn\u0131 olmay\u0131p gayet b\u00fcy\u00fck bir farkl\u0131l\u0131k […]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-138","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=138"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/138\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}