{"id":133,"date":"2008-11-24T13:30:25","date_gmt":"2008-11-24T12:30:25","guid":{"rendered":"http:\/\/archivio.fcvg.it\/?p=133"},"modified":"2020-02-17T15:38:17","modified_gmt":"2020-02-17T14:38:17","slug":"differenze-di-vedute-fra-fisici-e-matematici","status":"publish","type":"post","link":"http:\/\/www.fcvg.it\/archivio\/?p=133","title":{"rendered":"Differenze di vedute fra fisici e matematici"},"content":{"rendered":"<p>&#8220;<em>Since its inception in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Richard_Feynman\">Richard Feynman<\/a>&#8216;s 1942 doctoral thesis, the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Path_integral_formulation\">path integral<\/a> has been a physicist&#8217;s dream and a mathematician&#8217;s nightmare. To a physicist, the path integral provides a powerful and intuitive way to understand <a href=\"https:\/\/en.wikipedia.org\/wiki\/Quantum_Mechanics\">quantum mechanics<\/a>, building on the simple idea that quantum physics is fundamentally a theory of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Superposition_principle\">superposition<\/a> and <a href=\"https:\/\/en.wikipedia.org\/wiki\/Interference\">interference<\/a> of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Probability_amplitude\">probability amplitudes<\/a>. The &#8220;sum over histories&#8221; offers a framework for tackling problems ranging from <a href=\"https:\/\/en.wikipedia.org\/wiki\/Feynman_diagram\">Feynman diagrams<\/a> to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lattice_QCD\">lattice chromodynamics<\/a>, from quantum cosmology to superfluid vortices to stock-option pricing. To a mathematician, the path integral is at best an ill-defined formal expression. It is some sort of vaguely <a href=\"https:\/\/en.wikipedia.org\/wiki\/Integral\">integral<\/a>-like object involving a &#8220;sum&#8221; over a badly specified collection of functions, having an undefined <a href=\"https:\/\/en.wikipedia.org\/wiki\/Measure_(mathematics)\">measure<\/a>, and whose value is apparently determined by a group of unclear and perhaps incompatible <a href=\"https:\/\/en.wikipedia.org\/wiki\/Limit_(mathematics)\">limits<\/a> that may or may not yield finite answers.<\/em>&#8221;<\/p>\n<p>Steven Carlip (Physics Today, October 2008)<\/p>\n<p>Questo \u00c3\u00a8 un bellissimo esempio di come un matematico ed un fisico possano avere prospettive completamente diverse (vedi anche <a href=\"https:\/\/xkcd.com\/435\/\">http:\/\/xkcd.com\/435\/<\/a>).<\/p>\n<p>n.b. Sono troppo pigro per tradurlo (e comunque tutti quelli che potrebbero trovarlo interessante conoscono l&#8217;inglese).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Since its inception in Richard Feynman&#8216;s 1942 doctoral thesis, the path integral has been a physicist&#8217;s dream and a mathematician&#8217;s nightmare. To a physicist, the path integral provides a powerful and intuitive way to understand quantum mechanics, building on the simple idea that quantum physics is fundamentally a theory of superposition and interference of probability [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[14],"tags":[],"class_list":["post-133","post","type-post","status-publish","format-standard","hentry","category-scienza-e-dintorni"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/pdKGSU-29","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=\/wp\/v2\/posts\/133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=133"}],"version-history":[{"count":12,"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=\/wp\/v2\/posts\/133\/revisions"}],"predecessor-version":[{"id":1327,"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=\/wp\/v2\/posts\/133\/revisions\/1327"}],"wp:attachment":[{"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=133"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.fcvg.it\/archivio\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}