{"id":15,"date":"2008-12-13T07:34:26","date_gmt":"2008-12-13T11:34:26","guid":{"rendered":"http:\/\/blogs.williams.edu\/Morgan\/?p=15"},"modified":"2008-12-13T07:34:26","modified_gmt":"2008-12-13T11:34:26","slug":"alan-alda-and-curvature-in-space-time","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/Morgan\/2008\/12\/13\/alan-alda-and-curvature-in-space-time\/","title":{"rendered":"Alan Alda and Curvature in Space-Time"},"content":{"rendered":"<p>Actor <a href=\"http:\/\/en.wikipedia.org\/wiki\/Alan_Alda\">Alan Alda<\/a> appears with mathematician Bob Osserman in a <a href=\"http:\/\/www.msri.org\/communications\/vmath\/VMathVideosSpecial\/VideoSpecialInfo\/3911\/show_video\">video of a Berkeley Repertory Theatre conversation<\/a> sponsored by the <a href=\"http:\/\/www.msri.org\/\">Mathematical Sciences Research Institute.<\/a> It is a wonderful conversation between two very intelligent and curious individuals. Here I want to comment on Alda&#8217;s implicit, unanswered question:<\/p>\n<p>\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0What is meant by curvature in space-<em>time<\/em>?<!--more-->In space alone, e.g. in the Euclidean plane, a path is straight if it has constant slope, never getting more or less steep. In\u00a0space-<em>time<\/em>, a path is straight if it has constant <em>velocity<\/em>, i.e., if it never changes slope or speed. Galileo observed that in free space, objects move in straight lines at constant speed, i.e., move in straight lines in space-time. They do not &#8220;curve&#8221; in space-time by speeding up or slowing down or changing direction. Gravity, however, causes a ball thrown in the air to deviate from such straight lines and continually change speed and direction. In this sense, gravity causes objects to curve in space-time, to change speed as well as direction.<\/p>\n<p>Of course as Osserman explains, <a href=\"http:\/\/en.wikipedia.org\/wiki\/General_relativity\">Einstein&#8217;s Theory of General Relativity<\/a>\u00a0(see also my books on <a href=\"http:\/\/www.ams.org\/bookstore?co1=AND&amp;co2=AND&amp;co3=AND&amp;d=BOOK&amp;f=G&amp;fn=105&amp;l=100&amp;op1=ADJ&amp;op2=ADJ&amp;op3=ADJ&amp;p=1&amp;pg1=&amp;pg2=&amp;pg3=ALLF&amp;r=1&amp;s1=&amp;s2=&amp;s3=Frank%20Morgan&amp;subject=genint&amp;u=\">applied real analysis<\/a> and <a href=\"http:\/\/www.akpeters.com\/product.asp?ProdCode=0733\">Riemannian geometry<\/a>) is fundamentally deeper than this, but this is something I wished I could have told Alda first.\u00a0<\/p>\n<p>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Actor Alan Alda appears with mathematician Bob Osserman in a video of a Berkeley Repertory Theatre conversation sponsored by the Mathematical Sciences Research Institute. It is a wonderful conversation between two very intelligent and curious individuals. Here I want to comment on Alda&#8217;s implicit, unanswered question: \u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0What is meant by curvature [&hellip;]<\/p>\n","protected":false},"author":269,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[14042],"tags":[],"class_list":["post-15","post","type-post","status-publish","format-standard","hentry","category-general-interest"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/posts\/15","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/users\/269"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/comments?post=15"}],"version-history":[{"count":0,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/posts\/15\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/media?parent=15"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/categories?post=15"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/tags?post=15"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}