{"id":7111,"date":"2015-08-18T11:17:55","date_gmt":"2015-08-18T15:17:55","guid":{"rendered":"https:\/\/spinor.info\/weblog\/?p=7111"},"modified":"2015-08-18T11:17:55","modified_gmt":"2015-08-18T15:17:55","slug":"jacob-bekenstein","status":"publish","type":"post","link":"https:\/\/spinor.info\/weblog\/?p=7111","title":{"rendered":"Jacob Bekenstein"},"content":{"rendered":"<p>I woke up this morning to the news that Mexican-Israeli physicist <a href=\"https:\/\/en.wikipedia.org\/wiki\/Jacob_Bekenstein\">Jacob Bekenstein<\/a> <a href=\"http:\/\/blogs.scientificamerican.com\/cocktail-party-physics\/in-memorium-jacob-bekenstein-1947-2015-and-black-hole-entropy\/\">died two days ago<\/a>, at the age of 68, in Helsinki, Finland. I saw nothing about the cause of death.<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Jacob_Bekenstein\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-7112\" src=\"https:\/\/spinor.info\/weblog\/wp-content\/uploads\/2015\/08\/Bekenstein.jpg\" alt=\"\" width=\"640\" height=\"480\" srcset=\"https:\/\/spinor.info\/weblog\/wp-content\/uploads\/2015\/08\/Bekenstein.jpg 640w, https:\/\/spinor.info\/weblog\/wp-content\/uploads\/2015\/08\/Bekenstein-300x225.jpg 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<p>Bekenstein&#8217;s work is well known to folks dealing with gravity theory. Two of his contributions stand out in particular.<\/p>\n<p>First, Bekenstein was first to suggest that black holes should have entropy. His work, along with that of Stephen Hawking, led to the Bekenstein-Hawking entropy formula \\(S=kc^3A\/4G\\hbar\\), relating the black hole&#8217;s surface area \\(A\\) to its entropy \\(S\\) using the speed of light \\(c\\), the gravitational constant \\(G\\), the reduced Planck constant \\(\\hbar\\) and Boltzmann&#8217;s constant \\(k\\). With this work, the science of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Black_hole_thermodynamics\">black hole thermodynamics<\/a> was born, leading to all kinds of questions about the nature of black holes and the connection between thermodynamics and gravity, many of which remain unanswered to this day.<\/p>\n<p>Bekenstein&#8217;s second contribution was to turn Morehai Milgrom&#8217;s MOdified Newtonian Dynamics (MOND) into a respectable relativitistic theory. The MOND paradigm is about replacing Newton&#8217;s law relating force \\(({\\mathbf F})\\), mass \\((m)\\) and acceleration \\(({\\mathbf a})\\), \\({\\mathbf F}=m{\\mathbf a}\\), with the modified law \\({\\mathbf F}=\\mu(a\/a_0)m{\\mathbf a}\\), where all we know about the function \\(\\mu(x)\\) is that \\(\\lim_{x\\to 0}\\mu(x)=x\\) and \\(\\lim_{x\\to\\infty}\\mu(x)=1\\). Surprisingly, the right choice of \\(a_0\\) results in an acceleration law that explains the anomalous rotation of galaxies without the need for dark matter. However, in this form, MOND is theoretically ugly: it is a formula that violates basic conservation laws, including the consevation of energy, for instance. Bekenstein&#8217;s <a href=\"https:\/\/en.wikipedia.org\/wiki\/Tensor%E2%80%93vector%E2%80%93scalar_gravity\">TeVeS (Tensor-Vector-Scalar) gravity theory<\/a> provides a general relativistic framework for MOND, one that does respect basic conservation laws, yet reproduces the MOND acceleration formula in the low energy limit.<\/p>\n<p>I never met Jacob Bekenstein, and now I never will. A pity. May he rest in peace.<\/p>\n<fb:like href='https:\/\/spinor.info\/weblog\/?p=7111' send='false' layout='button_count' show_faces='true' width='450' height='65' action='like' colorscheme='light' font='lucida grande'><\/fb:like>","protected":false},"excerpt":{"rendered":"<p>I woke up this morning to the news that Mexican-Israeli physicist Jacob Bekenstein died two days ago, at the age of 68, in Helsinki, Finland. I saw nothing about the cause of death. Bekenstein&#8217;s work is well known to folks dealing with gravity theory. Two of his contributions stand out in particular. First, Bekenstein was <a href='https:\/\/spinor.info\/weblog\/?p=7111' class='excerpt-more'>[&#8230;]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-7111","post","type-post","status-publish","format-standard","hentry","category-physics","category-3-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/7111","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7111"}],"version-history":[{"count":6,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/7111\/revisions"}],"predecessor-version":[{"id":7118,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/7111\/revisions\/7118"}],"wp:attachment":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7111"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}