Article View: sci.physics.relativity
Article #5791Re: Fermat's principle and curved spacetime
From: Tom Roberts
Date: Sat, 19 Jan 2008 15:29
Date: Sat, 19 Jan 2008 15:29
22 lines
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2838 bytes
Dieter Heidorn wrote: > In his 1911 work "οΏ½ber den Einfluss der Schwerkraft auf die Ausbreitung > des Lichtes", Annalen der Physik 35 (1911); translated: "On the > Influence of Gravitation on the Propagation of Light" Einstein uses the > equivalence principle to derive the relation for gravitational red-shift > nu_1 = nu_2 (1 + V/c^2) > From this he concluded that the speed of light must vary according to > c = c_0 (1 + V/c^2) > Using this equation Einstein derives a relation for the deflection angle > for light passing the sun (1911): > alpha = 2 GM / (c^2 R) > This is wrong by a factor 2. [...] Yes. When I said the second equation above was approximately correct, I meant only for measurements of speed using distant standards. I did not consider the further elaboration of it to an invalid result for the deflection of light by the sun. The approximation used for speeds is not good enough for angles, because as you point out (and is well known), spatial curvature enters into the latter. Tom Roberts
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X-Google-Thread: 10f545,e60ad8b8bd890c74 X-Google-Thread: 10b271,4fd262761489fde X-Google-Thread: f74ae,4fd262761489fde X-Google-Thread: fa4c1,4fd262761489fde X-Google-Thread: 1139f8,4fd262761489fde X-Google-Attributes: gid10f545,gid10b271,gidf74ae,gidfa4c1,gid1139f8,public,usenet X-Google-Language: ENGLISH,ASCII Path: arc1-ca.pugleaf.net!g2news1.google.com!news1.google.com!newsfeed.stanford.edu!headwall.stanford.edu!newshub.sdsu.edu!newscon04.news.prodigy.net!prodigy.net!newsdst01.news.prodigy.net!prodigy.com!postmaster.news.prodigy.com!nlpi069.nbdc.sbc.com.POSTED!32b1cbcb!not-for-mail From: Tom Roberts <tjroberts137@sbcglobal.net> User-Agent: Thunderbird 2.0.0.9 (X11/20071115) MIME-Version: 1.0 Newsgroups: sci.physics.relativity,sci.physics,sci.astro,fr.sci.physique,fr.sci.maths Subject: Re: Fermat's principle and curved spacetime References: <acc87498-7d1a-4bf8-b205-e24b29b6f04b@s8g2000prg.googlegroups.com> <v2Wjj.38861$lD6.27743@newssvr27.news.prodigy.net> <f45cdd6a-6cba-49f6-aef9-089ac65e4d1b@k2g2000hse.googlegroups.com> <fmr47v$fqo$03$1@news.t-online.com> In-Reply-To: <fmr47v$fqo$03$1@news.t-online.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit Lines: 22 Message-ID: <mHokj.1300$nK5.581@nlpi069.nbdc.sbc.com> NNTP-Posting-Host: 70.131.130.253 X-Complaints-To: abuse@prodigy.net X-Trace: nlpi069.nbdc.sbc.com 1200756562 ST000 70.131.130.253 (Sat, 19 Jan 2008 10:29:22 EST) NNTP-Posting-Date: Sat, 19 Jan 2008 10:29:22 EST Organization: AT&T http://yahoo.sbc.com X-UserInfo1: FKPO@MC@O@SGB_TXLJJ@N\XBDPHHUUDO@HTHOCULF@^PGDTFOG[]FE[YETZPIWWI[FCIZA^NBFXZ_D[BFNTCNVPDTNTKHWXKB@X^B_OCJLPZ@ET_O[G\XSG@E\G[ZKVLBL^CJINM@I_KVIOR\T_M_AW_M[_BWU_HFA_]@A_A^SGFAUDE_DFTMQPFWVW[QPJN Date: Sat, 19 Jan 2008 09:29:03 -0600