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Article #5783Re: Fermat's principle and curved spacetime
From: Eric Gisse
Date: Sat, 19 Jan 2008 03:37
Date: Sat, 19 Jan 2008 03:37
90 lines
4652 bytes
4652 bytes
On Jan 18, 1:35 pm, Koobee Wublee <koobee.wub...@gmail.com> wrote: > On Jan 18, 1:03 pm, Dieter Heidorn wrote: > > > > > Pentcho Valev schrieb: > > > Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent > > > with the gravitational redshift factor 1+V/c^2 confirmed > > > experimentally by Pound and Rebka. > > > In his 1911 work "Über 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. Experimentally is found > > > alpha = 2 GM / (c^2 R) > > You mean the very liberal interpretation of the data from the solar > eclipse of 1919. It was already decided to be the following even > before Eddington set out his quest. > > alha = 4 G M / c^2 / R > > > > In other words Roberts Roberts, the > > > equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE: > > > This equation is not correct, because it leads to a wrong prediction for > > the deflection of light. The reason for the error was: In 1911 Einstein > > used "curved time" and "flat space", not curved space-time. > > The equation is correct for gravitational redshift. <shrug> > > > > > > any different > > > equation (that may seem correct to you) would be inconsistent with the > > > redshift factor. > > > The gravitational red-shift is not caused by a variable speed of light. > > > In his 1916 work "Die Grundlage der allgemeinen Relativitätstheorie", > > Annalen der Physik 49 (1916) Einstein shows: > > > * Space-time is described with the metric > > > ds^2 = g_mu,nu dx^mu dx^nu > > > * The gravitiational red-shift depends on the metric: > > > nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B)) > > > * In weak fields the following approximation holds: > > > nu_B / nu_A = 1 + Delta V/c^2 > > > * Speed of light: > > - In a local inertial frame of reference the speed of light > > is constant c > > - In general, global coordinates the speed of light varies > > (in weak fields) according to > > > c_A = c ( 1 + 2 V/c^2) > > This equation will lead to a wrong value of the gravitational > redshift. This is another example where GR is contradictory of itself > because it does not agree with the metric derivation as you have shown > above. Another assertion without proof. Do you really expect people to take you at your word that what you say is true?
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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!postnews.google.com!i72g2000hsd.googlegroups.com!not-for-mail From: Eric Gisse <jowr.pi@gmail.com> Newsgroups: sci.physics.relativity, sci.physics, sci.astro, fr.sci.physique, fr.sci.maths Subject: Re: Fermat's principle and curved spacetime Date: Fri, 18 Jan 2008 19:37:01 -0800 (PST) Organization: http://groups.google.com Lines: 90 Message-ID: <103d8159-99ea-4e36-ae69-9ec44ab0f656@i72g2000hsd.googlegroups.com> 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> <3783ed0d-aae7-4f13-b98e-cfe1317f8846@i29g2000prf.googlegroups.com> NNTP-Posting-Host: 137.229.60.138 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1200713822 17324 127.0.0.1 (19 Jan 2008 03:37:02 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 19 Jan 2008 03:37:02 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: i72g2000hsd.googlegroups.com; posting-host=137.229.60.138; posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8.1.11) Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe)