Article View: sci.physics.relativity
Article #5756Re: Fermat's principle and curved spacetime
From: Eric Gisse
Date: Fri, 25 Jan 2008 17:51
Date: Fri, 25 Jan 2008 17:51
154 lines
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7155 bytes
On Jan 24, 10:31 pm, Koobee Wublee <koobee.wub...@gmail.com> wrote: > On Jan 23, 1:09 pm, Dieter Heidorn schrieb: > > > Koobee Wublee schrieb: > > > Do you have a link to this article in the yearbook of radio and > > > electronics even if it is in German? > > > I only know where to find the original work - also leider auf Deutsch: > > >http://www.soso.ch/wissen/hist/SRT/E-1907.pdf > > Danke. It is going to take some time for me to sort through it. > > > > Pais declared Poincare to be a vegetable that could not even > > > understand the basics of special relativity. Pais' account cannot be > > > any accurate. > > > It's not a question of account but a question of historical sources, for > > instance: > > Yes, indeed. However, the modern historic sources are from the > usurpers like Pais who tried to write his own account of history. > <shrug> > > > * the correspondence between Einstein and Grossmann before 1912, > > when Einstein returned to ZΓΌrich and started working with Grossmann, > > > * the papers published by Einstein before 1912. > > Grossmann has nothing to do with Einstein's works before 1912. > > OK, from all the references I have uncovered all have claimed Einstein- > Grossmann cooperation began in 1912. > > > > These are not experimentations on deflection but measurements in speed > > > delay or rather gravitational time delay. <shrug> > > > These _are_ experiments on light deflection. Please have a look at > > >http://arxiv.org/abs/gr-qc/0510072 > > > pages 33 - 35. > > Have you not noticed that there are all claims and no specific > experiments shown with analyzable data given? > > > > G = 6.7e-11 in MKS system > > > M = Mass of the sun = 2.0e30 Kg > > > R = Radius of the sun = 1.4e9 m > > > In Europe we are told that the radius of the sun is > > > R = 6.96e8 m :-) > > OK, it is my mistake to use the diameter instead of the radius. > > > > By the way, this type of measurement on the delay time requires you to > > > know the accuracy of the distance involved. You'd better know this > > > accuracy from the earth to the Venus with a few centimeters or > > > better. Without an interferometer, how can you accept any > > > experimental results on this subject without any question? > > > The delta t (round trip) is equivalent to a seeming (virtual? > > apparent?) increase of the distance between Earth and Venus of > > > c delta t / 2 = 36 km > > What does this 36Km have anything to do with anything? > > > It's not necessary to know the distance with an accuracy of centimeters. > > Why? > > > The distance Earth - Venus when Venus stands between Earth and > > Sun can be measured by measuring the travel time of reflected radar > > signals. In combination with the data of Venus' orbit you get the > > distance needed for the Shapiro-Experiment. > > I am still not convinced this 240uSec is qualified. There is no > interferometer to detect such a minute difference in signal. There is > no way to nail down the distance from the earth to Venus to an > accuracy of mere centimeters. There is no reference signal to be > compared with. > > > > > > To derive the Shapiro time delay through gravitational time dilation, > > > we have > > > > T = 2 int[ds / c] (from -a_E to a_V) > > > = 2 int[dx / sqrt(1 - 2 U)] / c > > > ~ 2 int[dx (1 + U)] / c > > > = 2 x / c + (G M / c^3) sinh^-1(x / R) > > > ~ 2 (a_E + a_V) / c + 2 (G M / c^3) ln(4 a_E a_V / R^2) > > > > Where > > > > ** U = G M / c^2 / r > > > ** a_E >> R > > > ** a_V >> R > > > > This is the same derivation when we have the following 1911 equation > > > > C(r) = c (1 - U) > > > Your calculation is the same calculation as I have given - with a little > > meaningful difference. > > Well, I see my mistake. Thank you for pointing that out. There is an > extra curvature in the r direction. Thus, according to the > Schwarzschild metric, we have the round trip time derived as the > following. > > T = 2 int[ds / sqrt(1 - 2 U) / sqrt(1 - 2 U)] (from -a_E to a_V) > = 2 int[dx / (1 - 2 U)] / c > ~ 2 int[dx (1 + 2 U)] / c > = 2 x / c + (4 G M / c^3) sinh^-1(x / R) > ~ 2 (a_E + a_V) / c + (4 G M / c^3) ln(4 a_E a_V / R^2) > > Thus, the delay time is > > dt = (4 G M / c^3) ln(4 a_E a_V / R^2) > > > Starting with the equation > > > c' = c (1 + kV/c^2) > > > k = 1: 1911 > > k = 2: 1916 > > However, this does not mean > > C(r) = c (1 + 2 U), k = 2 > > Or > > C(r) = c (1 + U), k = 1 > > Under the concept of GR, the speed of light must be the same > everywhere. That is No, persistent idiot, the local speed of light is the same everywhere. GR makes no claims about the global speed. > > C(r) = c > > It is the gravitational time dilation and the curvature in space that > seems to affect the speed of light in an experiment.
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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!n22g2000prh.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, 25 Jan 2008 09:51:39 -0800 (PST) Organization: http://groups.google.com Lines: 155 Message-ID: <b72dbd90-7c1e-4459-9ecf-cfc126b9b33d@n22g2000prh.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$1@news.t-online.com> <3783ed0d-aae7-4f13-b98e-cfe1317f8846@i29g2000prf.googlegroups.com> <fmsv04$dkv$01$1@news.t-online.com> <a3fb1ad6-5537-4bc1-a0c3-c18a27fcad78@1g2000hsl.googlegroups.com> <fmvvcj$op6$01$1@news.t-online.com> <f9b17591-1643-485f-a111-5820f4769210@d70g2000hsb.googlegroups.com> <fn5668$age$01$1@news.t-online.com> <a24ea188-0152-49a6-93f2-b5dc67ce0cdb@i7g2000prf.googlegroups.com> <fn8adt$2im$00$1@news.t-online.com> <70d76ea7-ff98-4c90-8ba2-e54c1df3126c@d21g2000prf.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 1201283499 12235 127.0.0.1 (25 Jan 2008 17:51:39 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 25 Jan 2008 17:51:39 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: n22g2000prh.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)